Question

If the mode of some observations is 20 and mean is 26. The value of their median will be :

• A. 26
• B. 24
• C. 20
• D. 30

Hint:

A simple way to remember the formula is that the alphabetical order of the coefficients (3 and 2) matches the word length: {3} Median (6 letters) - {2} Mean (4 letters).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The relationship between the three measures of central tendency (Mean, Median, and Mode) is expressed by the empirical formula: $\text{Mode} = 3(\text{Median}) - 2(\text{Mean})$.
Step 2: Identifying Given Values:

Mode = 20
Mean = 26
Step 3: Calculation:
Substitute the values into the formula:
$$20 = 3(\text{Median}) - 2(26)$$
$$20 = 3(\text{Median}) - 52$$
Add 52 to both sides:
$$20 + 52 = 3(\text{Median})$$
$$72 = 3(\text{Median})$$
$$\text{Median} = \frac{72}{3} = 24$$
Step 4: Final Answer:
The value of the median is 24.