Final answer:
The interquartile range (IQR) is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) in an arranged set of data, representing the spread of the middle 50% of the data. The comparison of IQRs can reveal the variability in different data sets, and outliers can be identified as values that far deviate from the central tendency.
Step-by-step explanation:
Calculating the Interquartile Range
The interquartile range (IQR) is the difference between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile) in a set of data, representing the middle 50% of the data. To calculate the IQR for a given set of data, you must first arrange the data in ascending order, then find Q1 and Q3, which can be done by splitting the data into four equal parts.
For the two classes, we need to calculate the Q1 and Q3 separately:
- Class A: After arranging the scores in ascending order and finding the quartiles, subtract Q1 from Q3 to find the IQR.
- Class B: Again, arrange the scores, find the first and third quartiles, and subtract Q1 from Q3 to compute the IQR.
Comparing the IQRs of the two classes gives us an idea of which class has more variability in test scores.
To identify outliers, you can use the formula to find values that are 1.5 times the IQR above Q3 or below Q1. Outliers can affect the interpretation of the data, so it's important to identify and consider them in your analysis.