**Frequency Distribution Coefficient of Skewness**

The frequency distribution coefficient of skewness is a measure of the asymmetry or skewness of a frequency distribution. It indicates the degree to which the data is skewed to the left or right.

To calculate the frequency distribution coefficient of skewness, we need to know the mean, mode, and standard deviation of the data.

**Given Information:**
- Frequency distribution coefficient of skewness = 0.6
- Mean = 172
- Mode = 163

**Finding the Variance:**

To find the variance, we need to know the standard deviation. However, we can first calculate the coefficient of skewness using the formula:

Coefficient of Skewness = (Mean - Mode) / Standard Deviation

Given that the coefficient of skewness is 0.6, we can rearrange the formula to solve for the standard deviation:

Standard Deviation = (Mean - Mode) / Coefficient of Skewness

Substituting the given values:

Standard Deviation = (172 - 163) / 0.6 = 9 / 0.6 = 15

Now that we have the standard deviation, we can calculate the variance using the formula:

Variance = Standard Deviation^2

Variance = 15^2 = 225

Therefore, the value of the variance is 225.

**Explanation:**

The frequency distribution coefficient of skewness measures the asymmetry of the data distribution. A positive coefficient indicates a right-skewed distribution, meaning the data is concentrated towards the left side and has a longer tail on the right. A negative coefficient indicates a left-skewed distribution, where the data is concentrated towards the right side and has a longer tail on the left.

In this case, the coefficient of skewness is positive (0.6), which means the data is right-skewed. The mean (172) is greater than the mode (163), indicating that the distribution is skewed towards the right. The variance measures the spread of the data around the mean. A higher variance indicates more dispersion of the data points.

By calculating the standard deviation using the coefficient of skewness, mean, and mode, we find that the standard deviation is 15. Using the standard deviation, we can calculate the variance by squaring it. Therefore, the variance is 225.

The variance provides insight into the spread and variability of the data. In this case, a variance of 225 indicates that the data points are spread out from the mean by an average distance of 15 units.