Week 8 · Organizing data: statistical questions, frequency tables, dot plots, histograms, stem-and-leaf and box plots · 3 lessons
1
Statistical questions, collecting data, dot plots and bar graphs
Mathematics Prep 1 Term 1, Unit 3, Lesson 1
GoalTell a statistical question, collect data in a frequency table and show it with a dot plot or bar graph.
New words
statistical question · a question whose answers varydata · the facts or numbers we collectfrequency · how many times a value occursmode · the value with the highest frequency
Explanation
A statistical question has answers that vary: “How many brothers and sisters do the pupils in our class have?” is statistical, but “How many pupils are in our class?” has one answer and is not. We collect data by observing, interviewing or surveying. To organise it, write each value once in a frequency table and count how often it occurs. A dot plot puts one dot for each piece of data above its value, and a bar graph uses a bar whose height is the frequency. Both show the actual values. The mode is the value with the highest frequency, so it is the value itself, not the count.
Mark
Frequency
4
1
5
3
6
5
7
6
8
3
9
2
Total
20
Worked examples
Statistical or not? “How tall are the pupils in our class?” is statistical, because heights vary. “How tall is the Pyramid of Giza?” is not, because it has one answer.
Mark
Frequency
4
1
5
3
6
5
7
6
8
3
9
2
Total
20
Twenty pupils get these marks out of 10: 7, 7, 5, 8, 6, 7, 9, 6, 5, 7, 8, 6, 4, 7, 6, 9, 5, 7, 6, 8. Count each mark. The frequency table shows 1, 3, 5, 6, 3 and 2 pupils for the marks 4 to 9, and 1 + 3 + 5 + 6 + 3 + 2 = 20.
Read the dot plot. The tallest column is above 7 with 6 dots, so the mode is the mark 7. Pupils with at least 7: 6 + 3 + 2 = 11. Pupils with fewer than 6: 1 + 3 = 4.
Class activity
Class survey. With a grown-up, ask ten people how many brothers and sisters they have. Write the answers, make a frequency table and draw a dot plot with small circles. What is the mode?
Practice
1
Which is a statistical question: “How tall is the Pyramid of Giza?” or “How tall are the pupils in our class?”
“How tall are the pupils in our class?” because the answers vary.
2
Make a frequency table for 3, 4, 3, 5, 4, 3, 2, 4, 3, 5. What is the mode?
2 occurs 1 time, 3 occurs 4, 4 occurs 3, 5 occurs 2 (total 10). The mode is 3.
3
From the table of marks, how many pupils scored 8 or more?
3 + 2 = 5 pupils.
4
The dot plot shows the number of brothers and sisters of 16 pupils. How many pupils have 2 or more?
5 + 2 = 7 pupils.
5
Karim says the mode of the marks is 6, because the tallest column has 6 dots. What is wrong?
The mode is the value, not the count. The tallest column is above the mark 7, so the mode is 7, with frequency 6.
