The mode and median of a data set is 89.7 and 32, respectively. What is the mean of the data set? (Use empirical formula.)

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)

Answer 1

Given:

Mode = 89.7

Median = 32

Formula used:

Empirical formula (relationship between Mean, Median, and Mode):

Mode \(\approx\) 3 Median - 2 Mean

Calculations:

Rearrange the empirical formula to find the Mean:

2 Mean \(\approx\) 3 Median - Mode

Mean \(\approx \frac{(3 \times Median) - Mode}{2}\)

Substitute the given values:

Mean \(\approx \frac{(3 \times 32) - 89.7}{2} \)

⇒ Mean \(\approx \frac{96 - 89.7}{2}\)

⇒ Mean \(\approx \frac{6.3}{2}\)

⇒ Mean \(\approx 3.15\)

∴ The mean of the data set is approximately 3.15.