The table below shows the number of students from different classes of two schools who participated in a sports competition:
School A 25 21 2 22 20 21 20 23 1 School B 3 2 1 5 4 2 3 4 3
Part A: How can you use box plots to compare the median and interquartile range of the data? Write the minimum value, first quartile, median, third quartile, and interquartile range for the two sets of data.
Part B: Are the box plots symmetrical in shape? Justify your answer.
Part A: To compare the median and interquartile range of the data using box plots, follow these steps:
Step 1: Organize the data in ascending order for each school.
School A: 1, 2, 20, 20, 21, 21, 22, 23, 25
School B: 1, 2, 2, 3, 3, 3, 4, 4, 5
Step 2: Find the minimum value, first quartile, median, third quartile, and interquartile range for each dataset.
For School A:
- Minimum value: 1
- First quartile (Q1): The median of the lower half of the data, which is 20.
- Median (Q2): The middle value of the data, which is 21.
- Third quartile (Q3): The median of the upper half of the data, which is 22.
- Interquartile range (IQR): The difference between Q3 and Q1, which is 2.
For School B:
- Minimum value: 1
- First quartile (Q1): The median of the lower half of the data, which is 2.
- Median (Q2): The middle value of the data, which is 3.
- Third quartile (Q3): The median of the upper half of the data, which is 4.
- Interquartile range (IQR): The difference between Q3 and Q1, which is 2.
Part B: To determine whether the box plots are symmetrical in shape, we need to examine the position of the median relative to the quartiles.
For both School A and School B, the median value is closer to Q1 (the first quartile) than to Q3 (the third quartile). This suggests that the data is skewed to the right (positively skewed), meaning there are more students with smaller values in both schools.
Therefore, the box plots are not symmetrical in shape.
Note: To draw the box plots and visualize the data, you would need the actual range of the data values and additional information about the whiskers and outliers. However, based on the given information, we can still compare the median and interquartile ranges.