6.2 Frequency tables and cumulative frequency

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 6

Good morning!

Schedule: 

• Learning goals 
• Frequency tables 
• Modal class and median
• Homework 

Learning goals 

At the end of this lessons I can:

• Find the mode and median from a grouped frequency table
• Draw up a grouped frequency table from a set of data 
• Calculate the cumulative frequency in a frequency table

1. The maximum value is 18
2. If choosing a random value there is a 75% chance it will be larger than 9
3. The mean is 12
4. The data is positively skewed

Frequency Tables

Time spend, x (min)	Frequency	Cumulative frequency
0 ≤ x < 30
30 ≤ x < 60
60 ≤ x < 90
90 ≤ x < 120
120 ≤ x < 150
150 ≤ x < 180

Time spent on Youtube per day by MP4's

Frequency Tables

Time spend, x (min)	Frequency	Cumulative frequency
0 ≤ x < 30	6	6
30 ≤ x < 60	4	10
60 ≤ x < 90	3	13
90 ≤ x < 120	0	13
120 ≤ x < 150	2	15
150 ≤ x < 180	1	16

Time spent on Youtube per day by MP4's

Grouped frequency tables 

To determine the class width for your table: 
Divide the range by the amount of classes you want, then round the answer UP

Start value:  
Choose a start value less than or equal to your smallest value

Grouped frequency tables 

To determine the class width for your table: 
Divide the range by the amount of classes you want, then round the answer UP

Start value:  
Choose a start value less than or equal to your smallest value

Rule of thumb: 

20 or less data values     5 classes

21-50 values                      10 classes

51-100 values                     15 classes 

100 or more                       20 classes

Grouped frequency tables

Student grades: 64, 68, 73, 75, 78, 79, 81, 83, 83, 84, 89, 90, 91, 94, 96, 97

1. Range = 

2. n = 16

3. How many classes?

4. Class width = 

5. Start value 

Grouped frequency tables

Student grades: 64, 68, 73, 75, 78, 79, 81, 83, 83, 84, 89, 90, 91, 94, 96, 97

1. Range = 97-64 = 33

2. n = 16

3. I want 5 classes 

4. Class width = 

5. Start value can be 64 or 63 

​5​​33​​≈7

Grades	Frequency	Cumulative frequency
64 ≤ x < 71	2	2
71 ≤ x < 78	2

1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3

What is the correct choice
for class ?

Number of pets:

# of pets, x	frequency	cumulative frequency
a	8	8
2 < x ≤ 4	b	12
4 < x ≤ 6	1	c

a

1. 1 < x ≤ 3
2. 0 < x ≤ 2
3. 2 < x ≤ 6
4. 0 < x ≤ 4

1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3

What is the correct
frequency for ?

Number of pets:

# of pets, x	frequency	cumulative frequency
a	8	8
2 < x ≤ 4	b	12
4 < x ≤ 6	1	c

b

1. 4
2. 5
3. 6
4. 7

1, 2, 5, 3, 3, 2, 2, 1, 2, 1, 1, 4, 3

What is the correct
cumulative frequency for ?

Number of pets:

# of pets, x	frequency	cumulative frequency
a	8	8
2 < x ≤ 4	b	12
4 < x ≤ 6	1	c

c

1. 1
2. 20
3. 4
4. 12

Modal class 

What do you think the modal class is? 

# of pets, x	frequency	cumulative frequency
0 < x ≤ 2	8	8
2 < x ≤ 4	4	12
4 < x ≤ 6	1	13

Modal class 

The modal class  is the class with the highest frequency

# of pets, x	frequency	cumulative frequency
0 < x ≤ 2	8	8
2 < x ≤ 4	4	12
4 < x ≤ 6	1	13

Modal class

Time spend, x (min)	Frequency	Cumulative frequency
5 < x ≤ 20	7	7
20 < x ≤ 35	4	11
35 < x ≤ 50	2	13
50 < x ≤ 65	5	18
65 < x ≤ 80	0	18
80 < x ≤ 95	1	19

Time spent on math homework

Modal class: 

Median value

# of pets, x	frequency	cumulative frequency
0 < x ≤ 2	8	8
2 < x ≤ 4	4	12
4 < x ≤ 6	1	13

The median is the                th

value.

               = 

​2​​(n+1)​​

​2​​(n+1)​​

Median value

Time spend, x (min)	Frequency	Cumulative frequency
5 < x ≤ 20	7	7
20 < x ≤ 35	4	11
35 < x ≤ 50	2	13
50 < x ≤ 65	5	18
65 < x ≤ 80	0	18
80 < x ≤ 95	1	19

Find the class with the median value.

Median value

Time spend, x (min)	Frequency	Cumulative frequency
5 < x ≤ 20	7	7
20 < x ≤ 35	4	11
35 < x ≤ 50	2	13
50 < x ≤ 65	5	18
65 < x ≤ 80	0	18
80 < x ≤ 95	1	19

Find the class with the median value.

Time spend, x, (min)	Frequency	Cumulative frequency
	10	10
	3	13
	2	15
	0	15
	1	16

Modal class = 

Class with median value = 

Time spent on Instagram

0 ≤ x < 25

25 ≤ x < 50

50 ≤ x < 75

75 ≤ x <100 

100 ≤ x < 125  

Modal class

Class with median value

Grouped frequency tables

Cumulative frequency

4

10

18

24

30

​2​​(30+1)​​th

Median class

                     Value

= 15.5 th value 

Grouped frequency tables

How would you estimate the range in a grouped frequency table? 

Grouped frequency tables

Take out your diaries/notebook

Homework for Tuesday 14-3-2023:

                 p. 329-330: Practice 1  #1, 2, 3 , 4