Construct a frequency table using qualitative data given and compute the
mean. The following data taken from sampled survey of the sizes of school
shoes that mostly used by the college male costumers are as follows:
10 12 9 9 8 8 8 7 10 10
11 11 9 10 10 8 9 9 9 7
6 7 7 8 8 10 11 10 8 9

Let's first organize the given data into a frequency table based on the sizes of school shoes:

### Step 1: Organize the Data
The given data consists of the following shoe sizes:
```
10, 12, 9, 9, 8, 8, 8, 7, 10, 10,
11, 11, 9, 10, 10, 8, 9, 9, 9, 7,
6, 7, 7, 8, 8, 10, 11, 10, 8, 9
```

### Step 2: Frequency Table
We will now tally how many times each shoe size appears.

| Shoe Size | Frequency |
|-----------|-----------|
| 6         | 1         |
| 7         | 5         |
| 8         | 8         |
| 9         | 8         |
| 10        | 7         |
| 11        | 3         |
| 12        | 1         |

### Step 3: Compute the Mean

The mean (average) is calculated using the formula:

\[
\text{Mean} = \frac{\sum (\text{Shoe Size} \times \text{Frequency})}{\sum \text{Frequency}}
\]

Now, let's calculate the total frequency and the total value of all the shoe sizes:

- Total frequency = \( 1 + 5 + 8 + 8 + 7 + 3 + 1 = 33 \)

Next, compute the sum of all the values (Shoe Size \(\times\) Frequency):

\[
\text{Sum of Values} = (6 \times 1) + (7 \times 5) + (8 \times 8) + (9 \times 8) + (10 \times 7) + (11 \times 3) + (12 \times 1)
\]

\[
= 6 + 35 + 64 + 72 + 70 + 33 + 12 = 292
\]

Now, compute the mean:

\[
\text{Mean} = \frac{292}{33} \approx 8.85
\]

### Conclusion:
The mean shoe size is approximately **8.85**.

Would you like more details on any part of this calculation or any related concepts?

### Related Questions:
1. How is a frequency table used to find the mode of a data set?
2. What is the difference between the mean and median in qualitative data?
3. How does the mean change if a new value is added to the data set?
4. What is the median for this shoe size data set?
5. How can we use this frequency table to construct a bar chart?

**Tip:** The mean is sensitive to extreme values (outliers), which can affect the overall average.

Construct a frequency table using qualitative data given and compute the mean. The following data taken from sampled survey of the sizes of school shoes that mostly used by the college male costumers are as follows: 10 12 9 9 8 8 8 7 10 10 11 11 9 10 10 8 9 9 9 7 6 7 7 8 8 10 11 10 8 9

Learn how to construct a frequency table and calculate the mean for shoe size data from a college male customer survey. This problem covers descriptive statistics, frequency tables, and mean calculation, making it ideal for students in Grades 6-8. The mean shoe size is approximately 8.85.

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