- Use the heights for your class and complete the calculations.
- Now carefully study the frequency table for the heights of another class of 38 learners:
| cm |
158 |
159 |
160 |
161 |
162 |
163 |
164 |
165 |
166 |
| Total |
1 |
4 |
6 |
6 |
5 |
4 |
7 |
4 |
1 |
- Calculate the three measures of central tendency for this class as well.
- Compare the heights of the learners in the two classes and write a short essay about the similarities and differences you found.
ACTIVITY 2
To extract more information from data
[LO 5.3]
| Median |
162 cm |
| Mode |
164 cm |
| Mean |
162 cm |
As you see from the heights of the learners in the previous example, the two classes have different heights but the three averages are exactly the same.
We can tell a little more about the data by using measures of dispersion. These tell us more about how the values are distributed.
- The first is the
range , calculated by taking the highest value and subtracting the lowest value from it. Do this for both classes. As you can clearly see, the first class has a range of 13 cm and the second class has a range of 8 cm.
- The second measure of dispersion is the
mean deviation . This is calculated firstly determining how far each value deviates (or differs) from the
mean (which we have already calculated). Then we calculate the mean of these deviations to give the mean deviation.
- We make another table from the data for the second class, which has all the heights and the deviation of each value from the mean:
| 158 |
159 |
159 |
159 |
159 |
160 |
160 |
160 |
160 |
160 |
160 |
161 |
161 |
161 |
161 |
161 |
161 |
162 |
162 |
| 4 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
| 162 |
162 |
162 |
163 |
163 |
163 |
163 |
164 |
164 |
164 |
164 |
164 |
164 |
164 |
165 |
165 |
165 |
165 |
166 |
| 0 |
0 |
0 |
1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
3 |
3 |
3 |
3 |
4 |
- The total of all these deviations is 68. Dividing by 38 we get 1,79 when rounded to two places.
- Do the same calculation for the other class.
- Now you can calculate the two measures of dispersion for your own class.
Measures of dispersion are very useful when you want to compare two sets of data, like the heights of learners in two different classes. There are other measures of dispersion, but they are not taught in this course.
- At this stage you are very good at tabulating data, calculating values to describe the data as well as making some inferences about the data
ACTIVITY 3
To use new skills to investigate and compare some test marks
[LO 5.3]
- Compare the test marks for the same test obtained by two groups of learners, shown in the table below. You have to use all the skills you have learnt so far in this learning unit, to see whether you can say whether one group did better than the other. This is not a simple question, and you are not easily going to see an answer without some careful work and concentrated thinking.
| Group
A |
82 |
78 |
57 |
91 |
29 |
80 |
85 |
49 |
82 |
67 |
99 |
68 |
83 |
12 |
87 |
86 |
38 |
81 |
58 |
79 |
| Group
B |
72 |
82 |
74 |
84 |
81 |
84 |
76 |
12 |
2 |
71 |
70 |
93 |
13 |
90 |
80 |
73 |
91 |
70 |
99 |
88 |
ACTIVITY 4
To represent data in ways that make it easier to understand their meaning
[LO 2.2, 2.6, 5.4]
In the work on graphs you saw that a graph gives a much better picture of the meaning of data.
- Now you will be learning more about different kinds of
graphical representation of data. This means mainly that you make the meaning of data visible without always having to do intricate calculations.
