Calculation of Variance

To calculate the variance, we need to use the formula:

Variance = (sum of squared deviations from the mean) / (number of observations - 1)

Coefficient of Skewness

The coefficient of skewness is a measure of the asymmetry of a frequency distribution. A positive coefficient of skewness indicates that the distribution is skewed to the right (i.e., has a long tail on the right side of the distribution), while a negative coefficient of skewness indicates that the distribution is skewed to the left (i.e., has a long tail on the left side of the distribution). A coefficient of skewness of 0 indicates that the distribution is perfectly symmetrical.

In this case, the coefficient of skewness is 0.6, which indicates that the distribution is moderately skewed to the right.

Mean and Mode

The mean of the distribution is 172, which is the average of all the observations in the distribution.

The mode of the distribution is 163, which is the value that occurs most frequently in the distribution.

Using the Formula

To calculate the variance, we need to first calculate the deviations from the mean for each observation in the distribution. We can do this by subtracting the mean from each observation:

Observation 1: 163 - 172 = -9
Observation 2: (next observation)
…
Observation n: (last observation)

Next, we need to square each deviation:

Observation 1: (-9)^2 = 81
Observation 2: (next observation)^2
…
Observation n: (last observation)^2

We then sum the squared deviations:

81 + (next squared deviation) + … + (last squared deviation)

Finally, we divide the sum of squared deviations by the number of observations minus 1:

(sum of squared deviations) / (number of observations - 1)

This gives us the variance of the distribution.

Conclusion

Without knowing the number of observations in the distribution, we cannot calculate the variance exactly. However, we can use the given information to understand how the variance might be calculated and how the measures of skewness, mean, and mode are related to the variance.

169