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The mode and median of a data is 87.5 and 86, respectively. What is the mean of the data? (Use empirical formula.)
85.2
85.4
84.2
87.1
85.2
Use the relationship 3MeтИТMo=2x. Calculate 3├Ч86=258, then 258тИТ87.5=170.5. Dividing by 2 gives 85.25, which is closest to Option A.
Mode (Mo) = 87.5, Median (Me) = 86
Mo=3MeтИТ2x
Use the relationship 3MeтИТMo=2x. Calculate 3├Ч86=258, then 258тИТ87.5=170.5. Dividing by 2 gives 85.25, which is closest to Option A.
Many students confuse the empirical formula, incorrectly writing Mo=2MeтИТ3x instead of Mo=3MeтИТ2x.
Identify Empirical Relation
The relationship between mean, median, and mode for a moderately skewed distribution is given by the Pearson empirical formula.
Mo=3MeтИТ2x
Substitute Given Values
Substitute the given values of mode (Mo=87.5) and median (Me=86) into the equation to solve for the mean (x).
87.5=3(86)тИТ2x
Solve for Mean
Calculate 3├Ч86=258, then isolate 2x by rearranging: 2x=258тИТ87.5=170.5. Dividing by 2 yields x=85.25.
x=2170.5тАЛ=85.25
A is correct because the calculated value 85.25 aligns with the nearest provided option 85.2.
This empirical formula is a standard in statistics and often appears in questions involving data distribution characteristics. Remember the mnemonic 'Mode = 3 Median - 2 Mean' as M-M-M.
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