Question

The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.

Answer 1

Answer:

The median of the data is 20.

Step-by-step explanation:

Given information: Mean = 24, Mode = 12.

The relation among mead, median, mode is

Divide both sides by 3.

Therefore the median of the data is 20.

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

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$\tt given\begin{cases} \sf{Mean = 24} \\ \sf{Mode = 12} \end{cases}$

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$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the median.

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$\Large{\underline{\underline{\bf{Explanation :}}}}$

We know that,

$\Large{\star{\boxed{\rm{Mode = 3 \: Median - 2 \: Mean}}}}$

$\tt{3 \: Median = Mode + 2 \: Mean} \\ \\ \tt{→Median = \dfrac{Mode + 2 \: Mean}{3}} \\ \\ \sf{→Median = \dfrac{12 + 2(24)}{3}} \\ \\ \sf{→Median = \dfrac{12 + 48}{3}} \\ \\ \sf{→Median = \dfrac{\cancel{60}}{\cancel{3}}} \\ \\ \sf{→Median = 20 } \\ \\ \sf{\therefore \: Median \: is \: 20}$