The image you've uploaded provides information about a data set of student test scores. It gives specific values for the quartiles, interquartile range (IQR), and defines how outliers are identified. Here is a breakdown of the key information:

Given Information:

1. Lower quartile (Q1): 24
2. Median (Q2): 30
3. Interquartile range (IQR): 10
4. Upper quartile (Q3): (Q1 + IQR) = 24 + 10 = 34
5. Three lowest marks: 8, 10, 15.5
6. Three highest marks: 45, 52.5, 56

Outlier Definition:

An outlier is a value that is:

• More than $1.5 \times \text{IQR}$ below the lower quartile.
• More than $1.5 \times \text{IQR}$ above the upper quartile.

The IQR is 10, so:

• $1.5 \times 10 = 15$
• Lower outlier threshold: $Q1 - 15 = 24 - 15 = 9$
• Upper outlier threshold: $Q3 + 15 = 34 + 15 = 49$

Outliers:

• Any mark below 9 is an outlier: 8 is an outlier.
• Any mark above 49 is an outlier: 52.5 and 56 are outliers.

Box Plot:

To construct the box plot, ignoring the outliers (8, 52.5, 56), you would plot:

1. Minimum (excluding outliers): 10
2. Lower quartile (Q1): 24
3. Median (Q2): 30
4. Upper quartile (Q3): 34
5. Maximum (excluding outliers): 45

A box plot would have:

• The box spanning from 24 (Q1) to 34 (Q3).
• The line inside the box at 30 (the median).
• Whiskers extending from 10 (minimum, excluding outliers) to 45 (maximum, excluding outliers).
• Outliers plotted separately at 8, 52.5, and 56.

Do you have any questions or would you like further details?

5 Related Questions:

1. How would the box plot change if the outliers were included?
2. What does the interquartile range tell us about the distribution of the data?
3. How are whiskers in a box plot related to the concept of outliers?
4. Can you explain how the outliers affect the overall analysis of the data set?
5. What other methods can be used to identify outliers besides the IQR method?

Tip:

When analyzing data, always check for outliers as they can skew the mean and affect statistical interpretations.