Question

the most appropriate measure of center for this data is the median. complete 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. done 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 \(45,50,52,58,62,68,72,78,81,95\). There are \(n = 10\) data points.

Step2: Calculate the median

For a data set with \(n = 10\) (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. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5th value is \(62\) and the 6th value is \(68\). So, the median \(M=\frac{62 + 68}{2}=\frac{130}{2}=65\).

Step3: Calculate the mean

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

Step4: Compare the mean and the median

Since \(66.1>65\), the mean is greater than the median.

Answer:

The mean is greater than the median.