Question

The mean of a certain number of observations is 40. If two more items with value 40 and 64 are
added to the data the mean increases to 42. Find the number of items in the original data.
a) 10
b) 35
c) 42
d)45​

Answer 1

Answer:

No:of obsrvns=x

mean. . 40

Total. 40x

40x +104=(x+2) 42

40x+104=42x+84

- 2x = -20

x = 20/2=10

No. of items = 10

Answer 2

The number of items in the original data is 10

Solution:

Let the number of observations be "x"

$Mean = \frac{\text{ sum of all observations }}{\text{ number of observations }}$

Given that,

The mean of a certain number of observations is 40

$40= \frac{ \text{ sum of all observations }}{x }\\\\ \text{sum of all observations } = 40x$

If two more items with value 40 and 64 are  added to the data the mean increases to 42

Therefore,

$42 = \frac{ \text{ sum of all observations +40 + 64}}{x + 2}\\\\42(x + 2) = \text{ sum of all observations } +40 + 64\\\\42(x + 2) = 40x + 40 + 64\\\\42x + 84 = 40x + 104\\\\42x - 40x = 104 - 84\\\\2x = 20\\\\x = 10$

Thus number of items in the original data is 10

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