Question

the most appropriate measure of center for this data is the median. which statement about the data is true? the mean is greater than the median. the mean is equal to the median. the mean is less than the median. what is the median of the data? weight of male dogs (lb.) 4|5 5|0 2 8 6|2 8 7|2 8 8|1 9|5 8|1 means 81

Explanation:

Step1: Write out the data set

The data set from the stem - and - leaf plot is: 45, 50, 52, 58, 62, 68, 72, 78, 81, 95.

Step2: Calculate the number of data points

There are $n = 10$ data points.

Step3: Calculate the median

For $n = 10$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered data points. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is 62 and the 6th value is 68. So the median $M=\frac{62 + 68}{2}=\frac{130}{2}=65$.

Step4: Calculate the mean

The mean $\bar{x}=\frac{45+50+52+58+62+68+72+78+81+95}{10}=\frac{661}{10}=66.1$.

Answer:

The median of the data is 65. Since the mean is 66.1 and the median is 65, the mean is greater than the median.