find the mean, median, mode, range, mid range, standard deviation, variance and the coefficient of variation.
Number of cups of coffee drunk per day of the sample smokers:
6  3  2  4  7  8  6  9  3  5

Let's calculate the following statistical measures for the given data set:

The number of cups of coffee drunk per day of the sample smokers:  
6, 3, 2, 4, 7, 8, 6, 9, 3, 5

### 1. **Mean**:
The mean is calculated as the sum of all values divided by the number of values.

\[
\text{Mean} = \frac{6 + 3 + 2 + 4 + 7 + 8 + 6 + 9 + 3 + 5}{10} = \frac{53}{10} = 5.3
\]

### 2. **Median**:
The median is the middle value when the numbers are arranged in order.

Arranged dataLet's calculate the following statistical measures for the given data set:

The number of cups of coffee drunk per day of the sample smokers:  
6, 3, 2, 4, 7, 8, 6, 9, 3, 5

### 1. **Mean**:
The mean is calculated as the sum of all values divided by the number of values.

\[
\text{Mean} = \frac{6 + 3 + 2 + 4 + 7 + 8 + 6 + 9 + 3 + 5}{10} = \frac{53}{10} = 5.3
\]

### 2. **Median**:
The median is the middle value when the numbers are arranged in order.

Arranged  2, 3, 3, 4, 5, 6, 6, 7, 8, 9

There are 10 values, so the median is the average of the 5th and 6th values:

\[
\text{Median} = \frac{5 + 6}{2} = 5.5
\]

### 3. **Mode**:
The mode is the most frequent value.

The most frequent value is 6, which appears twice.

\[
\text{Mode} = 6
\]

### 4. **Range**:
The range is the difference between the maximum and minimum values.

\[
\text{Range} = 9 - 2 = 7
\]

### 5. **Mid-Range**:
The mid-range is the average of the maximum and minimum values.

\[
\text{Mid-Range} = \frac{9 + 2}{2} = \frac{11}{2} = 5.5
\]

### 6. **Standard Deviation**:
Standard deviation measures the spread of the data around the mean. First, we calculate the variance, then take the square root for the standard deviation.

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

Let’s compute:

\[
\text{Variance} = \frac{(6-5.3)^2 + (3-5.3)^2 + (2-5.3)^2 + (4-5.3)^2 + (7-5.3)^2 + (8-5.3)^2 + (6-5.3)^2 + (9-5.3)^2 + (3-5.3)^2 + (5-5.3)^2}{10}
\]

\[
= \frac{(0.7)^2 + (-2.3)^2 + (-3.3)^2 + (-1.3)^2 + (1.7)^2 + (2.7)^2 + (0.7)^2 + (3.7)^2 + (-2.3)^2 + (-0.3)^2}{10}
\]

\[
= \frac{0.49 + 5.29 + 10.89 + 1.69 + 2.89 + 7.29 + 0.49 + 13.69 + 5.29 + 0.09}{10} = \frac{47.1}{10} = 4.71
\]

Now, the standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{4.71} \approx 2.17
\]

### 7. **Variance**:
The variance is already computed as:

\[
\text{Variance} = 4.71
\]

### 8. **Coefficient of Variation**:
The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean, expressed as a percentage:

\[
\text{CV} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 = \left( \frac{2.17}{5.3} \right) \times 100 \approx 40.94\%
\]

---

Here’s a summary of the statistical measures:

- **Mean**: 5.3
- **Median**: 5.5
- **Mode**: 6
- **Range**: 7
- **Mid-Range**: 5.5
- **Standard Deviation**: 2.17
- **Variance**: 4.71
- **Coefficient of Variation**: 40.94%

Would you like any further details on these calculations?

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Here are five related questions:
1. How would the mean change if the highest value was removed from the data set?
2. How is the median affected by skewed data?
3. What is the significance of a high coefficient of variation in a data set?
4. How would you interpret the standard deviation in terms of data spread?
5. What are some applications of variance in real-world scenarios?

**Tip**: The coefficient of variation helps compare the relative variability of data sets with different units or means.

Find the mean, median, mode, range, mid-range, standard deviation, variance, and the coefficient of variation. Number of cups of coffee drunk per day of the sample smokers: 6, 3, 2, 4, 7, 8, 6, 9, 3, 5.

Explore the calculation of mean, median, mode, range, mid-range, variance, standard deviation, and coefficient of variation for the number of cups of coffee drunk by sample smokers. This problem uses basic descriptive statistics and is suitable for students in Grades 9-12.

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