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.)

2.6

11.26

5.9

3.15

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2025 • 06 Jun, 2025 • Shift-2

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.)

Correct Answer

3.15

Statistical Relationship: For a moderately skewed mathematical distribution, the exact relationship between the three core measures of central tendency is firml......

💡 Analysis & Explanation

Statistical Relationship ▼

For a moderately skewed mathematical distribution, the exact relationship between the three core measures of central tendency is firmly established by Karl Pearson's empirical formula: Mode = 3(Median) - 2(Mean).

Value Substitution ▼

Systematically plugging the provided known metrics into the formula gives the equation: 89.7 = 3 × (32) - 2 × (Mean). Multiplying out the median gives 89.7 = 96 - 2 × (Mean).

Algebraic Solution ▼

Rearranging the terms to isolate the unknown variable yields 2 × (Mean) = 96 - 89.7, which precisely calculates to 6.3. Finally, dividing by 2 isolates the Mean: 6.3 / 2 = 3.15.

Conclusion ▼

The statistical mean meticulously evaluates to 3.15.

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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.)