What is a box plot:
A Box plot consists of five main points; the lowest value in the data set, the lower quartile, the median, the upper quartile and the highest value in the data set. These are shown in the diagram below.
Using a box plot you can calculate the range of the data set and the interquartile range of the date set.
Calculating the range:
The range can be calculated by doing the following:
Highest value in the data set – Lowest value in the data set
Calculating the interquartile range:
The interquartile range can be calculated by doing the following:
Upper Quartile – Lower Quartile
The diagram represents the test scores of 60 students on a test which is marked out of 100. Answer the following questions:
- Calculate the median:
From the diagram we can see the median is 45 Marks
- Calculate the range of marks:
From the diagram we can see the highest mark is 95 and the lowest mark is 15.
95 – 15 = 80
- Calculate the interquartile range:
From the diagram we can see the upper quartile is 70 and the lower quartile is 30.
70 – 30 = 40
- Find the number of students who achieved over 70 marks.
Form the diagram we can see that each section represents 25% of the students.
We can also see that 70 marks lies on the upper quartile, which allows us to deduce that 25% of students achieved over this.
There are 60 students in total, so 25% of the students is 15 students.
Therefore the answer is 20 Students