Question

# If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately.

- 22.0
- 20.5
- 25.5
- 24.0

Hint:

### A frequency distribution table is a thorough representation of the arrangement of the raw data for a quantitative variable in statistics. This table displays the frequency distributions of different values of a variable. Here we have given the mean and median are 21 and 22 respectively, we have to find the mode.

## The correct answer is: 24.0

### A frequency distribution table is a thorough representation of the arrangement of the raw data for a quantitative variable in statistics. This table displays the frequency distributions of different values of a variable. It is possible to create two frequency distribution tables, though:

- Irregular frequency distribution
- Constant frequency distribution (ii) (Grouped frequency distribution)

The sum of all observations divided by the total number of observations yields the arithmetic mean of a set of data.

The median of the data is the value of the middle observation after the data have been arranged in either ascending or descending order.

A data mode is a value that appears the most frequently in the provided data or the observation with the highest frequency.

We have given:

mean = 21

median = 22

Using the Empirical relation, we have:

Mode = 3 Median - 2 Mean

Mode = 3(22) - 2(21)

Mode = 66-42

Mode = 24

So here we used the concept of frequency distribution to solve the question. We also understood what is mean, mode and the median. An empirically established link exists between the mean, median, and mode in statistics. So the mode is 24.

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