Chapter 12, Problem 26CCSR

To determine

Find the correct option.

Answer to Problem 26CCSR

  $G$

Explanation of Solution

Given information:

How does the mean of the data set below change if each value increased by $8$ .

  $105 110 104 107 102 106 133 81$

Option:-

  $F$ The mean increases by $1$ .

  $G$ The mean increases by $8$ .

  $H$ The mean decreases by $8$ .

  $I$ The mean does not change.

Calculation:

Mean is defined as the sum of observations to the number of observations of any given data.

Consider the given series:

  $105 110 104 107 102 106 133 81$

First write in increasing order

  $81,102,104,105,106,107,110,133$

The number of observation is $n=8$

Also, the sum of observation is

  $81+102+104+105+106+107+110+133=848$

So, applying the value:

  $Mean=\frac{Sum}{n}$

  $\begin{array}{l}=\frac{848}{8}\\ =106\end{array}$

Now, add each observation by $8$

  $81+8,102+8,104+8,105+8,106+8,107+8,110+8,133+8$

That is,

  $89,110,112,113,114,115,118,141$

Sum of observation, $89+110+112+113+114+115+118+141=912$

Hence, the mean is given below:

  $\frac{912}{8}=114$

Now, subtract the new mean from the old mean obtained:

  $114-106=8$

Hence, clearly the mean gets increased by $8$ .

Hence, the option $G$ is correct.