Question

Compute the appropriate coefficient of skewness from the following frequency distribution:

Income group: Below 100, 100-140, 140-180, 180-220, 220-260
No. of workers: 5, 12, 25, 14, 8
a. 0.25
b. 0.5
c. -0.25
d. -0.5

Answer 1

To compute the appropriate coefficient of skewness, first calculate the mean and standard deviation of the given frequency distribution. Then use the following formula to calculate the sample skewness: (n / ((n-1)(n-2))) * (sum of (xi - x)^3 / (n * s^3)), where n is the sample size, xi is each data point, x is the sample mean, and s is the sample standard deviation. The appropriate coefficient of skewness for this frequency distribution is approximately 0.45.

Step-by-step explanation:

To compute the appropriate coefficient of skewness, first calculate the mean and standard deviation of the given frequency distribution.

1. Calculate the midpoints of each income group: 50, 120, 160, 200, and 240.
2. Multiply each midpoint by its corresponding frequency: 250, 1440, 4000, 2800, and 1920.
3. Calculate the sum of these values: 250+1440+4000+2800+1920 = 10,410.
4. Calculate the sample mean: (10,410 / 54) = 192.78.
5. Calculate the sum of squared deviations from the mean: (50-192.78)^2(5)+(120-192.78)^2(12)+(160-192.78)^2(25)+(200-192.78)^2(14)+(240-192.78)^2(8) ≈ 97,245.37.
6. Calculate the sample variance: (97,245.37 / 53) ≈ 1,833.21.
7. Calculate the sample standard deviation: sqrt(1,833.21) ≈ 42.85.
8. Calculate the sample skewness: (54 / (53 * 52)) * (10,410 / 53) * (1,833.21 / 42.85^3) ≈ 0.45.

Therefore, the appropriate coefficient of skewness for this frequency distribution is approximately 0.45. So, the correct answer is b. 0.5.