Question

in a statistical data the difference between mode and mean is k times the difference between median and mean then the value of k is

Answer 1

The value of k is 3.

Step-by-step explanation:

Consider the provided information.

Let x is the difference between median and mean.

The difference between mode and mean is k times the difference between median and mean

Therefore, Difference between mode and mean is kx

Mode − mean = kx ......(1)

As we know:

Mode = 3 Median − 2 Mean

Mode − Mean = 3 Median − 2 Mean − Mean

Mode − Mean =  3 Median − 3 Mean

Mode − mean =  3(median − mean)

From 1 we get:

kx = 3x

k = 3

Hence, the value of k is 3.

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Answer 2

Answer:

k is 3

Step-by-step explanation:

First A.T.Q ,

mode - mean = kx

lets, assume median - mean as x.

using the emperical formula,

mode = 3median - 2mean

mode - mean = 3median - 2mean - mean

mode - mean = 3(median - mean) .......... (3 is taken as a common coefficient)

so substituting the values in the above equation,

kx = 3(x)

kx = 3x

therefore,

k = 3.