Question

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, find the 13th observation. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Mean of the first 13 observations = 32

Sum of the first 13 observations $=(32\times 13)=416$

Mean of the last 13 observations = 39

Sum of the last 13 observations $=(39\times 13)=507$

Mean of 25 observations = 36

Sum of all the 25 observations $=(36\times 25)=900$

$\therefore$ the 13th observation = (416 + 507 - 900) = 23

Hence, the 13th observation is 23.