The median of an ordered set is the middle value and the lower quartile marks the 25th percentile, so this Year 11 sheet is built on where in the data the describing points sit. The interquartile range is named as upper quartile minus lower quartile in the key.
Key Takeaways
The median is the middle value of an ordered set (Q1).
The lower quartile marks the 25th percentile (Q2).
The interquartile range is the upper quartile minus the lower quartile.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The median of an ordered data set is which value?
(a) the most common value(b) the middle value(c) the largest value(d) the average of the extremes
2.The lower quartile marks which point in a data set?
(a) the 50th percentile(b) the 75th percentile(c) the 25th percentile(d) the 100th percentile
3.The interquartile range is calculated as which difference?
(a) upper quartile - lower quartile(b) median - lower quartile(c) upper quartile - median(d) maximum - minimum
4.For a data set of 40 values, where is the median located?
(a) at the 10th value(b) at the 20th value(c) between the 20th and 21st values(d) at the 40th value
5.In a box plot, what does the box itself represent?
(a) the whole data set(b) the interquartile range(c) the median only(d) the range
6.Which statement is always true of a cumulative frequency graph?
(a) It always decreases(b) It never decreases(c) It is always a straight line(d) It always passes through the origin
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State what the median of a data set represents.
8.Define the interquartile range.
9.A data set has 60 values. Between which positions does the median lie?
10.The lower quartile of a data set is 12 and the upper quartile is 20. Find the interquartile range.
11.In a cumulative frequency diagram, what fraction of the data lies below the upper quartile?
12.A box plot has minimum 5, lower quartile 10, median 15, upper quartile 25 and maximum 40. Find the range.
13.State one advantage of a box plot for comparing two data sets.
14.On a cumulative frequency graph the cumulative frequency at 30 kg is 45 out of a total of 60. How many values exceed 30 kg?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A class of 30 students took a test and the median mark is 62, with no student scoring exactly 62. How many students scored below 62?
16.The interquartile range of a data set is 18 and the lower quartile is 24. Find the upper quartile.
17.From a cumulative frequency graph the median is 40 and the interquartile range is 16. Find the lower quartile.
18.A data set has 80 ordered values. The 60th value is 25 and the 20th value is 15. Use these to estimate the interquartile range.
19.The range of a box plot is 30 and the maximum value is 50. Find the minimum value.
20.In a survey of 100 heights, the median is 165 cm and 25 of the values are below 158 cm. What statistical measure does 158 cm represent?
Answer Key
1. b) the middle value
2. c) the 25th percentile
3. a) upper quartile - lower quartile
4. c) between the 20th and 21st values
5. b) the interquartile range
6. b) It never decreases
7. Refer to solution guide.
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11. Refer to solution guide.
12. Refer to solution guide.
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19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the median of an ordered data set?
The middle value, option (b) in this worksheet (Q1).
What percentile is the lower quartile?
The 25th percentile, option (c) in this worksheet (Q2).
How is the interquartile range found?
Upper quartile − lower quartile, from the answer key on this page.
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