https://file.aiquickdraw.com/mathbot/file/1726715732982ex7xdtvf.jpg

Let's work through the questions in the image. The table provided shows marks out of 100 for learners in Mathematics at **B school**. 

Here’s how we’ll tackle each question:

### 1.1.1. Determine the mean mark.
We can find the mean by adding all the marks and dividing by the total number of learners.

Marks provided:
\[ 65, 67, 70, 76, 80, 86, 86, 87, 92, 96, 96, 97, 98, 100 \]

There are 14 marks. Let's compute the sum and then the mean.

### 1.1.2. Write down the range of the marks.
The range is the difference between the highest and the lowest marks. So, it will be:
\[ \text{Range} = 100 - 65 \]

### 1.1.3. Determine the semi-interquartile range of the data.
The semi-interquartile range is half the difference between the third quartile \(Q_3\) and the first quartile \(Q_1\):
\[ \text{Semi-Interquartile Range} = \frac{Q_3 - Q_1}{2} \]
We need to find \(Q_1\) (the 25th percentile) and \(Q_3\) (the 75th percentile).

### 1.1.4. Draw a box and whisker plot.
We will create the box and whisker plot using the minimum, \(Q_1\), median, \(Q_3\), and maximum values.

### 1.1.5. Comment on the skewness of the data above.
We can comment on the skewness by comparing the mean, median, and the spread of data in the box plot.

### 1.1.6. Determine the 38th percentile of the data.
The 38th percentile lies between the 25th and 50th percentiles. We will calculate the exact value using interpolation.

### 1.1.7. The percentage of learners who got less than 65 is 75%. How many learners are doing mathematics in grade 10?
Given that 75% corresponds to marks less than 65, we can set up a proportion to calculate the total number of learners.

I'll now begin solving these. Starting with the mean and range.### 1.1.1. Mean mark:
The mean mark is approximately **85.43**.

### 1.1.2. Range of the marks:
The range of the marks is **35**.

Next, I'll proceed with calculating the semi-interquartile range and other questions.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through how to calculate the semi-interquartile range and the 38th percentile:

1. **To calculate the semi-interquartile range**:
   - First, sort the marks. The first quartile \(Q_1\) is the 25th percentile and the third quartile \(Q_3\) is the 75th percentile.
   - Find the difference between \(Q_3\) and \(Q_1\), and then divide by 2.

2. **To find the 38th percentile**:
   - You would locate the value at 38% of the ordered data set. This can be done through interpolation if it falls between two data points.

If you'd like, I can continue guiding you through the remaining questions. Let me know!

### Here are five related questions:
1. How do you interpret the quartiles in a data set?
2. Why is the semi-interquartile range a useful measure of spread?
3. What is the relationship between percentiles and quartiles?
4. How would skewness affect the mean and median of a data set?
5. How can you use a box-and-whisker plot to identify outliers?

### Tip:
In statistics, the interquartile range (IQR) is often more informative than the range because it focuses on the middle 50% of the data, reducing the influence of outliers.

Below are the marks of the top-performing learners in Mathematics June examinations at B school out of 100. Perform the following tasks:
1. Determine the mean mark.
2. Write down the range of the marks.
3. Determine the semi-interquartile range of the data.
4. Draw a box and whisker plot.
5. Comment on the skewness of the data.
6. Determine the 38th percentile of the data.
7. The percentage of learners who got less than 65 is 75%. How many learners are doing mathematics in grade 10?

Explore a Grade 10 math problem set covering mean calculation, range, semi-interquartile range, box and whisker plot, skewness analysis, and percentile determination. This problem is based on the top-performing learners' marks in Mathematics at B school.

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