Welcome GCSE Maths

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

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?

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: 93 30 =𝟑.𝟏

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

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.

Exam style questions on averages from tables

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?

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)

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