Question

calculate the mean, median, and mode of the data. based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
median, mode, mean
median, mean, mode
mode, median, mean
mean, median, mode

Explanation:

Step1: Count data - point frequencies

There is 1 data - point at 2, 3 data - points at 5, 3 data - points at 6, 5 data - points at 7, 6 data - points at 8. Total number of data points $n=1 + 3+3 + 5+6=18$.

Step2: Calculate the mean

The mean $\bar{x}=\frac{2\times1 + 5\times3+6\times3 + 7\times5+8\times6}{18}=\frac{2+15 + 18+35+48}{18}=\frac{118}{18}\approx6.56$.

Step3: Calculate the median

Since $n = 18$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. First, order the data. The 9th and 10th ordered data values are both 7, so the median $M = 7$.

Step4: Calculate the mode

The mode is the value that appears most frequently. The value 8 appears 6 times, so the mode $Mo = 8$.

Step5: Compare the measures

Comparing the values $6.56$ (mean), $7$ (median), and $8$ (mode), the order from least to greatest is mean, median, mode.

Answer:

Mean, median, mode