Question

arithmetic mean of 50 observations is found to be 24 later on checking the data it was observed that two items having value 23 and 30 are taken as 32 and 3 find the arithmetic mean by mkaking necessary conditions

Answer 1

Correct Arithmetic Mean = 24.36

Step-by-step explanation:

We are given that arithmetic mean of 50 observations is found to be 24, later on checking the data it was observed that two items having value 23 and 30 are taken as 32 and 3.

Now, the mean of any data is given by the following formula;

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

                                   Or

                     $\bar X = \frac{\sum X}{n}$

So, the arithmetic mean of 50 observations is given as 50, i.e;

                      $\bar X = \frac{\sum X}{n}$  

                      24 = $\frac{\sum X}{50}$

SO, Incorrect  $\sum X$ = $24 \times 50$ = 1200

Now, we are given that the two items having value 23 and 30 are taken as 32 and 3, so to find the correct mean we will subtract the incorrect values and add the correct values.

Correct  $\sum X$ = 1200 - 32 - 3 + 23 + 30 = 1218

Correct  n = 50 - 2 + 2 = 50

Hence, Correct Mean  = $\frac{Correct \sum X}{\text {Correct n} }$

                                      = $\frac{1218}{50}$ = 24.36

Therefore, the arithmetic mean by making necessary conditions is 24.36.