https://file.aiquickdraw.com/mathbot/file/1726721574659qkj6hrkj.jpg

Let's analyze and answer the questions based on the image provided.

### Question 1:
The stem-and-leaf plot shows the distribution of test scores in Mr. M. Math's class. Here are the tasks:

**(a) Median Score:**
- First, we list the scores in ascending order: 
  \[
  25, 26, 28, 35, 36, 38, 42, 45, 52, 56, 57, 57, 57, 58, 59, 64, 65, 68, 68, 72, 74, 78, 79, 89
  \]
- There are 24 scores, so the median is the average of the 12th and 13th values, which are both 57.
  \[
  \text{Median} = 57
  \]

**(b) Range:**
- The range is the difference between the highest and lowest values.
  \[
  \text{Range} = 89 - 25 = 64
  \]

**(c) Mode:**
- The mode is the value that appears most frequently. In this case, 57 appears three times, more than any other score.
  \[
  \text{Mode} = 57
  \]

**(d) Shape of the distribution:**
- The distribution is positively skewed because most of the data is concentrated towards the lower end, and the tail extends towards the higher values.

---

### Question 2:
This question involves comparing two box plots representing the number of wristbands sold daily by two stores (Store A and Store B).

**(a) Which store performed better?**
- Store A performed better. It has a higher median and overall higher range of values in the box plot.

**(b) Make 3 statistical comparisons:**
1. **Median:**
   - The median of Store A is higher (approximately 60) compared to Store B (approximately 40), meaning Store A sold more wristbands on average.
  
2. **Interquartile Range (IQR):**
   - The IQR (difference between Q3 and Q1) for Store A is larger, indicating more variability in daily sales compared to Store B.
  
3. **Range:**
   - The overall range of wristbands sold is larger for Store A (approximately 20 to 80) compared to Store B (approximately 30 to 60). Store A had both higher maximum sales and a wider range of performance.

---

If you'd like more detailed explanations or have further questions, feel free to ask! Here are some related questions for further exploration:

1. What is the significance of the median in a skewed distribution?
2. How would you calculate the mean of the test scores from the stem-and-leaf plot?
3. What other types of distribution shapes can a dataset have?
4. What does a large interquartile range suggest about a dataset?
5. How would a histogram for the wristband sales look based on the box plot data?

**Tip:** When analyzing a skewed distribution, the median provides a better central measure than the mean because it is less affected by extreme values.

The image contains two statistical problems. The first is a stem-and-leaf plot asking for the median, range, and mode, and for identifying the skewness of the data. The second problem is a box plot comparison of two stores' wristband sales, requiring analysis of which store performed better and three statistical comparisons.

This Grade 10 math problem involves analyzing a stem-and-leaf plot and a box plot. Learn how to calculate the median, range, mode, and identify skewness. Additionally, compare two box plots for wristband sales using median, IQR, and range to determine which store performed better.

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