Question

The mean of 20 items is 55. If two items 45 and 30 are removed, the new mean of the remaining items is ? 65.5 65,3 56.9

Answer 1

Solution

Given :-

• Mean of 20 items = 55

• Items removed = 30 , 45

♦As mean of any observation

$= \dfrac{\textsf{ Sum of all observations}}{\textsf{Total number of observations}}$

Or

$x' = \dfrac{\sum\limits_{i=1}^{i=n}x_i}{n}$

♦Hence From above ,

→ Sum of all observations = n × x'

= 20 × 55

= 1100

♦Now Sum after removing 30 & 45

= 1100 - (30 + 45)

= 1100 - (75)

= 1025

♦Now after removing two items :-

→Total number items = 20 - 2

= 18

♦ Now From the formula

$x' = \dfrac{\sum\limits_{i=1}^{i=n}x_i}{n}$

$\implies x'_{2} = \dfrac{ 1025}{18}$

$\implies x'_{2} = 56.94$

$\implies x'_{2} = 56.9$

So new mean = 56.9

Answer 2

Answer:

Step-by-step explanation:

According to the question

Mean of 20 items is = 55

Sum of 20 items is = 55 × 20 = 1100

Two items removed = 45 + 30 = 75

Now, Sum of 18 items = 1100 - 75 = 1025

∴ Average = 102518=56.9