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Answer:
<em>Learning Objective</em>: Use the mean and range to <u>compare</u> the spread and averages.
a) Sarah Mean = 70.9, Katie Mean = 78.9
b) Sarah Range = 15, Katie Range = 25
c) Sentences
- The <u>mean</u> shows, on average, Sarah was 8 seconds quicker than Katie.
- The <u>range</u> shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.
Step-by-step explanation:
Given:
Sarah's Data Set:
- 79, 70, 68, 75, 69, 64, 69, 75, 64, 76
Katie's Data Set:
- 79, 79, 76, 81, 89, 76, 64, 85, 82, 78
To Find:
- The mean and range of both data sets separately.
Work:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is .
The formula for the mean of a sample is .
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values given above, the solution is:
Therefore, the mean of Sarah's data set is 70.9.
For Katie's Data Set, .
Therefore, the mean of Katie's data set is 78.9.
To fill in the summary, we have to use the data we just calculated.
That summary can be found in the answer section.