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Pertimbangkan dua set data yang mewakili berat peserta (dalam kg) untuk dua programkecergasan yang berbeza. (a)

Kira min, varians dan sisihan piawai bagi Program A dan Program B.

(b)

Ulas mengenai serakan dengan membandingkan pekali variasi untuk kedua-dua data.

To solve the problem, we need to calculate the mean, variance, and standard deviation for both Program A and Program B. Then, we'll compare the spread of the data using the coefficient of variation.

### Given Data:
- **Program A:** 85, 70, 72, 88, 67, 71, 69, 66, 73, 74
- **Program B:** 60, 65, 70, 75, 80, 85, 90, 95, 100, 105

### (a) Calculating the Mean, Variance, and Standard Deviation:

#### Program A:
1. **Mean (\(\mu_A\)):**
\[
\mu_A = \frac{85 + 70 + 72 + 88 + 67 + 71 + 69 + 66 + 73 + 74}{10}
\]

2. **Variance (\(\sigma_A^2\)):**
\[
\sigma_A^2 = \frac{\sum (x_i - \mu_A)^2}{n}
\]
Where \(x_i\) are the individual data points and \(n\) is the number of data points.

3. **Standard Deviation (\(\sigma_A\)):**
\[
\sigma_A = \sqrt{\sigma_A^2}
\]

#### Program B:
1. **Mean (\(\mu_B\)):**
\[
\mu_B = \frac{60 + 65 + 70 + 75 + 80 + 85 + 90 + 95 + 100 + 105}{10}
\]

2. **Variance (\(\sigma_B^2\)):**
\[
\sigma_B^2 = \frac{\sum (x_i - \mu_B)^2}{n}
\]

3. **Standard Deviation (\(\sigma_B\)):**
\[
\sigma_B = \sqrt{\sigma_B^2}
\]

Let's calculate these values.### Results:
#### Program A:
- **Mean (\(\mu_A\))**: 73.5
- **Variance (\(\sigma_A^2\))**: 53.61
- **Standard Deviation (\(\sigma_A\))**: 7.32

#### Program B:
- **Mean (\(\mu_B\))**: 82.5
- **Variance (\(\sigma_B^2\))**: 229.17
- **Standard Deviation (\(\sigma_B\))**: 15.14

### (b) Coefficient of Variation (CV):
The coefficient of variation is calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage.

\[
\text{CV} = \frac{\sigma}{\mu} \times 100
\]

Let's calculate the CV for both programs.### Coefficient of Variation (CV):
- **Program A**: 9.96%
- **Program B**: 18.35%

### Interpretation:
- **Program A** has a lower coefficient of variation (9.96%) compared to **Program B** (18.35%). This indicates that the data for Program A is less dispersed relative to its mean compared to Program B, meaning Program A's participant weights are more consistent and less spread out.

Would you like any further details or analysis?

Here are some related questions:
1. How does the standard deviation influence the overall interpretation of the data?
2. What conclusions can be drawn about the effectiveness of each program based on these statistics?
3. How would the range of the data contribute to the understanding of its spread?
4. Can the median provide additional insights that the mean and standard deviation do not?
5. What are potential outliers in these data sets, and how could they affect the variance?

**Tip:** The coefficient of variation is particularly useful when comparing the relative variability between different datasets, especially when the means are significantly different.

Learn how to calculate the mean, variance, and standard deviation for two different fitness programs. Compare the spread of participant weights using the coefficient of variation. Understand the implications of these statistics in evaluating program effectiveness.

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