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# Descriptive statistics and z-scores

1.Senator Hayes is considering a a run for the U.S. presidency, but she is only 35 years of age, which is the minimum required age. While investigating this issue, she finds the ages of past presidents when they were inaugurated, and those ages are listed below. Using the ages listed find the (a) mean; (b) median; (c) mode; (d) midrange; (e) range; (f) standard deviation; (g) variance; (h)Q1; (I) Q3; (J)P10-

57 61 57 57 58 57 61 54 68 51 49 64 50 48

65 52 56 46 54 49 51 47 55 55 54 42 51 56

55 51 54 51 60 62 43 55 56 61 52 69 64 46

54

2.

(a) John F. kennedy was 43 years of age when he was inaugurated. Using the results from exercise 1, convert his age to a z score.

(b) Is Kennedy's age of 43 years "unusual"? Why or why not?

(c) Using the range rule of thumb, identify any other listed ages that are unusual.

(D) Although the list of ages does not include an age of 35 years, would that age be unusual? Is it likely that a presidential candidate of age 35 would find that his or her age would be a major campaign issue?

3. Frequency Distribution

Using the same ages listed in exercise Exercise 1, construct a frequency distribution. Use six classes with 40 as the lower limit of the first class, and use a class width of 5.

#### Solution Preview

The first question and 2a answers are in excel file .

range rule of thumb is that the range of a data set is approximately 4 standard deviations (4s). Thus the maximum data element will be about 2 standard deviations ...

#### Solution Summary

Calculation of mean median mode and range. Z-scores are also calculated.

\$2.19