Chapter 14.2, Problem 7CFU

To determine

To find: Themean, median and the mode of the data represented by the stem and leaf plot at the right.

Answer to Problem 7CFU

The mean of the data set is $10323$ , the median is 10500.

Explanation of Solution

Given:

The given stem and leaf plot is shown in Figure 1

  

Figure 1

Calculation:

Consider the sum of the numbers that is contributed by the stem 9 having 5 leaves is,

  $\begin{array}{c}5\left(9000\right)+100\left(1+4+5+8+9\right)=4500+2700\\ =47700\end{array}$

Consider the sum of the numbers that is contributed by the stem 10 having 5 leaves is,

  $\begin{array}{c}5\left(10000\right)+100\left(5+5+7+7+7\right)=50000+3100\\ =53100\end{array}$

Consider the sum of the numbers that is contributed by the stem 11 having 3 leaves is,

  $\begin{array}{c}5\left(11000\right)+100\left(1+1+2\right)=33000+400\\ =33400\end{array}$

Consider the mean of the data is,

  $\begin{array}{c}\overline{X}=\frac{47700+53100+33400}{13}\\ =\frac{134200}{13}\\ =10323\end{array}$

From the data set the median is the middle term that is 10500.

By the observation of the mode and the leaf plot, the leaf 7 in the stem 10 repeats 3 times then the mode is 10700.

Thus, the mean of the data set is $10323$ , the median is 10500.