Concept explainers
For the following population of N = 6 scores: 2, 9, 6, 8, 9, 8
- a. Calculate the
range and the standard deviation. (Use either definition for the range.) - b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures of variability.
(a)
To find: The range and standard deviation for the population of scores.
Answer to Problem 21P
The range and standard deviation for the population of scores is 7 or 8 and 2.45.
Explanation of Solution
Given info:
The set of scores are 2, 9, 6, 8, 9, and 8.
Calculation:
The formula for range set of scores is,
If the scores are whole numbers, the formula for range set for scores is,
The formula of standard deviation is,
From the set of scores, the maximum and minimum values are 9 and 2.
The range is,
If the scores are whole numbers, the range is,
The mean is,
The standard deviation is,
Conclusion:
The obtained range and standard deviation for the scores is 7 or 8 and 2.45.
(b)
To find: The range and standard deviation for the population of scores.
Answer to Problem 21P
After adding 2 points for each score, the range and standard deviation for the population of scores is 7 or 8 and 2.45.
Explanation of Solution
Given info:
The set of scores are 2, 9, 6, 8, 9, and 8.
Calculation:
The formula for range set of scores is,
If the scores are whole numbers, the formula for range set for scores is,
The formula of standard deviation is,
First add 2 points for each score, the new data set of scores is, 4, 11, 8, 10, 11, and 10
The maximum and minimum values for set of scores are 4 and 11.
The range is,
If the scores are whole numbers, the range is,
The mean is,
The standard deviation is,
Conclusion:
The required new range and standard deviation for the scores is 7 or 8 and 2.45.
Based on the results, it can be concluded that the range and standard deviation does not change when adding the two points for each score.
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Chapter 4 Solutions
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill