The length of ribbons found at a seamstress are listed.
2, 10, 10, 12, 12, 20
What is the appropriate measure of variability for the data shown, and what is its value?
Answers
The most appropriate measure of variability for this data set is the IQR,
Option B is the correct answer.
Since,
An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
We can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
To determine the appropriate measure of variability for the given data, let's first calculate some descriptive statistics:
Mean: (2 + 10 + 10 + 12 + 12 + 20) / 6 = 11
Median: the middle value is 11, since there are an even number of values
Range: the difference between the maximum value (20) and the minimum value (2) is,
20 - 2 = 18
Interquartile range (IQR): Q3 (the third quartile) is the median of the upper half of the data, which is (12, 12, 20), and Q1 (the first quartile) is the median of the lower half of the data, which is (2, 10, 10). Thus, Q3 = 12 and Q1 = 10, and the IQR is 12 - 10 = 2.
Now, we need to determine which measure of variability is most appropriate for this data set.
Option A suggests using the range, which is the difference between the maximum and minimum values.
The range is affected by outliers and extreme values, and in this data set, the value of 19 is significantly larger than the other values, which might make the range an unreliable measure of variability.
Option B suggests using the IQR, which is a measure of the spread of the middle 50% of the data.
The IQR is less affected by extreme values than the range and is often preferred when there are outliers or skewed distributions.
Option C suggests using the mean, which is a measure of central tendency, not variability.
Option D suggests using the median, which is also a measure of central tendency, not variability.
Therefore,
The most appropriate measure of variability for this data set is the IQR,
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Complete question is,
The length of ribbons found at a seamstress are listed.
2, 10, 10, 12, 12, 20
What is the appropriate measure of variability for the data shown, and what is its value?
A. The range is the best measure of variability and equals 14.
B. The IQR is the best measure of variability and equals 2.
C. The mean is the best measure of variability and equals 11.
D. The median is the best measure of variability and equals 11.
Related Questions
the successor of the set a is the set a ∪ {a}. identify the successor of the given set. {1, 2, 3}
Answers
In the successor set, we add a new element to the original set, which is the set itself. This is denoted by the union symbol (∪) followed by the element we are adding, {1, 2, 3}.
The resulting set is {1, 2, 3, {1, 2, 3}}, indicating that the successor set includes the original set as well as the new element.
Essentially, the successor of a set adds the set itself as a new element to the original set.
This concept is often used in mathematical set theory and has applications in various branches of mathematics and computer science.
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sufficient and necessary? 1 point possible (graded) suppose that we have some loss function that may or may not have multiple critical points. we have found a critical point such that f''(w)>0 , so that we know that it is a minimum. what can we say about it being a global minimum?
Answers
In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.
If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.
In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.
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Help me please with this math question asap
Answers
Answer:
5
Step-by-step explanation:
A function
\(a \times {b}^{x} \)
where a is the initial value and b is the multiplicative rate of change.
In the function,
\(f(x) = 2 \times {5}^{x} \)
5 is the value of b so
5 is the multipicative rate of change
The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the
hypotenuse by the formula a? + b2 = -2
If a is a rational number and b is a rational number, why could c be an irrational number?
Answers
Answer:
For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.
Step-by-step explanation:
We all know, the Pythagorean theorem can be stated as follows:
The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.
i.e.
\(a^2+b^2=c^2\)
Where, \(c\) is the hypotenuse and \(a, b\) are the two other legs of the right angled triangle.
Given that:
\(a\) and \(b\) are rational numbers.
To find:
Situation for which \(c\) is irrational.
Square of a rational number is always rational.
So, \(a^{2} , b^{2}\) both will be rational.
And sum of squares of two rational numbers will also be rational.
Therefore, \(a^2+b^2\) will also be rational.
and
\(c = \sqrt{a^2+b^2}\)
For the value of \(c\) can be irrational, sum of squares of other two legs might be imperfect square number.
One spring day, Jeriel noted the time of day and the temperature, in degrees
Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 56° F. For the
next 3 hours, the temperature rose 1° per hour. For the next 4 hours, it rose 2° per
hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 3° per hour. The temperature then dropped steadily until the
temperature was 60° at midnight. On the set of axes below, graph Jeriel's data.
Answers
The temperature variations is represented on the graph attached with the answer.
What is graph?
A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight
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X
< - 1)x
1
X
*+8
That’s it
Answers
Answer:2x^2-23x-8
Step-by-step explanation: ASSUMING IT MEANS THE AREA OF THE SHADED AREA: First you say that the area of the big circle
(4x-1)(x+8) minus (2x(x+4)) Then once you have that you just simplify, as shown on my paper:
GUYS I NEED HELP ILL GIVE YOU ALL MY POINTS AND BRAINLIEST (95 pts)
1.Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. (I used arm span on y int and height on x)
2.Write the equation of the line of best fit using the slope-intercept form of the line y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
3.What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
4.Test the residuals of two other points to determine how well the line of best fit models the data.
5.Use the line of best fit to help you to describe the data correlation.
6.Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
7.According to your line of best fit, what is the arm span of a 74-inch-tall person?
Answers
1. Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the points used to determine the slope and how the equation was determined.
Here it seems like you would use your two points - (62,63) and (70,72) to find the equation of the best fit line. Use the slope formula and once finding the slope plug that and one point into the y=mx+b formula to find b.
2. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
The slope of the line would represent the average change in armspan with respect to height. The y intercept represents the predicted armspan if a person was 0 inches tall.
3. Test the residuals of two other points to determine how well the line of best fit models the data.
To do this you would take two other points on the graph and find the difference between the predicted y and the actual y. For example, if another point was (66,65), you would plug 66 into your best fit equation solve and then subtract the actual value (65) from your best fit value. A high residual indicates that the best fit line does not do a good job of modeling the data.
4. Use the line of best fit to help you to describe the data correlation.
If the line of best fit is positive, you may say that the data has a positive correlation. If the line of best fit has a slope of around one, you may say that a change in height yields an approximately equal change in armspan.
5.Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
Use your line of best fit - plug in 66 as y
6. According to your line of best fit, what is the arm span of a 74-inch-tall person?
Use your line of best fit - plug in 74 as y
A number cube is tossed 60 times. outcome frequency 1 12 2 13 3 11 4 6 5 10 6 8 determine the experimental probability of landing on a number greater than 4.
Answers
The experimental probability of landing on a number greater than 4 is 0.25 or 25%.
To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).
The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.
So, the experimental probability is 18/60 = 0.3 or 25%.
It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.
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the answer in fraction form is 18/60
if thats what you are looking for.
Find the slope of the line passing through the points (9,7) and (9, -2)
Answers
i did the same thing
the number of rushing yards in game 16 is an outlier in the x direction. what effect do you think this game has on the correlation? on the equation of the least- squares regression line? calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.
Answers
The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.
We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.
Effect on Correlation:
An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.
Effect on Equation of the Least-Squares Regression Line:
An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.
Calculation of Correlation and Equation of Least-Squares Regression Line:
Without game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.94
The equation of the least-squares regression line:
y = 2.25x + 10.5 With game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.93
The equation of the least-squares regression line:
y = 1.92x + 22.8
From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.
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-2a3 - 3a2 + 4a + 6, 2a3 + 5a2 + 7
sum the expression
Answers
Answer:
2a2 + 4a + 7
Step-by-step explanation:
As, - (2a3 - 3a2 + 4a + 6) + (2a3 + 5a2 + 7)
= 2a2 + 4a + 13
The base of a rectangular prism is a rectangle
with
sides that are 7 inches and 5 inches long. Its height is
10 inches. Write two different equations that you can
uise to find the volume
Answers
Two different equations that are used to calculate the volume of a rectangular prism are V = B × h and V = l× w× h, where, V --> volume and B --> base area.
We have a rectangular prism with base as a rectangle with the following information
Length of base rectangle, l = 7 inches
Width of base rectangle, w = 5 inches
Height of rectangular prism, h = 10 inches
The first equation for the volume of a rectangular prism is equal to multiplcation of its base area by its height. Mathematically, it can be written as, V = B × h --(1)
where, B --> base area
V --> volume
Here base is a rectangle, so base area is equivalent to area of rectangle. The second equation used for calculating the volume of rectangular prism is written
V = l× w× h
where l, w and h are dimensions of prism.
So, using one of above equation, the
volume of rectangular prism is 350 inch³.
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Change to slope intercept form, please do fast! No work needed just a brief description of how u got it :)
Answers
Step-by-step explanation:
the slope intercept form is
y = ax + b
the slope is always the factor a of x. as it is the same for parallel lines, you can simply copy the term of x.
to get b you put the coordinate values (x, y) of the given points into the equation and solve for b.
Find mZN.
62°
K
N
Need help with this question?
Answers
Answer:
118degrees
Step-by-step explanation:
Assuming we are given the following and m<k and ,<N lies on the same straight line, hence;
m<K = 62 degrees
n<N = ?
Since are on the same straight line, hence;
m<N + m<K = 180
m<N + 62 = 180
m<N = 180 - 62
m<N = 118
Hence the measure of m<N is 118degrees
'
,
Savita is dividing 3 1/4 kg of sweets equally among her seven friends. How much does each
friend receive?
Answers
Answer:
13/28 kg
Step-by-step explanation:
Convert to 28 in the denominator.
\(\frac17 \cdot (3+\frac14) = \frac37+ \frac{1}{28} = \frac{3\cdot4}{7\cdot4}+ \frac{1}{28} = \frac{12}{28}+ \frac{1}{28} = \frac{13}{28}\)
You can identify sample spaces for compound events using organized lists, tables, and tree diagrams. Which of the three methods do you find easiest to use? Which method is the most helpful? Why? Use the Internet or another resource to find the definition of the Fundamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example.
Answers
The fundamental counting principle is used to count the total number of possible outcomes that are in a situation.
What does the fundamental counting principle state?The fundamental counting principle states that if there are n ways of doing something, as well as m ways of doing another thing, then there are n×m ways to perform both of these actions.
The Fundamental Counting Principle helps when determining the sample space of probability as it figures out the total number of ways the combination of events can occur. Therefore, it is used as a guide when determining the sample space of a probability.
Lastly, the limitation is that the Fundamental Counting Principle is that it assumes that each basic event is equally probable, which does not necessarily have to be true.
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Answer:
The fundamental counting principle is used to count the total number of possible outcomes that are in a situation
Step-by-step explanation:
Hello! It would be wonderful if someone could help me with these 3 questions! Instead giving you 10 points, i'll bump it up to 20 points if someone could help me with these 3 questions <3
Answers
Answer:
Ration is the root word
They all have been described as a rational number because they all have a ratio.
I am so sorry I do not know the last one
Step-by-step explanation:
I hope this helps
Donna bought 5 bags of dog treats for $10.65. What is the cost per bag of dog treats?
Answers
Answer:
$10.65 divide by 5 equals $2.13
Answer:
The cost per bag of dog treats is $2.13.
Step-by-step explanation:
We have the total, so to find the cost per bag you would take the total and divide by how many bags there are.
Total = $10.65
How many bags there are : 5
$10.65 divided by 5 = 2.13
The cost per bag of dog treats is $2.13.
The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 60 laptops, the sample mean is 122 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p-value?
Answers
The p-value can be calculated to test the null hypothesis that the average running time of HP laptops is 120 minutes against the alternative hypothesis that it is not equal to 120 minutes.
The p-value for testing the hypothesis that the average time for the HP laptops is not equal to 120 minutes can be calculated using a t-test. Given a sample mean of 122 minutes, a sample size of 60, a null hypothesis mean of 120 minutes, and a standard deviation of 25 minutes, we can calculate the t-value and find the corresponding p-value.
To calculate the t-value, we use the formula: t = (sample mean - null hypothesis mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values, we get: t = (122 - 120) / (25 / sqrt(60))
Calculating the t-value, we find t ≈ 0.894
To find the p-value associated with this t-value, we can refer to a t-distribution table or use statistical software. The p-value represents the probability of observing a t-value as extreme as the one obtained, assuming the null hypothesis is true.
Since the p-value (0.757) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that the average running time of HP laptops is significantly different from 120 minutes.
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i genuinely can't seem to understand how to do these equations,i have issues comprehending math due to autism,please include the full work so i can help understand it,I would like assistance please.
Answers
Answer:
Step-by-step explanation:
Multiply the figure outside the bracket with each figure inside the bracket, and also be cautious of the signs.
1) -5(x + 2)
= -5x - 10 (multiply -5 with x and then multiply it with +2)
3) 7(1-9x)
= 7 - 63x (multiply 7 with 1 then multiply it with 9x)
5) 9(8 - 8a)
= 72 - 72a (multiply 9 with 8 then multiply it with 8a)
7) 4n - 7n
= -3n (subtract the numbers only, as both are being multiplied with n, they can be subtracted)
9) n - 2 + 6
= n + 4
What is the answer to this question?
Answers
Answer:
9 I think don't trust me 100%
Step-by-step explanation:
Answer:
x= 9
Step-by-step explanation:
Fifteen years from now, Atli’s age will be 4 times his current age. What is his current age?
Answers
Answer:
he is three i think
Step-by-step explanation:
the gallup poll has decided to increase the size of its random sample of canadian voters from about 1500 people to about 4000 people right before an election. the effect of this increase is to
Answers
The effect of increasing the random sample size of Canadian voters in the Gallup poll from 1,500 to 4,000 people is to reduce the margin of error and increase the accuracy of the poll results.
By increasing the sample size, the Gallup poll is able to gather more data points from a diverse group of voters, which improves the representativeness of the sample.
This helps to minimize biases and better capture the opinions of the population as a whole. In turn, the increased sample size leads to a lower margin of error, meaning that the poll results are more likely to accurately represent the true opinions of Canadian voters.
This is particularly important right before an election, as accurate poll results can inform strategies for political parties and provide insights for voters. Ultimately, increasing the sample size of the random sample in the Gallup poll enhances its reliability and validity, making it a more valuable tool in understanding voter sentiment.
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My victory will be in your hands if you answer this ✌✌✌✌✌
Answers
Add dress and shoes together:
30 + 25 = 55
1/5 off means the total after discount would be 4/5 ( 1 - 1/5 = 4/5)
Multiply total price by 4/5:
55 x 4/5 = (55 x4)/5 = 220/5 = 44
Total after discount is 44
Now add shipping:
44 + 8 = 52
Total paid = £52
Answer:
She will pay $52
Step-by-step explanation:
So she buys them both, which equals 55 dollars. But the website has a deal that is if you buy both of them it's 1/5 of the price off. And 1/5 of 55 is $11, so 55-11=44. You might think you're done but your not. At the end it says they add $8 for the shipping/handling, which is 44+8. This equals 52 dollars. By the way substitute this money sign $ for the one on your page
Let's say someone is conducting research on whether people in the community would attend a pride parade. Even though the population in the community is 95% straight and 5% lesbian, gay, or some other queer identity, the researchers decide it would be best to have a sample that includes 50% straight and 50% LGBTQ+ respondents. This would be what type of sampling?
A. Disproportionate stratified sampling
B. Availability sampling
C. Snowball sampling
D. Simple random sampling
Answers
The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."
A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.
B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.
C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.
D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.
Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.
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PLEASE HELP ME! find the measure of each numbered angle. pls
Answers
Answer: ∠1 = 37.5°; ∠2 = 37.5°; ∠3 = 133°.
Step-by-step explanation:
∠1 = ∠2 = (180° - 105°) ÷ 2 = 37.5°
∠3 = 180° - 23° - 24° = 133°
2 < x <8
x is an integer.
write down the possible values of x.
Answers
Answer:
3, 4, 5, 6, 7
Step-by-step explanation:
Answer
3,4,5,6,7 because they are between 2 and 8
A recent government program required users to sign up for services on a website that had a high failure rate. If each user's chance of failure is independent of another's failure, what would the individual failure rate need to be so that out of 20 users, only 20% failed?
Answers
The individual failure rate needs to be approximately 24.5% so that out of 20 users, only 20% fail.
A recent government program required users to sign up for services on a website that had a high failure rate. If each user's chance of failure is independent of another's failure, the individual failure rate needed for out of 20 users, only 20% to fail can be calculated using the binomial probability formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, k is the number of successful trials, and (n choose k) is the binomial coefficient.
Here, the number of trials (n) is 20, and the probability of success is 1-p, which is the probability of failure. We want only 20% of users to fail, which means that 80% should succeed. Therefore, p = 0.8. The formula can now be used to find the probability of exactly 16 users succeeding:
P(X=16) = (20 choose 16) * 0.8^16 * (1-0.8)^(20-16)
= 4845 * 0.0112 * 0.0016
= 0.0847
This means that the probability of 16 users succeeding is about 8.47%. To find the individual failure rate, we need to adjust the probability of failure (1-p) so that the probability of exactly 16 users failing is 20%. Let x be the individual failure rate. Then:
P(X=16) = (20 choose 16) * (1-x)^16 * x^4
= 0.2
Solving for x, we get:
x = 0.245
Therefore, the individual failure rate needs to be approximately 24.5% so that out of 20 users, only 20% fail.
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Find the magnitude and direction of the vector <3,9>
Round angles to the nearest degree and other values to the nearest tenth.
9; 72°
9.5; 80°
9; 80°
9.5; 72°
Answers
The magnitude of the vector (3, 9) is 3√10 and the measure of the angle is 71.6°
What are dot products and cross products?The cosine of the angle between the vectors and their magnitude are combined to form the dot product.
The dot product is represented by A.B = ABCos θ.
The sine of the angle between the vectors and their magnitude are combined to form the cross-product.
The cross product is represented by A×B = ABSin θ.
We know, The magnitude of a vector (a, b) is √(a² + b²), and the angle it possesses with respect to the positive x-axis is, tan(b/a).
Therefore, The magnitude of the vector (3, 9) is,
= √(3² + 9²).
= √90.
= 3√10.
And the angle is, Ф = tan⁻¹(9/3).
Ф = tan⁻¹(3).
Ф = 71.6°.
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The number 1.725 appears in the t chart corresponding to 20 degrees of freedom and aType I error value of 5%. Write down a deductive statement (that is, starting with the word "If")indicating how the number 1.725 was derived. (You do not have to discuss any mathematicalcalculation, which is indeed very difficult. Just outline the nature of the deductive statement.)
Answers
If a t-distribution with 20 degrees of freedom is used to test a hypothesis with a Type I error value of 5%, then the critical t-value corresponding to the given significance level is 1.725.
The critical t-value is the value beyond which we reject the null hypothesis in a t-test. The value is determined by the significance level (Type I error) and the degrees of freedom.
In this case, with a significance level of 5% and 20 degrees of freedom, the critical t-value is 1.735. This means that if the calculated t-value for a sample falls beyond 1.735, we reject the null hypothesis at the 5% level of significance.
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