1. Welcome
GCSE Maths

3. So what are we going to cover today?
What is a good sample?
Finding the mean, median, mode and range from sets of data and from frequency tables

4. Heights of 10 students:
175cm; 154cm; 198cm; 145cm; 134cm; 156cm; 156cm; 167cm; 145cm; 156cm How would you calculate the mean, median, mode and range of this set of data?

5. People living in a house
Averages from a table
1,1,1,1, 2,2,2,2,2,2
3,3,3,3,3,3,3
4,4,4,4,4,4,4,4,4,
5,5,5,5
People living in a house 1 2 3 4 5
Frequency 6 7 9
Range: The most people in a house is 5, the least is 1, so the range is 4. Mode: The group with the largest frequency is 4. Median: There are 30 bits of data so the value between the 15th and 16th values. That value lies in the “3” group. Mean: total ÷ how many (frequency) Mean: =𝟑.𝟏

6. Mean and Median from frequency table
Are there different ways to do this?
Do I need another column?

7. Problem solving
There are 32 students in Mr Newton’s Class.20 are boys and 12 are girls.
The mean height of the boys is 151cm.
The mean height for the girls is 148cm.
Calculate the mean height of all the students in Mr Newton’s class.
A group of students take a test. The group consists of 12 boys and 8 girls.
The mean mark for boys is 18. The mean for the girls is 16.5
Calculate the mean mark for the whole group.
The mean of four numbers is 2.6
One of the numbers is 5.
Find the mean number of the other three numbers.

8. Exam style questions on averages from tables

9. Sam and his partner recorded the number of times they could hit the ping pong ball between them without it going off the table. Their results are in the table below.
Consecutive hits (h)
Frequency
0 < h ≤ 20 3
20 < h ≤ 40 17
40 < h ≤ 60 25
60 < h ≤ 80 56
80 < h ≤ 100 8
100 < h ≤ 120
Total
What is different about this table?
What difference does this make to what you know or do not know about the data?
What can you say about the mode, mean, median or range?

10. Sam and his partner recorded the number of times they could hit the ping pong ball between them without it going off the table. Their results are in the table below.
Consecutive hits (h)
Frequency
Midpoint
Midpoint x Frequency
0 < h ≤ 20 3
20 < h ≤ 40 17
40 < h ≤ 60 25
60 < h ≤ 80 56
80 < h ≤ 100 8
100 < h ≤ 120
Total
Frequency 3 17 25 56 8
112 
Midpoint
10 
 30
 50
 70
 90
 110
Midpoint x Frequency
 30
 510
 1250
 3920
 720
 330
Midpoint x Frequency
 30
 510
 1250
 3920
 720
 330
6760
Estimated total
Estimated mean =
Estimated total= add all the midpoint x frequency column
Estimated mean = total of midpoint x frequency column divided by total Frequency (6760 ÷ 112)

11. Sam and his partner recorded the number of times they could hit the ping pong ball between them without it going off the table. Their results are in the table below.
Consecutive hits (h)
Frequency
Cumulative frequency
0 < h ≤ 20 3
20 < h ≤ 40 17
40 < h ≤ 60 25
60 < h ≤ 80 56
80 < h ≤ 100 8
100 < h ≤ 120
Total
Consecutive hits (h)
Frequency
Cumulative frequency
0 < h ≤ 20 3
20 < h ≤ 40 17 20
40 < h ≤ 60 25 45
60 < h ≤ 80 56
101
80 < h ≤ 100 8
109
100 < h ≤ 120
112
Total
Modal class
Median class