Chapter 10.1, Problem 22STP

To determine

To Find: To find the appropriate measure of the given data.

Answer to Problem 22STP

The answer is mean that is option C.

Explanation of Solution

Given information:Number of books read by the students in each reading class.

Formulaused:

  $\begin{array}{l}\text{For}\text{Mean}=\frac{\text{Total}\text{number}\text{of}\text{observation}}{\text{Number}\text{of}\text{observation}}\\ \text{For}\text{Median}={\left(\frac{n+1}{2}\right)}^{\text{th}}\text{observation}\text{if}n\text{is}\text{odd}\\ \text{and},\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{observation}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{observation}}{2}\text{if}n\text{is}\text{even}\\ \text{For Mode}=\text{Observation}\text{with}\text{highest}\text{frequency}\end{array}$ .

Calculation:

Calculation of mean

  $\begin{array}{l}\text{Mean}=\frac{104+162+110+145+90+134+97+126}{8}\\ \text{Mean}=\frac{968}{8}\\ \therefore \text{Mean}=121\end{array}$

Thus, mean of the given data is 121.

Calculation of median

First, we arrange the data in ascending order

  $90,97,104,110,126,134,145,162$

  $\begin{array}{l}\because n=8\text{which}\text{is}\text{even}\\ \therefore \text{Median}=\frac{{\left(\frac{8}{2}\right)}^{\text{th}}\text{observation}+{\left(\frac{8}{2}+1\right)}^{\text{th}}\text{observation}}{2}\\ \text{Median}=\frac{4^{\text{th}}\text{observation}+5^{\text{th}}\text{observation}}{2}\\ \text{Median}=\frac{110+126}{2}\\ \text{Median}=\frac{236}{2}\\ \text{Median}=118\end{array}$

Thus, median is 118

Calculation of mode

Since the frequency of all the observations are same

Therefore, mode can not be calculated by inspection

So, using empirical relation

  $\begin{array}{l}\text{Mode}=3\text{Median}-2\text{Mean}\\ \text{Mode}=3\times 118-2\times 121\\ \text{Mode}=354-242\\ \text{Mode}=112\end{array}$

Thus, mode is 112.

Hence, the maximum measure of central value represented by mean.