Quartiles and Data Analysis Worksheet
A Grade 12 math worksheet on calculating and interpreting quartiles, interquartile range, and identifying outliers in data sets.
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Quartiles and Data Analysis
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Date:
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
1. Consider the following data set: 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38.
a) Calculate the first quartile (Q1).
b) Calculate the second quartile (Q2), also known as the median.
c) Calculate the third quartile (Q3).
2. The interquartile range (IQR) is a measure of statistical dispersion, representing the range of the middle 50% of the data. It is calculated as Q3 minus Q1. For the data set in Question 1, the IQR is .
3. Outliers are data points that significantly differ from other observations. They can be identified using the following formulas:
- Lower Bound: Q1 - (1.5 * IQR)
- Upper Bound: Q3 + (1.5 * IQR)
Given the data set: 5, 10, 12, 15, 18, 20, 22, 25, 50.
a) Calculate Q1, Q2, and Q3 for this data set.
b) Calculate the IQR.
c) Determine if there are any outliers in the data set using the formulas above. If so, list them.
4. The median of a data set is always equal to the second quartile (Q2).
True
False
5. Which of the following is NOT a measure of central tendency?
Mean
Median
Mode
Interquartile Range
6. A teacher recorded the test scores of her students. The five-number summary for the scores is as follows:
Minimum: 60
Q1: 72
Median (Q2): 80
Q3: 88
Maximum: 95
a) What percentage of students scored between 72 and 88?
b) What is the range of the middle 50% of the scores?