Question: The cumulative frequency for the distribution of the distance (in miles) that 20 randomly selected runners ran during a week is given in the ogive. Find the interquartile range for the data by constructing a box plot.
A ) 18.5, Figure 2 B ) 11.2, Figure 2 C ) 23.5, Figure 1 D ) 12, Figure 1
Steps to derive
1 The x-axis in an ogive graph represents the class boundaries and the y-axis represents the cumulative frequency.
2 The class boundaries for the first class limits are 5.5 - 10.5.
3 So, the first class limits are 6 - 10. [5.5 + 0.5 = 6, 10.5 - 0.5 = 10.]
4 To construct a box plot, it is required to know the the five - number summary of the given data.
5 The lowest value is 6.
6 The class boundaries for the last class are 35.5 - 40.5.
7 So, the class limits for the last class are 36 - 40. [35.5 + 0.5 = 36, 40.5 - 0.5 = 40.0.]
8 The highest value is 40.
9 Median, Q2 = 24.5
10 Lower quartile, Q1 = 19.2
11 Upper quartile, Q3 = 30.4
12 The five number summary for the given data is 6, 19.2, 24.5, 30.4, 40.
