Introduction
This question focuses on two important areas of statistics: measuring skewness and understanding sampling methods. Skewness helps in understanding the symmetry of a data distribution, while convenience and judgment sampling are non-probability methods used to collect data in specific contexts.
a) Compute Karl Pearson’s Coefficient of Skewness
Given:
- Arithmetic Mean (x̄) = 40.11
- Standard Deviation (σ) = 2.96
- Modal Class = 39–42
Data:
| Class | Frequency |
|---|---|
| 30–33 | 2 |
| 33–36 | 4 |
| 36–39 | 26 |
| 39–42 | 47 |
| 42–45 | 15 |
| 45–48 | 6 |
Step 1: Find Mode (Z)
- Modal Class = 39–42
- f1 (frequency of modal class) = 47
- f0 (frequency of previous class) = 26
- f2 (frequency of next class) = 15
- h (class width) = 3
Mode = L + [(f1 – f0) / (2f1 – f0 – f2)] × h
L = 39
Mode = 39 + [(47 – 26)/(2×47 – 26 – 15)] × 3 = 39 + (21 / 53) × 3 ≈ 39 + 1.188 ≈ 40.19
Step 2: Karl Pearson’s Skewness
Sk = (Mean – Mode) / SD = (40.11 – 40.19) / 2.96 ≈ –0.08 / 2.96 ≈ –0.027
Interpretation: The skewness is –0.027, which is very close to zero, indicating that the data is nearly symmetric.
b) Convenience and Judgement Sampling Methods
1. Convenience Sampling
This method involves collecting data from a population that is easy to access. It is widely used when quick results are needed and formal sampling techniques are not feasible.
Features:
- Low cost and fast
- Non-random selection
- Susceptible to bias
Example: Surveying students in your class because they are easily reachable.
2. Judgement Sampling
Also known as purposive sampling, this method involves selecting samples based on the researcher’s expertise and judgment.
Features:
- Selection based on researcher’s decision
- Useful in qualitative research
- Can yield good results if expert judgment is accurate
Example: A marketing expert selects specific influencers for a campaign based on their brand relevance.
Conclusion
Karl Pearson’s skewness helps understand the symmetry of data. In this case, the distribution is nearly symmetric. Convenience and judgement sampling are easy and cost-effective methods of collecting data but carry a risk of bias, making them suitable mostly for exploratory or preliminary research.