Question

The mean of 25 observation is 36. Out of these observation if the mean of the first 13 observations is 32 and that of the last 13 observation is 40, the 13th observation would be?

Answer 1

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Answer 2

Hi Ghazala,

Your problem can be solved by two methods.

Method 1: (Lengthy but helps in understanding concept of mean)

Mean of 25 observations = 36 .....means total sum = 25*36 = 900
Mean of first 13 observations = 32....sum here = 13*32 = 416
Mean of last 13 observations = 40.....sum here = 13*40 = 520

Total observations = 13+13 =26....means the 13th observation is common in both since we only have 25 observations. Hence, 13th term is same from both starting and ending.

we can easily find this common value which is nothing but the 13th value
sum of first 13 observs + sum of last 13 observs - sum of all 25 observs
= (416+520)-900
= 36

Method 2: (Easy but tricky- involves application of mean concept)

Mean of first 13 observations+Mean of last 13 observations - Mean of 25 observations = (32+40)-36 = 36


Hope it helped you.
Please let me know if any further doubt.
Cheers !!!
 :)