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The mean of $6$ observation is $17.5$ . If five of them are $14$ , $9$ , $23$ , $25$ and $10$ , find the Sixth observation.

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Calculate quartiles and interquartile range

Full solution

Q. The mean of

6

observation is

17.5

. If five of them are

14

,

9

,

23

,

25

and

10

, find the Sixth observation.

Calculate Total Sum: Calculate the total sum of all six observations using the mean. $\newline$ The mean of the observations is given as $17.5$ . Therefore, the total sum of all observations = mean $\times$ number of observations = $17.5 \times 6 = 105$ .
Calculate Sum of Known: Calculate the sum of the five known observations. $\newline$ Sum of the known observations = $14 + 9 + 23 + 25 + 10 = 81$ .
Find Sixth Observation: Find the sixth observation by subtracting the sum of the known observations from the total sum. $\newline$ Sixth observation = Total sum - Sum of known observations = $105 - 81 = 24$ .

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