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. 11.4 11.2 11.1 11.7 11.7 9.7 11.7 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 11.2 (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 not a 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 the largest 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

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. 11.4 11.2 11.1 11.7 11.7 9.7 11.7 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 11.2 (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 not a 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 the largest 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 $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 7$, and the data set is $x_1=11.4,x_2 = 11.2,x_3=11.1,x_4 = 11.7,x_5=11.7,x_6=9.7,x_7=11.7$. Then $\sum_{i=1}^{7}x_i=11.4 + 11.2+11.1+11.7+11.7+9.7+11.7=78.5$. So, $\bar{x}=\frac{78.5}{7}\approx11.2$.

Step2: Find the median

First, order the data set: $9.7,11.1,11.2,11.4,11.7,11.7,11.7$. Since $n = 7$ (an odd - numbered data set), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{7+1}{2}=4$ - th value. So the median is $11.4$.

Step3: Determine the mode

The mode is the data value that appears most frequently. In the data set $9.7,11.1,11.2,11.4,11.7,11.7,11.7$, the number $11.7$ appears 3 times, more frequently than any other number. So the mode is $11.7$.

Answer:

The mean score is $11.2$. The mean represents the center. The median score is $11.4$. The mode is $11.7$.