Egypt Primary 6 Mathematics, Week 11: Statistical questions and kinds of data

Statistical questions, dot plots and histograms

Week 11 · Statistical questions, dot plots and the histogram · 3 lessons

Statistical questions and kinds of data

Discover Mathematics P6: Term 1, Unit 6, Lessons 1–2

GoalTell a statistical question from one with a single answer, and say whether data are categorical or numerical.

New words

statistical question · a question that expects different answers from different people or thingsdata · facts or numbers that we collect to answer a questioncategorical data · data in words or groups, such as colours or fruitsnumerical data · data that are numbers, such as counts or measurements

Explanation

A statistical question is a question where we expect the answers to vary. “How many pupils are in my class?” has one answer, so it is not statistical. “How many brothers and sisters do the pupils in Primary 6 have?” has many different answers, so it is statistical. To answer it we collect data from many pupils. Data come in two kinds. Categorical data are words or groups, such as a favourite fruit or the colour of a bag. Numerical data are numbers, such as the number of brothers and sisters or the minutes of a walk. Ask yourself two things: do I expect different answers, and are the answers words or numbers?

★Remember

Statistical question = we expect different answers. Words or groups = categorical data. Numbers = numerical data.

Worked examples

Question	Statistical?	Kind of data
What colour is Mina’s bag?	No	—
What colours are the bags of the pupils in Primary 6?	Yes	categorical
How many books are in the school library?	No	—
How many books did each pupil in Primary 6 borrow this year?	Yes	numerical

Which of these are statistical? Look at the table: a question about one thing has one answer, a question about many pupils or many things has answers that vary.

Minutes	Pupils
5	5
10	8
15	4
20	2
25	1

Rana asks 20 pupils: “How many minutes do you walk to school?” She writes the answers: 5, 10, 10, 15, 5, 20, 10, 5, 15, 10, 10, 25, 5, 15, 10, 20, 10, 15, 5, 10. The answers differ, so the question is statistical, and the data are numerical. She sorts them into a frequency table. Check: 5 + 8 + 4 + 2 + 1 = 20 pupils.

Choosing a display. Favourite fruit is categorical, so we use a bar graph with a gap between the bars. Of 20 pupils, 8 chose mango, 5 orange, 4 guava and 3 banana (8 + 5 + 4 + 3 = 20). Numerical data, like the walking minutes, are shown on a dot plot or a histogram, which you will meet in the next lessons.

Class activity

Question detective. Ask a grown-up to read you ten questions from a newspaper or a family chat (for example about prices, ages or the weather). For each one say: is it statistical, yes or no, and why? Then write one statistical question of your own about your neighbourhood.

Practice

Is “How many pupils are absent from your class today?” a statistical question?

Write a statistical question about the heights of the pupils in your school.

Say whether each is categorical or numerical: (a) favourite sport, (b) goals scored by each player, (c) colour of a bus.

Karim asks “How old is my brother?” and says it is statistical. Is he right? Change the question so that it is.

Marwan wrote how many pages 12 pupils read yesterday: 10, 25, 10, 30, 15, 10, 20, 25, 10, 15, 30, 10. Make a frequency table. Which number of pages is the most common?