Question

The mean of 47 observations is 30, out of which mean of first 24 observations is 29 and mean of last 24 observations is 35. Find the 24th observation.​

Answer 1

Step-by-step explanation:

$\frac{sum \: of \: 47 \: observations}{47} = 30 \\ sum \: of \: 47 \: observations = 47 \times 30 = 1410 \\ \\ \frac{sum \: of \:first 24 \: observations}{24} = 29 \\ sum \: of \: first \: 24\: observations = 24\times29 = 696 \\ \\ \frac{sum \: of \: last \: 24 \: observations}{24} = 35 \\ sum \: of \: last \: 24 \: observations = 35 \times 24 = 840$

24th observation is counted twice, in the first 24 and the last 24.

Sum of 47 observations= 1410

Sum of first 24 observations= 696

Sum of last 24 observations= 840

Sum of last 24 observations + Sum of first 24 observations = 696 + 840= 1536

Now 1536 - 1410 = 126

24th observation is 126.

LOGIC!

24th observation was calculated twice( once in last 24 and once in first 24) and once in 47 observations.

48 observations - 47 observations = the one observation that is counted twice (the 24th observation.