https://file.aiquickdraw.com/mathbot/file/1725854805224y9wf3l2n.jpg

The image appears to show a table with age intervals and corresponding frequencies, along with some questions related to class limits, midpoints, and the total number of individuals included in the summary.

Let's break it down and solve the problems based on the information I can see:

### Age Intervals and Frequencies:
- **5-9**: 31
- **10-14**: 32
- **15-19**: 19
- **20-24**: 13
- **25-29**: 3
- **30-34**: 1
- **35-39**: 1

### 1. Identify the class midpoints:
To find the midpoint for each class interval, we use the formula:

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

- **5-9**: \( \frac{5 + 9}{2} = 7 \)
- **10-14**: \( \frac{10 + 14}{2} = 12 \)
- **15-19**: \( \frac{15 + 19}{2} = 17 \)
- **20-24**: \( \frac{20 + 24}{2} = 22 \)
- **25-29**: \( \frac{25 + 29}{2} = 27 \)
- **30-34**: \( \frac{30 + 34}{2} = 32 \)
- **35-39**: \( \frac{35 + 39}{2} = 37 \)

So the class midpoints are:
\[ 7, 12, 17, 22, 27, 32, 37 \]

### 2. Identify the number of individuals in the summary:
To find the total number of individuals, sum the frequencies:

\[
31 + 32 + 19 + 13 + 3 + 1 + 1 = 100
\]

Thus, the total number of individuals is **100**.

### 3. Other class-related values:
- **Lower Class Limits**: The lower limit is the first value in each class: \(5, 10, 15, 20, 25, 30, 35\)
- **Upper Class Limits**: The upper limit is the last value in each class: \(9, 14, 19, 24, 29, 34, 39\)
- **Class Width**: This is the difference between the lower limits of two consecutive classes. For example, \(10 - 5 = 5\). Hence, the class width is **5**.

Would you like more details on any of these points?

### 5 Related Questions:
1. How do we calculate the class boundaries for these intervals?
2. How would we calculate the cumulative frequency for the given data?
3. What would be the relative frequency for each age group?
4. How would this data look represented in a histogram?
5. Can we calculate the mean age from this frequency distribution?

### Tip:
The midpoint of a class is crucial when estimating the mean from grouped data, as it represents the "center" of the interval.

Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also, identify the number of individuals included in the summary.

Learn how to analyze a frequency distribution by identifying class limits, midpoints, and boundaries. Calculate the class width and determine the total number of individuals using key statistical formulas. Suitable for high school students studying data analysis.

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