Question

Sum of deviation of some items from 13 is 74 & from 17 is 26. Find the mean of these items?
a, 19.16
b. 27
C. 51
d. 12​

Answer 1

Answer:

The correct answer is 19.16

Answer 2

Answer:

The mean of the items is determined to be 19.16.

Therefore, option a) 19.16 is the correct choice.

Explanation:

Given,

The sum of the observations of some items from 13 = 74

• In this first case, the observation begins at 13

The sum of the observations of some items from 17 = 26

• In this second case, the observation begins at 17

Let us consider, the items whose sum of deviation is 74 and 26 = x

As we know,

• The mean is described as the average of the given numbers and is calculated by dividing the sum of observations by the total number of observations.
• $Mean = \frac{Sum of observation}{Total number of observation}$

In the first case;

• $Mean = \frac{74}{x}$
• As in this case, the observation begins at 13

Therefore,

• $Mean = \frac{74}{x} + 13$ =
• Mean = $\frac{74 + 13x}{x}$   ---------------equation(1)

 

In the second case,

• $Mean = \frac{26}{x}$
• As in this case, the observation begins at 17

Therefore,

• $Mean = \frac{26}{x} + 17$
• Mean = $\frac{26+ 17x}{x}$   ----------------equation (2)

By comparing equations 1 and 2, we get;

• $\frac{74 + 13x}{x} = \frac{26+ 17x}{x}$
• 74 + 13x = 26 + 17x
• 17x - 13x = 74 -26
• 4x = 48
• x = 12

After putting the value of x in equation 1, we get;

• Mean = $\frac{74 + 13x}{x}$ = $\frac{74 + 13\times12}{12}$ = 19.16

After putting the value of x in equation 2, we get;

• Mean = $\frac{26+ 17x}{x}$ = $\frac{26+ 17\times12}{12}$ = 19.16

Hence, the mean of these items is 19.16.