find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a…

find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a measure does not represent the center of the data, explain why. a sample of seven admission test scores for a professional school are listed below. 11.6 10.4 11.8 11.5 10.9 10.2 10.2 what is the mean score? select the correct choice below and fill in any answer box to complete your choice. a. the mean score is 10.9 (round to one decimal place as needed.) b. there is no mean score. does the mean represent the center of the data? a. the mean represents the center. b. the mean does not represent the center because it is the largest data value. c. the mean does not represent the center because it is the smallest data value. d. the mean does not represent the center because it is not a data value. what is the median score? select the correct choice below and fill in any answer box to complete your choice. a. the median score is (round to one decimal place as needed.) b. there is no median score.
Answer
Explanation:
Step1: Calculate the mean
The formula for 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. $\sum_{i=1}^{7}x_{i}=11.6 + 10.4+11.8+11.5+10.9+10.2+10.2=76.6$ $n = 7$ $\bar{x}=\frac{76.6}{7}\approx10.9$
Step2: Determine if the mean represents the center
The mean of 10.9 is a reasonable measure of the center as it takes into account all the data values. It is not the largest or the smallest data value. So, the mean represents the center of the data.
Step3: Find the median
First, order the data: 10.2, 10.2, 10.4, 10.9, 11.5, 11.6, 11.8. Since $n = 7$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{7+1}{2}=4$ - th value. The 4 - th value in the ordered list is 10.9.
Step4: Find the mode
The mode is the value that appears most frequently in the data - set. The value 10.2 appears twice, and all other values appear only once. So, the mode is 10.2.
Answer:
The mean score is 10.9. The mean represents the center. The median score is 10.9. The mode score is 10.2.