Maths · Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data
Assertion If the value of mode and mean are 60 and 66 respectively, then the val
Assertion If the value of mode and mean are 60 and 66 respectively, then the value of median is 64 Reason Median \( =\frac{1}{2}(\bmod e+2 \text { mean }) \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Assertion is incorrect but Reason is correct
Step-by-step solution
The empirical relation between mean, median, and mode is mode = 3 median - 2 mean. Rearranging gives median = (mode + 2 mean)/3. Substituting mode=60 and mean=66 yields median = (60+132)/3 = 64, so Assertion is correct. The Reason states an incorrect formula (median = 1/2(mode + 2 mean)), so Reason is incorrect. Hence option C.
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