find the mean, median, mode, range, mid range, standard deviation, variance and the coefficient of variation. Scores  in a Trigonometry examination:
Class limits
f

35 - 45
2

46 - 56
3

57 - 67
4

68 - 78
8

79 - 89
5

90-100
2

To solve this, I will first organize the data into a frequency distribution table and calculate the required measures step by step. Here’s how we can proceed:

### Step 1: Organize the Data
You have the following class limits and their corresponding frequencies:

| Class Limits | Frequency (f) |
|--------------|----------------|
| 35 - 45      | 2              |
| 46 - 56      | 3              |
| 57 - 67      | 4              |
| 68 - 78      | 8              |
| 79 - 89      | 5              |
| 90 - 100     | 2              |

### Step 2: Calculate the Class Midpoints (x)
We calculate the midpoints of each class as:

\[
\text{Class Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
\]

\[
\begin{array}{|c|c|}
\hline
\text{Class Limits} & \text{Midpoint (x)} \\
\hline
35 - 45 & \frac{35 + 45}{2} = 40 \\
46 - 56 & \frac{46 + 56}{2} = 51 \\
57 - 67 & \frac{57 + 67}{2} = 62 \\
68 - 78 & \frac{68 + 78}{2} = 73 \\
79 - 89 & \frac{79 + 89}{2} = 84 \\
90 - 100 & \frac{90 + 100}{2} = 95 \\
\hline
\end{array}
\]

### Step 3: Calculate Mean (\(\mu\))
The mean is calculated as:

\[
\mu = \frac{\sum (f \times x)}{\sum f}
\]

Where:
- \( f \) is the frequency
- \( x \) is the midpoint of each class
- \( \sum f \) is the total frequency

Let me calculate the mean.It seems like I can’t do more advanced data analysis right now. Please try again later. Would you like me to guide you through the calculations step-by-step manually?

If so, here are 5 follow-up questions you might want to consider:
1. Do you need help calculating any other statistical measures like skewness or kurtosis?
2. Should I show how to calculate the variance and standard deviation manually?
3. Would you like to explore how these statistics might be interpreted in terms of student performance?
4. Are you interested in visualizing this data through graphs or charts?
5. Would you like more practice problems involving grouped data like this?

**Tip:** When calculating variance, remember that it measures how spread out the data is around the mean!

Find the mean, median, mode, range, mid range, standard deviation, variance, and the coefficient of variation. Scores in a Trigonometry examination: 
Class limits and frequency: 
35-45 (2), 46-56 (3), 57-67 (4), 68-78 (8), 79-89 (5), 90-100 (2).

Learn how to calculate the mean, median, mode, range, mid range, standard deviation, variance, and coefficient of variation for a set of scores from a trigonometry examination. This solution explores key concepts in descriptive statistics for grouped data, suitable for Grades 11-12.

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