4.13 Data and statistics

Mathematics

More geometry, data handling and probability

Educator section

Memorandum

10.2.2 (a) 60

(c) 17

33

16

5

24

10.2.6

Leaner section

Content

Activity: data and statistics [lo 5.7, lo 5.9, lo 5.5]

9 DATA AND STATISTICS

9.1 Class discussion

• Precisely what are “data” and “statistics”?
• When do we use these terms?
• Where do we get the information?
• How can we represent the information that is obtained?

9.2 Something more to discuss

• Divide into groups of three. How would you answer the following questions?

a) What is the average height of a Grade 7 boy in South Africa?

b) Which TV programme do Grade 7 girls in South Africa watch the most?

c) What is the most popular brand of chips in South Africa?

d) How many learners play tennis in the Western Cape?

e) What is the average mass of the Grade 7 educators in your school?

f) What is the average age of the Grade 7 learners in your school?

10. COUNTING AND GROUPING OF DATA

10.1.1 Did you know?

Sometimes it is very difficult to get information from the whole group that you had to interview (see 9.2(c) above). That is why often only a part of the group is questioned. This is seen as a sample of the bigger group.

If you do a sample of the larger group, it must be representative of the larger group, i.e.:

• You must ask enough people.
• You must ask a large variety of people. (age, sex, etc.)

10.1.2 Class discussion:

• Which of you and how many will allow yourselves to be questioned as part of a sample to find out the following? Remember: you will want realistic answers!

a) What is the favourite sport of the girls in your school?

b) What is the favourite magazine of English-speaking South Africans?

c) What is the most common illness/ailment that people over 50 years old in South Africa suffer from?

10.2.1 Study the following data that was collected during a sample. It indicates the ages of secretaries.

10.2.2 Answer the following questions:

a) How many secretaries were questioned in the sample?

b) Work together with a friend. How can you organise/group this information so that it makes sense? Report back tot he class!

c) Complete:

• The youngest secretary is __________________________________ years old.
• The oldest secretary is ____________________________________ years old.
• The difference between the oldest and the youngest secretaries is _____ years.
• ________________________________________ secretaries are 21 years old.
• The largest number of secretaries that were the same age, were all _____ years old.

10.2.3 Did you know?

One way of organising information is by means of the “stem” and “leaf” diagram.

The first row is thus 32, 33, 30 etc.

10.2.4 Find out the mass of 15 of your classmates. Represent the data by means of a stem and leaf diagram.

10.2.5 Did you also know?

You can also count the data by drawing lines/sticks and then drawing up a tally. Every fifth line/stick crosses out the precious.4. The numbers will look like this:

one: I

two: II

three: III

four: IIII

five: IIII

10.2.3 Use the information below to complete the table. The information shows how many marks out of 30 the Grade 7 girls achieved:

Assessment

Learning Outcome 5: The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment Standard 5.7: We know this when the learner identifies the largest and smallest scores in a data set and determines the difference between them in order to determine the spread of the data (range);

Assessment Standard 5.9: We know this when the learner critically reads and interprets data presented in a variety of ways to draw conclusions and make predictions sensitive;

Assessment Standard 5.5: We know this when the learner organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays.