The histogram of a frequency distribution of an end-point convention is given below,
14
12
10
8
6
4
2
(a) What are the class boundaries? Use end-point convention.
(b) What's the width of the classes?
(c) Calculate the Mean and Standard deviation using the frequency distribution table.

In order to answer these questions, I need more specific data from the frequency distribution (e.g., the class intervals and corresponding frequencies). Since you mentioned a histogram, I'll assume there are class intervals along the horizontal axis, with frequencies on the vertical axis.

Let's break this down step-by-step based on what we can infer:

### (a) **Class Boundaries (using End-Point Convention)**:
Class boundaries are the actual limits of the class intervals. If you are using an end-point convention (where class intervals are inclusive of the end-points), the lower class boundary of the first class is the smallest value in the distribution, and the upper class boundary of the last class is the largest value.

Without exact class intervals, I can’t calculate the boundaries precisely, but here’s a general guide:
- If your class intervals are given as something like 10-20, 21-30, etc., the class boundaries would adjust to remove gaps, so they'd become:
  - **Lower Bound**: The starting value of the class (e.g., 9.5 for 10-20).
  - **Upper Bound**: The upper value of the class plus a small amount (e.g., 20.5 for 10-20).
  
### (b) **Class Width**:
The class width is the difference between the upper and lower boundaries of any given class. 
- Class width formula:
  \[
  \text{Class Width} = \text{Upper class boundary} - \text{Lower class boundary}
  \]

For example, if a class interval is 10-20, then:
\[
\text{Class Width} = 20.5 - 9.5 = 11
\]
You can calculate this once the specific class intervals are known.

### (c) **Mean and Standard Deviation**:
To calculate these, we need to create a **frequency distribution table** with midpoints of each class and their frequencies. Let’s assume you have the data from your histogram (such as class intervals and frequencies). Here's how you'd compute:

1. **Calculate the Mean**:
   \[
   \text{Mean} (\mu) = \frac{\sum (f \cdot x)}{\sum f}
   \]
   where:
   - \( f \) = frequency of the class
   - \( x \) = midpoint of the class
   - \( \sum f \) = sum of frequencies

2. **Calculate the Standard Deviation**:
   \[
   \text{Standard Deviation} (\sigma) = \sqrt{\frac{\sum f(x - \mu)^2}{\sum f}}
   \]
   where:
   - \( \mu \) is the mean (from step 1)
   - \( x \) is the class midpoint
   - \( f \) is the class frequency

### Next Steps:
Please provide the specific class intervals and frequencies from the histogram, and I can calculate the class boundaries, mean, and standard deviation for you.

---

Would you like more details on any of these steps, or do you have any questions?

### Follow-Up Questions:
1. What is the exact set of class intervals and frequencies in your histogram?
2. Are there any gaps between your class intervals?
3. Do you want me to guide you through calculating midpoints and setting up a frequency distribution table?
4. Are you familiar with how to adjust for class boundaries in cases where intervals are given?
5. Do you need a visual guide to understand the computation of standard deviation?

### Tip:
When calculating the mean and standard deviation from grouped data, always start by finding the midpoints of the class intervals as they serve as representatives of all the data within each class.

The histogram of a frequency distribution of an end-point convention is given below, 14 12 10 8 6 4 2 (a) What are the class boundaries? Use end-point convention. (b) What's the width of the classes? (c) Calculate the Mean and Standard deviation using the frequency distribution table.

Explore how to determine class boundaries using the end-point convention, calculate class width, and find the mean and standard deviation from a frequency distribution table. This problem involves essential statistical concepts suitable for students in Grades 10-12.

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