Question

If mean of a frequency distribution is 20.5 and median is 21 then mode will be

• A. 20.5
• B. 21
• C. 21.5
• D. 22

Hint:

Memorize the empirical relationship: Mode = 3 Median - 2 Mean. A simple way to remember it is to note that the median is "in the middle" of the mode and mean in the formula, and it has the largest coefficient (3).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
There is an empirical relationship that connects the three measures of central tendency: mean, median, and mode for a moderately skewed distribution. This relationship allows us to estimate one measure if the other two are known.
Step 2: Key Formula or Approach:
The empirical formula relating mean, median, and mode is:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] Step 3: Detailed Explanation:
We are given the following values:
Mean = 20.5
Median = 21
Substitute these values into the empirical formula to find the mode:
\[ \text{Mode} = 3 \times (21) - 2 \times (20.5) \] \[ \text{Mode} = 63 - 41 \] \[ \text{Mode} = 22 \] Step 4: Final Answer:
The mode of the frequency distribution will be 22.