A lecturer asked students in his class to estimate their body weight (kg). The following data were obtained:
Students: 92: 115: 52: 90: 65: 80: 85

Students 75: 97: 87: 63: 87: 85: 97: 85: 95

a. Calculate the mean and median of each!

b. Calculate the variance, standard deviation, and CC!

Let's break down the problem and solve it step by step.

### Given dataLet's break down the problem and solve it step by step.

### Given 
The body weights (in kg) of the students are:
- First group: 92, 115, 52, 90, 65, 80, 85
- Second group: 75, 97, 87, 63, 87, 85, 97, 85, 95

#### (a) **Mean and Median of Each Group**

**Group 1:** 92, 115, 52, 90, 65, 80, 85  
**Group 2:** 75, 97, 87, 63, 87, 85, 97, 85, 95

### Mean Formula:

\[
\text{Mean} = \frac{\sum x_i}{n}
\]

Where \( \sum x_i \) is the sum of all the values, and \( n \) is the number of values.

### Median Formula:
For an odd number of data points, the median is the middle value when sorted. For an even number, the median is the average of the two middle values.

#### (b) **Variance, Standard Deviation, and Coefficient of Variation**

### Variance Formula:

\[
\text{Variance} = \frac{\sum (x_i - \text{mean})^2}{n}
\]

### Standard Deviation (SD) Formula:

\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]

### Coefficient of Variation (CC or CV):

\[
\text{Coefficient of Variation} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100
\]

I'll now calculate these values.### Results:

#### **Group 1:** 92, 115, 52, 90, 65, 80, 85
- **Mean**: 82.71 kg
- **Median**: 85.0 kg
- **Variance**: 350.20 kg²
- **Standard Deviation**: 18.71 kg
- **Coefficient of Variation (CV)**: 22.62%

#### **Group 2:** 75, 97, 87, 63, 87, 85, 97, 85, 95
- **Mean**: 85.67 kg
- **Median**: 87.0 kg
- **Variance**: 108.44 kg²
- **Standard Deviation**: 10.41 kg
- **Coefficient of Variation (CV)**: 12.16%

Would you like more details or have any further questions?

### Related Questions:
1. How does variance affect the spread of data in each group?
2. Why is the standard deviation higher in Group 1 compared to Group 2?
3. How does the Coefficient of Variation help compare variability between groups?
4. What can the difference in means tell us about the groups?
5. How does skewness affect the median and mean in these datasets?

**Tip:** The coefficient of variation (CV) is useful for comparing the degree of variation between datasets with different means.

A lecturer asked students in his class to estimate their body weight (kg). The following data were obtained: Students: 92, 115, 52, 90, 65, 80, 85; Students 75, 97, 87, 63, 87, 85, 97, 85, 95. a. Calculate the mean and median of each! b. Calculate the variance, standard deviation, and CC!

Solve a problem involving two groups of students' body weights to calculate mean, median, variance, standard deviation, and coefficient of variation (CV). This step-by-step solution covers essential concepts in descriptive statistics, suitable for high school students (Grades 9-12).

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