Question

If the difference between mean and mode of a data is 10.5,
then the difference between its median and mean is (where
mode, median > mean)​

Answer 1

Step-by-step explanation:

3 Median= 2 Mean + Mode (Empirical relation)

That is Mode= 3 Median- 2 Mean

= (3× 9.6) - (2×10.5) since given Mean= 10.5 and Median = 9.6

= 7.8

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Answer 2

Answer: 3.5

Step-by-step explanation:

Since mode is greater than mean,

mode - mean = 10.5

or, mode = 10.5+ mean------1

Emperical formula is:

3Median= 2Mean + Mode

Use value of mode as found in equation 1, we get:

3Median = 2Mean + 10.5 + Mean

or, 3Median = 3Mean + 10.5

or, 3Median - 3Mean = 10.5

or, 3(Median - Mean) = 10.5

Therefore Median- Mean=10.5/3 = 3.5 Answer

Hope it helps.