Worked examples
The question
Question: draw a histogram of 12, 25, 31, 18, 27, 22, 35, 29, 15 and 24, in classes of 10.
Which class has the most?
12, 25, 31, 18, 27, 22, 35, 29, 15, 24
1 Make the classes
The smallest number is 12 and the biggest is 35.
In classes of 10: 10 to 19, 20 to 29 and 30 to 39.
classes of 10: 10-19, 20-29, 30-39
2 Make a frequency table
A frequency table first: one row for each class.
12 is in 10 to 19: a mark there, and we cross out 12.
25 is in 20 to 29.
And so on for every number.
We count the marks: 3, 5 and 2.
3 Draw the bars
Along the bottom: the numbers, from 10 to 40.
Up the side: how many.
10 to 19: 3 numbers.
The bar covers 10 to 20 and goes up to 3.
20 to 29: 5.
30 to 39: 2.
Careful!
The bars touch.
The numbers go on with no gaps, like a number line.
A bar chart has gaps; a histogram does not.
Careful: histogram bars touch: no gaps
4 Read the histogram
The tallest bar is 20 to 29.
It reaches 5.
So the class with the most is 20-29, with 5 numbers.
= most: 20-29 (5 numbers)
5 Check
Let's check: all the bars together are 3 plus 5 plus 2, which is 10.
That is every number in the list.
So it is right!
3 + 5 + 2 = 10 numbers
Let's look back.
First: make the classes.
Then: make a frequency table.
Then: draw the bars.
Then: read the histogram.
Last: check.
Answer = most: 20-29 (5 numbers)
▶ Watch it solved
The question
Question: draw a histogram of 52, 67, 71, 58, 63, 75, 69, 81, 66, 72, 64 and 77, in classes of 10.
Which class has the most?
52, 67, 71, 58, 63, 75, 69, 81, 66, 72, 64, 77
1 Make the classes
The smallest number is 52 and the biggest is 81.
In classes of 10: 50 to 59, 60 to 69, 70 to 79 and 80 to 89.
classes of 10: 50-59, 60-69, 70-79, 80-89
2 Make a frequency table
A frequency table first: one row for each class.
52 is in 50 to 59: a mark there, and we cross out 52.
67 is in 60 to 69.
And so on for every number.
We count the marks: 2, 5, 4 and 1.
3 Draw the bars
Along the bottom: the numbers, from 50 to 90.
Up the side: how many.
50 to 59: 2 numbers.
The bar covers 50 to 60 and goes up to 2.
60 to 69: 5.
70 to 79: 4.
Careful!
The bars touch.
The numbers go on with no gaps, like a number line.
A bar chart has gaps; a histogram does not.
Careful: histogram bars touch: no gaps
4 Read the histogram
The tallest bar is 60 to 69.
It reaches 5.
So the class with the most is 60-69, with 5 numbers.
= most: 60-69 (5 numbers)
5 Check
Let's check: all the bars together are 2 plus 5 plus 4 plus 1, which is 12.
That is every number in the list.
So it is right!
2 + 5 + 4 + 1 = 12 numbers
Let's look back.
First: make the classes.
Then: make a frequency table.
Then: draw the bars.
Then: read the histogram.
Last: check.
Answer = most: 60-69 (5 numbers)
▶ Watch it solved
The question
Question: draw a histogram of 2, 13, 25, 8, 17, 21, 34, 11, 19, 15, 28, 16, 23 and 12, in classes of 10.
How many are 20 or more?
2, 13, 25, 8, 17, 21, 34, 11, 19, 15, 28, 16, 23, 12
1 Make the classes
The smallest number is 2 and the biggest is 34.
In classes of 10: 0 to 9, 10 to 19, 20 to 29 and 30 to 39.
classes of 10: 0-9, 10-19, 20-29, 30-39
2 Make a frequency table
A frequency table first: one row for each class.
2 is in 0 to 9: a mark there, and we cross out 2.
13 is in 10 to 19.
And so on for every number.
We count the marks: 2, 7, 4 and 1.
3 Draw the bars
Along the bottom: the numbers, from 0 to 40.
Up the side: how many.
0 to 9: 2 numbers.
The bar covers 0 to 10 and goes up to 2.
10 to 19: 7.
20 to 29: 4.
Careful!
The bars touch.
The numbers go on with no gaps, like a number line.
A bar chart has gaps; a histogram does not.
Careful: histogram bars touch: no gaps
4 Read the histogram
20 to 29: 4.
30 to 39: 1.
We add those bars: 4 plus 1 is 5.
= 20 or more: 4 + 1 = 5
5 Check
Let's check: all the bars together are 2 plus 7 plus 4 plus 1, which is 14.
That is every number in the list.
So it is right!
2 + 7 + 4 + 1 = 14 numbers
Let's look back.
First: make the classes.
Then: make a frequency table.
Then: draw the bars.
Then: read the histogram.
Last: check.
Answer = 20 or more: 4 + 1 = 5
▶ Watch it solved
