Question

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

• A. \(34\)
• B. \(43\)
• C. \(38.5\)
• D. \(41.5\)

Hint:

A simple mnemonic to remember this is "3 Medians minus 2 Means equals 1 Mode". Note the alphabetical order: Median comes before Mean if you reverse the order of subtrahends.

Answer 1

The Correct Option is A

To find the mode of the frequency distribution, we can use the empirical relationship between the Mean, Median, and Mode. This relationship is given by Karl Pearson's formula:

\(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\)

Given:

• Mean = 43
• Median = 40

Substituting the given values into the formula, we compute:

\(\text{Mode} = 3 \times 40 - 2 \times 43\)

Calculate each term separately:

• \(3 \times 40 = 120\)
• \(2 \times 43 = 86\)

Now, substitute these results back into the equation:

\(\text{Mode} = 120 - 86 = 34\)

Thus, the value of the mode is \(34\).

Therefore, the correct answer is 34.