Marks of $12$ students in a unit test are given as $4, 21, 13, 17, 5, 9, 10, 20, 19, 12, 20, 14$ . Assume a mean and calculate the arithmetic mean of the data. Assume another number as mean and calculate the arithmetic mean again. Do you get the same result? Comment

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Solution

Let assumed mean be $13$
$∴$ Arithmetic mean $= 13 + ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{\begin{matrix} (4 - 13) + (21 - 13) + (13 - 13) + (17 - 13) + (5 - 13) + (9 - 13) + (10 - 13) + (20 - 13) + (19 - 13) + (12 - 13) + (20 - 13) + (14 - 13) \end{matrix}}{12} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$

$= 13 + \frac{8}{12}$
$= 13 + 0.67$
$= 13.67$

Now let assumed mean be $14$
$∴$ Arithmetic mean $= 14 + ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{\begin{matrix} (4 - 14) + (21 - 14) + (13 - 14) + (17 - 14) + (5 - 14) + (9 - 14) + (10 - 14) + (20 - 14) + (19 - 14) + (12 - 14) + (20 - 14) + (14 - 14) \end{matrix}}{14} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$

$= 14 + [\frac{- 4}{12}] = 13.67$

Yes, $9$ got the same result.

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