Mean

Mean

GCSE(F),

The Mean is the total of the values in the data, divided by the number of values.

In a simple example, the mean of the numbers 3, 5, 6, 9, 13 and 15 is:

(3 + 5 + 6 + 9 + 13 + 15) ÷ 6 = 8.5

(Note the use of brackets to follow BIDMAS rules).

Data can be placed into tables. In this instance, the numbers:

2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6

are placed into a table:

Number (N)Frequency (f)N x f
222 x 2 = 4
313 x 1 = 6
4416
5420
6424
TOTAL1570

The total of all the values add up to 70. There are 15 values in total. The mean is 70 ÷ 15 = 4.67 (to 2 decimal places).

Examples

1. A supermarket is checking how long customers have to wait in a queue before being served. The times recorded, in minutes, is shown in the table below. What is the mean waiting time?

Wait (W) minutesFrequency f
0 5
1 22
2 12
3 8
4 2
5 1

Answer: 1.66 minutes

Wait (W) minutesFrequency fW x f
050
12222
21224
3824
428
515
TOTAL5083

Mean = 83 ÷ 50 = 1.66 minutes

2. A group of 6 friends collect game cards. The mean number of game cards that they have is 12. One of the friends leaves, and the mean number of game cards is now 11. How many cards did the friend who left have?

Answer: 17

Total number of cards for all 6 players is 6 x 12 = 72.

Number of cards when there are 5 players is 5 x 11 = 55.

Cards owned by leaver = 72 - 55 = 17