chapter 4 mean-median-mode

• newEditor
• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

mean-median-mode

Learning goals

You know how to calculate the mean, the median and the mode of a data sequence

You know how to calculate the mean of a frequency table

You know how to calculate the relative frequencies of a frequency table

Mean

The average of all data values

8 6 4 9 3 1 5

Calculate the mean of

8 3 0 10 5 4

A

30

B

5

C

6

D

7

Mean - frequency table

1. Calculate the total frequency: sum of frequencies

2. Multiply each data value with its frequency and add up the results. This is the sum of the data values

3. now use:

   
   

1. total frequency: 1 + 2 + 4 + 7 + 10 + 4 + 1 + 1 = 30

2. sum of data values: 1 · 0 + 2 · 1 + 4 · 2 + 7 · 3 + 10 · 4 + 4 · 5 + 1 · 7 + 1 · 8 = 106

Calculate the mean of

A

2,9

B

3,0

C

2

D

3

A granddad who is 97 years old celebrates his birthday with his great-grandchildren of 3, 6, 9 and 10 years.

What is the mean of this group?

A

7

B

9

C

23

D

25

Discuss with your neighbour:

• Is the mean of the example above a good representation of the average age of the group?

• Why?/Why not?

A granddad who is 97 years old celebrates his birthday with his great-grandchildren of 3, 6, 9 and 10 years.

Median

Middle number of a data sequence

8 6 4 9 3 1 5

Sort

1 3 4 5 6 8 9

Median: 5

Median

What if you have two middle numbers?

-> Take the average

8 6 4 9 11 3 1 5

Sort

1 3 4 5 6 8 9 11

Median: (5 + 6) / 2 = 5.5

What is the median of

8 3 0 10 5 4

A

4

B

5

C

4.5

D

5.5

Mode

The data value with the largest frequency

1 1 4 9 3 1 4

Mode: 1

What if two or more numbers have the largest frequency?

-> Then there is no mode

What is the mode of

1 5 2 8 6 4 2

A

2

B

3

C

4

D

5

Central tendency

The mean, median and mode are measures of central tendency

Relative frequency

In this example, data value 5 has frequency 4

This is called the absolute frequency

The relative frequency is the percentage of the total frequency

In the example, the relative frequency is:

What is the relative frequency of data value 4 and 5 together?

A

46,7%

B

33,3%

C

30,0%

D

52,9%

Data sequence

Mean:

Median:

If the data sequence is in order of magnitude, then

• the median is the middle number in case of an odd amount of numbers

• the median is the average of the middle two numbers in case of an even amount of numbers

Mode:

• the mode is the data value with the largest frequency

• there is no mode if there are multiple numbers with the largest frequency

1. Calculate the total frequency: sum of frequencies

2. Multiply each data value with its frequency and add up the results. This is the sum of the data values

3. Now use:

Relative frequency:

Frequency table

Mean: