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

find the (a) mean, (b) median, (c) mode, and (d) mid - range 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? 9.7 10.3 9.1 10.3 9.8 9.4 9.0 10.2 9.9 9.1 9.1 e. are the statistics representative of the current population of all women in that countrys military? choose the best answer below. a. since the sample does not include men, the sample should not be considered to be representative of the population. b. since the sample is not a random sample, it should not be considered to be representative of the population. c. since the sample is random and the sample size is greater than 10, the sample can be considered to be representative of the population. d. since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the countrys military.
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. First, sum up all the data: $9.7+10.3 + 9.1+10.3+9.8+9.4+9.0+10.2+9.9+9.1+9.1=106.9$, and $n = 11$. So, $\bar{x}=\frac{106.9}{11}\approx9.72$.
Step2: Calculate the median
Arrange the data in ascending order: $9.0,9.1,9.1,9.1,9.4,9.7,9.8,9.9,10.2,10.3,10.3$. Since $n = 11$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+1}{2}=6$ - th value, so the median is $9.7$.
Step3: Calculate the mode
The mode is the value that appears most frequently in the data - set. The value $9.1$ appears 3 times, more frequently than any other value, so the mode is $9.1$.
Step4: Calculate the mid - range
The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is $9.0$ and the maximum value is $10.3$. So, the mid - range is $\frac{9.0 + 10.3}{2}=\frac{19.3}{2}=9.65$.
Step5: Analyze representativeness
The sample should be random to be considered representative. Since the sample is not a random sample (it is from a specific study in 1988 of women in the country's military), it should not be considered representative of the population.
Answer:
(a) Mean: $\approx9.72$ (b) Median: $9.7$ (c) Mode: $9.1$ (d) Mid - range: $9.65$ (e) B. Since the sample is not a random sample, it should not be considered to be representative of the population.