3.6 Analyse data for meaningful patterns and measures

Mathematics

Grade 9

Number patterns, graphs, equations,

Statistics and probability

Module 18

Analyse data for meaningful patterns and measures

ACTIVITY 1

To analyse data for meaningful patterns and measures

[LO 5.3]

• Now we need to gather information about the heights of the learners in your class. Fasten a measuring tape like the one dressmakers use to the side of the door, so that it is perfectly vertical. If you can’t find a tape, you can use some other way – maybe making small marks very accurately every centimetre on the wall, using rulers.

• Each learner takes off her shoes and stands with her heels and back tightly against the wall. Someone who is tall enough holds a ruler or piece of cardboard flat on her head to see exactly how tall she is. It is a good idea to take the measurement in centimetres and not in millimetres. Write the answer on her hand (or on a piece of paper).

• We do our first calculation in an interesting way: When everyone has been measured, all the pupils stand in line in the order of their heights.

• From this line of pupils we get the first measurement of the average of the class. Write down the height of the pupil who is exactly in the centre of the line (equally far from the beginning as from the end). This number is called the median . There are as many learners shorter than she is, as there are taller than she is. Note: if there are an even number of learners in the class, then of course there will not be a middle person. In that case we take the two middle persons, add their heights and divide the answer by two.

• Write down the median height for your class. If you are in a class with both boys and girls, work out the medians for the boys and girls separately

• Next make a frequency table for the heights and use tallies to count how many of each height you have in the class.

Go back to the table of ages of siblings and find the median age of the boys and girls separately. Your table is likely to be very big, but here is a smaller example of what you should do:

• See whether you agree that the median height for this group is 162 cm.

• If you study the numbers in the last row (they give the frequencies of the different heights) you will see that 164 cm is the height that occurs most often as there are six learners who are 164 cm tall. This number is called the mode . We can think of it as the most popular height.

• The ne x t calculation is the one that gives us the value that we usually call the average . Its proper name is the arithmetic mean , or just mean . You may already know how to calculate it: you add all the values and then divide the answer by the number of values. For the table above you divide 6156 by 38 to get a mean height for the class of 162 cm.

• .We can make a table of these values:Use the table of ages of siblings again and calculate the mode and mean for boys and girls separately and then fill these values in on a table like the one alongside

• These values (mode, median and mean) are together called measures of central tendency . They are all different kinds of averages . That is why, when we use the word average to refer to the arithmetic mean, we are not being perfectly accurate. From now on, you can use the word mean where you would have said average before.