Question

find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. listed below are foot lengths in inches of randomly selected women in a study of a country’s military in 1988. are the statistics representative of the current population of all women in that country’s military? 9.1, 9.3, 9.9, 9.3, 8.8, 8.6, 8.9, 10.3, 8.7, 9.9, 9.9. a. the mean is 9.34 inch(es). (type an integer or a decimal rounded to two decimal places as needed.) b. find the median. the median is 9.3 inch(es). (type an integer or a decimal. do not round.) c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode(s) is(are) 9.9 inch(es). (type an integer or a decimal. do not round. use a comma to separate answers as needed.) b. there is no mode. d. find the midrange. the midrange is 9.45 inch(es). (type an integer or a decimal. do not round.) e. are the statistics representative of the current population of all women in that country’s military? choose the best answer below. a. since the sample is random and the sample size is greater than 10, the sample can be considered to be representative of the population. b. since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the country’s military. c. since the sample is not a random sample, it should not be considered to be representative of the population. d. since the sample does not include men, the sample should not be considered to be representative of the population.

Explanation:

Part (a): Mean

Step1: Sum all data points

The data set is \( 9.1, 9.3, 9.9, 9.3, 8.8, 8.6, 8.9, 10.3, 8.7, 9.9, 9.9 \).
Sum \( = 9.1 + 9.3 + 9.9 + 9.3 + 8.8 + 8.6 + 8.9 + 10.3 + 8.7 + 9.9 + 9.9 \)
\( = 103.7 \)

Step2: Divide by number of data points

There are 11 data points.
Mean \( = \frac{103.7}{11} \approx 9.427 \approx 9.34 \) (rounded as given, but precise calculation: \( \frac{103.7}{11} \approx 9.43 \), but the problem states mean is 9.34? Wait, recalculating:
Wait, let's sum again:
9.1 + 9.3 = 18.4; +9.9=28.3; +9.3=37.6; +8.8=46.4; +8.6=55; +8.9=63.9; +10.3=74.2; +8.7=82.9; +9.9=92.8; +9.9=102.7. Oh, I miscalculated earlier. Sum is 102.7. Then mean \( = \frac{102.7}{11} \approx 9.336 \approx 9.34 \). Correct.

Step1: Order the data

Ordered data: \( 8.6, 8.7, 8.8, 8.9, 9.1, 9.3, 9.3, 9.9, 9.9, 9.9, 10.3 \)

Step2: Find the middle value

There are 11 values (odd), so the 6th value is the median.
6th value: \( 9.3 \)

Step1: Identify the most frequent value

Count occurrences:

• 8.6: 1
• 8.7: 1
• 8.8: 1
• 8.9: 1
• 9.1: 1
• 9.3: 2
• 9.9: 3
• 10.3: 1

The value 9.9 occurs most (3 times).

Answer:

\( 9.34 \)

Part (b): Median