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Data Handling

The following test marks were obtained by 17 learners in their most recent test on statistics.
40; 60; 100; 70; 30;
80; 10; 80; 20; 10;
90; 30; 20; 40; 100; 100; 40

1. Determine the range for the scores.
SOLUTION
It is advisable to arrange the numbers in ascending (or descending) order first!
10; 10;
20; 20;
30; 30;
40, 40; 40
60;
70;
80; 80;
90;
100; 100; 100

Range is (highest)–(lowest).
Range = 100 - 10 = 90.

2. What is the mode?
SOLUTION
Mode is the most frequently occurring score.
Mode = 40 and 100.
Two modes so we say that this set of scores is bi-modal.

3. Create a five number summary.
SOLUTION
Five number summary is the following:
Min value;
Q₁;
Q₂;
Q₃;
Max Value

Mimimum: 10
Q₁ is the average of the 4th and 5th values:
Q₂ is the median.
In this case the middle (9th) value
Q₂ = 40
Q₃ is the average of the 13th and 14th values
Maximum: 100

4. Draw a box and whisker plot.
SOLUTION
Now draw box plot as follows: