Consider the following summary statistics for two data sets: DATA A DATA B Mean 59.5 7.5 Standard Deviation 8.4 1.3 a. Compute the Coefficients of Variation for each sample. Round results to 1 decimal place. DATA A DATA B CVA= % CVB= % b. In which population, DATA A or DATA B, is the data more variable? c. Compute a 81 % Chebyshev's Theorem interval for DATA B: First find the corresponding value of kk for a 81 % interval. E.g, determine the value of kk (round to 1 decimal place) such that: 1−1k2= 0.81 k= Now construct the upper and lower bounds of the interval (round results to 1 decimal place). By Chebyshev's Theorem, at least 81 % of the data falls within the interval that is ±k±k standard deviations of the mean. So the interval is: to d. An intern computed the following Chebyshev’s theorem interval for DATA B: [5.6,9.5][5.6,9.5] What value of kk did the intern use, and what does it mean in the context of this interval? Give result to 1 decimal place. What is the minimum proportion of DATA B that is contained in the interval? Give result to nearest whole percent.
Consider the following summary statistics for two data sets: DATA A DATA B Mean 59.5 7.5 Standard Deviation 8.4 1.3 a. Compute the Coefficients of Variation for each sample. Round results to 1 decimal place. DATA A DATA B CVA= % CVB= % b. In which population, DATA A or DATA B, is the data more variable? c. Compute a 81 % Chebyshev's Theorem interval for DATA B: First find the corresponding value of kk for a 81 % interval. E.g, determine the value of kk (round to 1 decimal place) such that: 1−1k2= 0.81 k= Now construct the upper and lower bounds of the interval (round results to 1 decimal place). By Chebyshev's Theorem, at least 81 % of the data falls within the interval that is ±k±k standard deviations of the mean. So the interval is: to d. An intern computed the following Chebyshev’s theorem interval for DATA B: [5.6,9.5][5.6,9.5] What value of kk did the intern use, and what does it mean in the context of this interval? Give result to 1 decimal place. What is the minimum proportion of DATA B that is contained in the interval? Give result to nearest whole percent.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Question
Consider the following summary statistics for two data sets:
| DATA A | DATA B | |
|---|---|---|
| Mean | 59.5 | 7.5 |
| Standard Deviation | 8.4 | 1.3 |
a. Compute the Coefficients of Variation for each sample. Round results to 1 decimal place.
| DATA A | DATA B |
| CVA= % | CVB= % |
b. In which population, DATA A or DATA B, is the data more variable?
c. Compute a 81 % Chebyshev's Theorem interval for DATA B:
- First find the corresponding value of kk for a 81 % interval. E.g, determine the value of kk (round to 1 decimal place) such that:
1−1k2= 0.81 k=
- Now construct the upper and lower bounds of the interval (round results to 1 decimal place). By Chebyshev's Theorem, at least 81 % of the data falls within the interval that is ±k±k standard deviations of the mean. So the interval is:
to
d. An intern computed the following Chebyshev’s theorem interval for DATA B:
[5.6,9.5][5.6,9.5]
- What value of kk did the intern use, and what does it mean in the context of this interval? Give result to 1 decimal place.
- What is the minimum proportion of DATA B that is contained in the interval? Give result to nearest whole percent.
%
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