Questions: 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? 10.5, 10.3, 9.4, 10.3, 9.3, 9.5, 9.7, 8.5, 8.9, 9.4, 9.4 c. Find the mode. A. The mode(s) is(are) 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.

Solution Steps

The mean \( \mu \) of the data is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of data points and \( x_i \) are the individual data points. For the given data:

\[ \mu = \frac{105.2}{11} = 9.56 \]

To find the median, we first sort the data:

\[ \text{Sorted data} = [8.5, 8.9, 9.3, 9.4, 9.4, 9.4, 9.5, 9.7, 10.3, 10.3, 10.5] \]

The median is the value at the position given by the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (11 + 1) = 6.0 \]

The quantile is at position 6, which corresponds to the value:

\[ \text{Median} = 9.4 \]

To determine the mode, we count the frequency of each value in the dataset. The value that appears most frequently is:

\[ \text{Mode} = 9.4 \text{ inch(es)} \]

Final Answer