Question

The mean of 10 observation is 15.if one of the observation is taken 20 instead of 15.find the correct mean

Answer 1

Let the mean be x
x/10=15
x=150
Real sum=150-5=145
Real mean=145/10=14.5

Answer 2

Answer:

New mean is 14.5.

Step-by-step explanation:

Mean is defined as average of numbers that is total of all the items divided by number of items.

Given mean of 10 observation is 15.

that is $\dfrac{x_{1} +x_2+x_3+x_4+x_5+x_6+x_7+x_7+x_8+x_9+x_{10}}{10}= 15$

${x_{1} +x_2+x_3+x_4+x_5+x_6+x_7+x_7+x_8+x_9+x_{10}}= 15\times 10$

${x_{1} +x_2+x_3+x_4+x_5+x_6+x_7+x_7+x_8+x_9+x_{10}}= 150$ ....(1)

Also, Given he takes one observation as 20 instead of 15

Let the misread observation be $x_5$

To find the correct mean we subtract (20-15) 5 from sum of observations.

Then new mean is,

$\dfrac{x_{1}+x_2+x_3+x_4+x_55+x_6+x_7+x_7+x_8+x_9+x_{10}}{10}=M$

Using (1), We get

$\frac{150-5}{10}=M$

$\frac{145}{10}=M$

${14.5}=M$

Thus, new mean is 14.5.