find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given…

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 countrys military in 1988. are the statistics representative of the current population of all women in that countrys military? 9.0 8.6 10.4 8.6 10.3 9.3 9.4 9.8 10.1 10.4 10.4 \n\nb. there is no mode.\nd. find the midrange.\nthe midrange is 9.5 inch(es).\n(type an integer or a decimal. do not round.)\ne. are the statistics representative of the current population of all women in that countrys military? choose the best answer below.\n\na. since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the countrys military.\nb. since the sample is not a random sample, it should not be considered to be representative of the population.\nc. since the sample is random and the sample size is greater than 10, the sample can be considered to be representative of the population.\nd. since the sample does not include men, the sample should not be considered to be representative of the population.
Answer
Explanation:
Step1: Calculate the mean
The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. $\sum_{i=1}^{11}x_{i}=9.0 + 8.6+10.4 + 8.6+10.3+9.3+9.4+9.8+10.1+10.4+10.4=106.3$, $n = 11$. $\bar{x}=\frac{106.3}{11}\approx9.66$
Step2: Calculate the median
First, arrange the data in ascending order: $8.6,8.6,9.0,9.3,9.4,9.8,10.1,10.3,10.4,10.4,10.4$. Since $n = 11$ (odd), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+1}{2}=6$-th value, so the median is $9.8$.
Step3: Calculate the mode
The mode is the value that appears most frequently in the data - set. The number $10.4$ appears $3$ times, more frequently than any other number, so the mode is $10.4$.
Step4: Calculate the mid - range
The mid - range is $\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is $8.6$ and the maximum value is $10.4$. Mid - range$=\frac{8.6 + 10.4}{2}=\frac{19}{2}=9.5$
Step5: Answer the representativeness question
The measurements were made in 1988. Over time, the population characteristics may change. So, since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the country's military.
Answer:
a. Mean: $9.66$ b. Median: $9.8$ c. Mode: $10.4$ d. Mid - range: $9.5$ e. A. Since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the country's military.