Question

Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80, were
wrongly read as 40, 20, 50 respectively. The correct mean is

Answer 1

STATISTICS :

Mean of 100 items, Σ M = 49

Incorrect Σ M = $\mathsf{\dfrac{Sum \:of \:incorrect\: observations} {Number\: of\: observations}}$ = Σ$\mathsf{\dfrac{x_i}{n}}$

49 = Σ$\mathsf{\dfrac{x_i}{100}}$

Σ$\mathsf{x_i}$ = 4900

Correct sum of observations, Σ$\mathsf{x_i}$ = 4900 - 40 - 20 - 50 = 4790

Correct sum of observations, Σ$\mathsf{x_i}$ = 4790 + 60 + 70 + 80 = 5000

Correct Mean, Σ M' = $\mathsf{\dfrac{Sum \:of \:incorrect\: observations} {Number\: of\: observations}}$ = Σ$\mathsf{\dfrac{x_i}{n}}$

Correct Mean, Σ M' = $\mathsf{\dfrac{5000} {100}}$

➡️ Correct Mean, Σ M' = 50

Answer 2

Answer:

Step-by-step explanation:

Sum of observation = 100 × 49 = 4900

Correct sum

= 4900 – [40 + 20 + 50 ] + [60 + 70 + 80] = 5000

∴ Correct mean =  

5000/100

= 50