Statistics

Discrete or Continuous Data Discrete data is data that has no in betweens e.g. shoes sizes or hair colour Continuous data can be a range of values e.g. your weight or height

Averages There are different types of averages; The Mean: is the most commonly used average The Mode: is easy to work out (it is the number that appears the most times) The Median is the middle value, when the numbers are grouped from smallest to biggest

The Mean To get the mean you have to add all the values together and divide by the number of people E.g. Here are the number of Olympic medals won by Italy from 1972-1996 18, 13, 15, 32, 14, 19, 34 The mean is: 18 + 13 + 15 + 32 + 14 + 19 + 34 = 145 There were 7 Olympics in this time so 145/7 = 20.7 medals were won This looks right because it is between 13 and 34

Try these; The mean weight of 8 people is 60 kg. Alex weighs 52 kg. What is the mean weight of the 9 people including Alex? There are 29 pupils in 9x. Jason is away when there is a test. The mean test score for the other 28 pupils is 76.5. Jason takes the test late and gets 86. What is the new mean score or 9x? There are 33 pupils in set 1. When 32 of them take a test, their mean score is 86.5. Rubina is absentfor the test and takes it late. The teacher tells her that the mean for the whole class is now 86 ⅔. How many marks did Rubina get in the test?

Answers 59.1 kg 76.8 92

The Mode Mode is most Here are the distances for the winners of the Olympic Javelin competitions 90, 90, 95, 91, 89, 84, 90 What is the modal length? 90 because it occurs three times There can be more than one mode

Now try these; Find the mode of these sets of numbers; 90, 90, 95, 91, 89, 84, 90, 88 89, 90, 88, 90, 86, 84, 87, 87 87, 84, 87, 87, 84, 83, 83, 87

Answers 90 87 and 90 87

Median Median is the middle Here are the number of Olympic medals won by Italy from 1972-1996 18, 13, 15, 32, 14, 19, 34 These first need to be sorted from smallest to biggest 13, 14, 15, 18, 19, 32, 34 18 is the middle number so it is the median There can only be one median

Now try these; Find the median of these sets of values; 90, 90, 95, 91, 89, 84, 90, 88 89, 90, 88, 90, 86, 84, 87, 87 87, 84, 87, 87, 84, 83, 83, 87

Answers 90 87.5 85.5

Range This is the biggest number take away the smallest What is the range for this question; Here are the number of Olympic medals won by Italy from 1972-1996 18, 13, 15, 32, 14, 19, 34 34-13= 21 The range is 21

The Mid-Point The following table shows how long it takes pupils to get to school Time (mins) 1-5 6-10 11-15 16-20 21-25 26-30 31-50 Number of pupils 2 7 10 5 3 1 Mid-point 8 13 18 23 28 33 How can you find the mean time taken to get to school when the times are ranges e.g. 1-5 We take the middle of 1-5 which is 3 as our mid point!

The Mid-Point What is the average time taken to get to school? Time (mins) 1-5 6-10 11-15 16-20 21-25 26-30 31-50 Number of pupils 2 7 10 5 3 1 Mid-point 8 13 18 23 28 33 Total 6 56 130 90 69 We add up our totals to get 440 and then divide by the total number of pupils (30) The mean time taken was 14.7 mins

Cumulative Frequency Tables Cumulative means to add together or accumulate. This means the values never get smaller These are the marks scored by 750 GCSE students. They are percentages. Mark Frequency 1-10 11-20 21-30 31-40 41-50 20 48 65 124 157 51-60 61-70 71-80 81-90 91-100 147 84 64 24 17

Cumulative Frequency Tables Mark Frequency 1-10 11-20 21-30 31-40 41-50 20 48 65 124 157 51-60 61-70 71-80 81-90 91-100 147 84 64 24 17 The frequency is the number of people getting these results To get the cumulative frequency you start at the lowest marks and add the others to it e.g.

Cumulative Frequency Tables Mark Frequency Cumulative frequency Less than 10 <20 <30 <40 <50 20 48 65 124 157 68 133 257 414 <60 <70 <80 <90 <100 147 84 64 24 17 561 645 709 733 750

Cumulative Frequency Graphs They are always s-shaped This is because the cumulative frequency always gets bigger Except at the end where the values tail off

The Median Because the frequency goes up to 40 the median is 20 We draw across from 20 until we reach our graph Then we draw a straight line down The median length is 28.75 mm

Inter quartile Range First we find the lower quartile (1/4 of 40) 10 = 23.5 mm Then we find the upper quartile (3/4 of 40) 30 = 31.5 mm Then we take them away from each other 31.5 – 23.5= 8 mm