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The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, then the 13th observation is:

Solution

✅ Correct Option: 2

Overall mean = 3636

Total sum = 36×25=90036 × 25 = 900

First 13 observations mean = 3232

Sum of first 13 = 32×13=41632 × 13 = 416

Last 13 observations mean = 3939

Sum of last 13 = 39×13=50739 × 13 = 507

The 13th observation is counted in both sets

Let the 13th observation be xx

416+507−x=900416 + 507 - x = 900 (total sum)

923−x=900923 - x = 900

x=23x = 23

Therefore, the 13th observation is 23.

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