Starter Any strategies? Identify the tens column first?
Average rainfall, examination marks, height
Class poll of number of letters in first name, pupils answer on individual whiteboards/ show of hands Responses recorded on board Pupils do question 1, exercise 5A, page 51.
Pupils do question 2 of exercise 5A, page 51.
Class hold up there birthdays, responses recorded on board and range calculated A small range would imply that the class are closely centred around certain months, maybe the summer or winter months for example. A large range implies that the class birthdays are spread out throughout the year Pupils do question 3, exercise 5A, page 51
SUMMARY OF WORK DONE IN MODULE I INTERMEDIATE
1) Mode, median, mean and range 2) Pictograms 3) Bar-charts 4) Bar-graphs 5) Tally charts 6) Grouped Data and bar charts 7) Frequency polygons 8) Data in Tables 9) Pie charts SUMMARY OF WORK COVERED SO FAR
Mode, Median and Range Aim : To find the mode, median and range, and the modal class for grouped data.
Averages(mean) An average is a useful statistic because it represents a whole set of values by just a single or typical value. <ul><li>Where have you heard the word average before? </li></ul><ul><li>Where have you seen it used? </li></ul>
The Mode <ul><li>The mode is a type of average </li></ul><ul><li>The mode is the value that occurs most often in a set of data </li></ul><ul><li>Example </li></ul>5, 6, 8, 2, 4, 5, 3, 5 MODE = 5 Sometimes there is no mode because either all the values are different, or no single value occurs more often than other values
<ul><li>What letter does your first name begin with? </li></ul>What is the mode first letter for a name in class 7Y2? F P W T H THE MODE DOESN’T HAVE TO BE A NUMBER
The Median <ul><li>The median is another type of average </li></ul><ul><li>The median is the middle value for a set of data when the values are put in numerical order. </li></ul>Example 6, 8, 3, 7, 5, 2, 4 in order 2, 3, 4, 5, 6, 7, 8 Median = 5 For an odd number of values in data set, there is only one middle value. This is the median.
What is the median test score for the following set of results? 5, 7, 7, 8, 10, 12, 14, 15 For an even number of values in a data set, there are two middle values. The median is the value in the middle of these two values. Median = 9
The Range <ul><li>The range is not an average. </li></ul><ul><li>The range of a set of data is the largest value minus the smallest value. </li></ul><ul><li>It shows how the data is spread out. </li></ul>A small range shows that the values in a set of data are similar in size A large range shows that the values differ considerably
Find the range: What number month were you born in? Range = Largest number – smallest number Range = What does this tell us about the birthdays of class 7Y2? For example, January = 1, June = 6, and December = 12
Modal Class For grouped data such as the example below, we cannot find the mode. Instead, we find the MODAL CLASS. This is the group that occurs most often. Modal class = 3-5 Why isn’t it possible to calculate an exact mode or median from grouped data? Frequency Time (Mins.) 1 9-11 3 6-8 4 3-5 2 0-2
Write down: 5 numbers with a mode of 7 7 numbers with a median of 3 7 numbers with a mode of 6 and a median of 12 7 numbers with a mode of 5, median of 8, and a range of 10
Pie Charts Be able to construct a pie chart from a collection of data, using a protractor.
Makes of car in a school car park Construct a pie chart to show this information. A full circle is 360 o There are a total of 3+2+4+1 = 10 cars We use 36 o to represent each car 360 o 1 4 2 3 Frequency Volvo Rover Ford Cavalier Make
Work out the missing numbers on this number spider ÷ 30 ÷ 12 ÷ 24 ÷ 20 ÷ 10 ÷ 15 ÷ 90 ÷ 4 360 12 30 15 18 36 24 4 90
Makes of car in a school car park We use 36 o to represent each car so the 3 Cavaliers are represented by 3x36 o = 108 o Work out the angle needed for each of the other models of car 3x36 o =108 o 2x36 o =72 o 4x36 o =144 o 1x36 o =36 o Angle in pie chart 1 4 2 3 Frequency Volvo Rover Ford Cavalier Make
Makes of car in a school car park Mark the centre of the pie and draw the circle. Draw a line from the centre to the edge Measure the first angle needed ( 108 o ) Draw in the line and label the section 108 o Cavalier 36 o 144 o 72 o 108 o Angle Volvo Rover Ford Cavalier Make
Makes of car in a school car park From this line measure the next angle, draw the line and label the section. Continue in this way Check that the last section has the correct angle and label it. 72 o Cavalier Ford 144 o Rover 36 o Volvo 36 o 144 o 72 o 108 o Angle Volvo Rover Ford Cavalier Make
Why? <ul><li>Why do we use 36 o to represent 1 car? </li></ul><ul><li>What would happen if there were 20 cars? </li></ul><ul><li>What about 60 cars? Or 15 cars? </li></ul><ul><li>If there were 20 cars in your survey, what angle would you use to represent 4 cars? 7 cars? 12 cars? </li></ul>
<ul><li>Q1 A survey of how 30 pupils got to school </li></ul><ul><li>Q2 How Cameroon spent his £40 birthday money </li></ul><ul><li>Q3 Who is your favourite Telly-Tubby survey. </li></ul>Construct Pie charts questions 3 7 5 15 Frequency Bus Car Cycle Walk Method £6 £9 £19 £6 Amount Cinema Books Clothes Games How 40 18 20 12 Frequency Po La-La Dipsy Tinky-Winky Telly-Tubby
Interpreting Pie Charts <ul><li>20 pupils in class 3B travel to school. From the chart find the number of pupils who travel by each method. </li></ul><ul><li>Walk = </li></ul><ul><li>Cycle = </li></ul><ul><li>Bus = </li></ul>
180 boys in year 5 chose their favourite sport. From the chart find how many chose each sport.
300 passengers boarded a train in London. From the chart find how many are travelling to each destination.
150 packets of crisps were sold from a vending machine. From the chart find the number for each flavour. Find also the percentage for each.