Question

. If arithmetic mean is 15 and median is 17 then what will be the value of mode.


Obtain Median. X 10 20 30 40 Frequency 2 4 10 4
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Answer 1

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Answer 2

SOLUTION

TO DETERMINE

• Arithmetic mean is 15 and median is 17 then what will be the value of mode.

• mean is 15 and median is 17 then what will be the value of mode.Obtain Median.

X 10 20 30 40 Frequency 2 4 10 4

X 10 20 30 40 Frequency 2 4 10 4

EVALUATION

CALCULATION OF MODE

For moderately asymmetrical distribution there is an approximate relation between them and it is given by

Mean - Mode = 3 ( Mean - Median)

That is,

$\sf{}Mode + 2 × Mean = 3 × Median$

$\implies\sf{}Mode= 3 × Median - 2 × Mean$

$\implies\sf{}Mode= 3 ×17 - 2 × 15$

$\implies\sf{}Mode= 51 - 30$

$\implies\sf{}Mode= 21$

Hence Mode is 21

CALCULATION FOR MEDIAN

$\sf{ x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: f \: \: \: \: \: \: \: \: \: \: \: \: \:cumulative \: frequny\:( < ) \: }$

$\sf{ 10 \: \: \: \: \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2\: }$

$\sf{ 20 \: \: \: \: \: \: \: \: \: \: \: \: 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6 \: \: \: }$

$\sf{ 30 \: \: \: \: \: \: \: \: \: \: \: 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 16}$

$\sf{ 40 \: \: \: \: \: \: \: \: \: \: \: \: 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 20}$

Here total values of sample values

= N = 20 which is even

So there are two middle terms 10 th term and 11 th term

So

$\sf{ \: Median = }$

$\displaystyle \sf{ = \frac{X_{10} +X_{11} }{2} }$

$\displaystyle \sf{ = \frac{30 + 30 }{2} }$

$= \sf {30}$

Hence Median = 30

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