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

To find the median when the mode and mean of a series are given, we can use the following empirical relationship between the mean, median, and mode:

\(3 \times \text{Median} = \text{Mode} + 2 \times \text{Mean}\)

1. Given:
   • Mode = 20
   • Mean = 26
2. Substitute these values into the formula:

\(3 \times \text{Median} = 20 + 2 \times 26\)

1. Simplify the equation:
   • \(3 \times \text{Median} = 20 + 52\)
   • \(3 \times \text{Median} = 72\)
2. Now, solve for the median:

\(\text{Median} = \frac{72}{3} = 24\)

Thus, the value of the median is 24, which corresponds to the correct option.