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When two values of data are changed, the mode of the data changes from 31 to 45. What will be the new mean of the data if the mean with unchanged values was 52 and the median remains the same?

When two values of data are changed, the mode of the data changes from 31 to 45. What will be the new mean of the data if the mean with unchanged values was 52 and the median remains the same? Correct Answer 45

Given:

Original mode = 31

New mode = 45

Original mean = 52

Formula used:

Mode = 3 × Median - 2 × Mean

Calculations:

Let the original median be M and the new mean be Mn

⇒ 31 = 3M - 2 × 52

⇒ 3M = 31 + 104

⇒ 3M = 135

⇒ M = 45

When two values are changed, the median remains the same

⇒ 45 = 3 × 45 - 2 × Mn

⇒ 2Mn = 45 × (3 - 1)

⇒ 2Mn = 45 × 2

⇒ Mn = 45

∴ The new mean is 45

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