To calculate the coefficient of skewness for a frequency distribution, we use the following formula:

$\text{Coefficient of Skewness (CS)} = \frac{\text{Q3} + \text{Q1} - 2\text{M}}{\text{Q3} - \text{Q1}}$

Where:

• $\text{Q3}$ = Third quartile
• $\text{Q1}$ = First quartile
• $\text{M}$ = Median

Step 1: Determine $\text{Q3}$ and $\text{Q1}$

From the problem: $M - Q3 = 10.2 \implies Q3 = M - 10.2$ $M - Q1 = 4.8 \implies Q1 = M - 4.8$

Step 2: Substitute $\text{Q3}$ and $\text{Q1}$ into the formula

Using the formula for the coefficient of skewness: $\text{CS} = \frac{(M - 10.2) + (M - 4.8) - 2M}{(M - 10.2) - (M - 4.8)}$

Simplify the numerator: $\text{Numerator} = (M - 10.2) + (M - 4.8) - 2M = 2M - 15 - 2M = -15$

Simplify the denominator: $\text{Denominator} = (M - 10.2) - (M - 4.8) = -10.2 + 4.8 = -5.4$

Step 3: Calculate $\text{CS}$

$\text{CS} = \frac{-15}{-5.4} = 2.78$

Final Answer:

The coefficient of skewness is: $\boxed{2.78}$

Do you want a detailed breakdown of any part or have further questions? 😊

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Here are 5 related questions for further exploration:

1. What does the coefficient of skewness tell us about a dataset's shape?
2. How is skewness related to mean, median, and mode?
3. Can you calculate skewness using the Pearson's coefficient method?
4. What are the implications of positive vs. negative skewness?
5. How do quartiles differ in grouped vs. ungrouped frequency distributions?

Tip: Skewness helps identify whether data leans more towards the right (positive skew) or left (negative skew), aiding in better data interpretation.