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.