Statistics Year 9

Note 1: Statistical Displays

IWB Ex Pg 859 IWB Ex Pg Oliver Sally and Mark (with 4 each)

Note 1: Statistical Displays

Note 2: Dot Plots A dot plot uses a marked scale Each time an item is counted it is marked by a dot

Dot Plots - Symmetry A symmetric distribution can be divided at the centre so that each half is a mirror image of the other.

Dot Plots - Skewness

Dot Plots - Outliers A data point that diverges greatly from the overall pattern of data is called an outlier.

Dot Plots e.g. This graph shows the number of passengers on a school mini bus for all the journeys in one week. How many journeys were made altogether? What was the most common number of passengers? 19 6 IWB Ex Pg 863 IWB Ex Pg 863

Note 3: Pie Graphs

Pie Graphs are used to show comparisons ‘Slices of the Pie’ are called sectors Skills required: working with percentages & angles e.g. 20 students in 9Ath come to school by the following means: 10 walk 5 Bus 3 Bike 2 Car Represent this information on a pie graph.

Note 3: Pie Graphs e.g. 20 students in 9Ath come to school by the following means: 10 walk 5 Bus 3 Bike 2 Car All 20 Students represent all 360° of a pie graph How many degrees does each student represent? = 18° = 10 × 18° = 5 × 18° = 3 × 18° = 2 × 18° = 180° = 90° = 54° = 36°

Note 3: Pie Graphs IWB Ex Pg 870 IWB Ex Pg 870 We can also use percentages and fractions to calculate the angles e.g. 500 students at JMC were surveyed regarding their TV provider at home. 180 had Skyview, 300 had Freeview and 20 had neither. Represent this in a pie chart. × 360° = 129.6° = 216° = 14.4°

Note 4: Stem & Leaf Graphs Daily absences from JMC for a six week period in Term 3 are as follows:

Note 4: Stem & Leaf Graphs Daily absences from JMC for a six week period in Term 3 are as follows: These figures can be summarized in a stem and leaf graph

Note 4: Stem & Leaf Graphs

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Note 5: Scatter Plot Eg: this has a positive relationship – the taller the person the longer they can jump IWB Ex Pg 879 IWB Ex Pg 879 Scatter Plots show the relationship between two sets of data.

Note 6: Time Series Graph This ‘line graph’ shows what happens to data as time changes Time is always on the x-axis Data values are read from the y axis Time # of advertisements What are some of the features of this graph?

Note 6: Time Series Graph Each week, roughly the same amount of advertisements are sold The most popular days to advertise are: What are some of the features of this graph? Wednesday & Saturday The least popular days to advertise are: Monday & Tuesday IWB Ex Pg 884 IWB Ex Pg 884 IWB Ex Pg 879 IWB Ex Pg 879

Calculating Statistics - averages Mean (average) – The mean can be affected by extreme values Median – middle number, when all data is placed in order. Not affected by extreme values Mode – the most common value/s

Note 7: Mean Mean (average) – The mean can be affected by extreme values x =

Median – middle number, when all the number are placed in order. Not affected by extreme values Note 7: Median

Median – middle number, when all the number are placed in order. Not affected by extreme values Note 7: Median

Mode – is the most common value, one that occurs most frequently Note 7: Mode e.g. Find the mode of the following

Note 7: Calculating Averages In statistics, there are 3 types of averages: mean median mode Mean - x Median The middle value when all values are placed in order The most common value(s) Mode Affected by extreme values Not Affected by extreme values IWB Ex Pg 892 Ex Pg 896 Ex Pg 901 IWB Ex Pg 892 Ex Pg 896 Ex Pg 901

Starter 1. Calculate the mean for each of the following: a) 4, 8, 12, 4, 1, 1 b) 40, 50 c) 21, 0, 19, Ten numbers add up to 89, what is their mean 3. Calculate the mean to 2dp a) 84, 31, 101, 6, 47, 89, 49, 55, 111, 39, 98 b) 1083, 417, 37.8, A rowing ‘eight’ has a mean weight of kg. Calculate their combined weight 5. A rugby pack of 8 schoolboy players with a mean weight of 62kg is pushing against a pack of 6 adult players with a mean weight of 81kg. Which pack is heavier? Explain why?

Note 8: Frequency Tables A frequency table shows how much there are of each item. It saves us having to list each one individually , # of houses

Note 8: Frequency Tables How would you display this information in a graph?

Note 8: Frequency Tables Tables are efficient in organising large amounts of data. If data is counted, you can enter directly into the table using tally marks e.g 33 students in 10JI were asked how many times they bought lunch at the canteen. Below is the tally of individual results # of timesTallyFrequency, f 0IIII IIII I11 1IIII4 2III3 3IIII4 4I The data can be summarised in a frequency table

Note 8: Frequency Tables Calculate the mean = # of timesTallyFrequency, f 0IIII IIII I11 1IIII4 2III3 3IIII4 4I Why is this mean misleading? = Total 33 = = 2.3 Most students either do not buy their lunch at the canteen or buy it there every day. IWB Ex Pg 910 IWB Ex Pg 910

Starter 1. Write down the median of each of these sets of numbers a) {12, 19, 22, 28, 31} b) {0, 6, 9, 11, 19, 20} 2. Write down the mode foe each of these sets of numbers a) {6, 8, 9, 9, 10, 6, 7, 9, 8} b) {4, 6, 8, 6, 4, 8} c) {3, 1, 0, 1, 5, 0, 6} 3. A roadside stall has some avocados for sale at $2 a bag. These are the coins in the ‘honesty’ box on Tuesday. 5 x 20c coins 2 x 50c coins 2 x $1 coins 1 x $2 coins a) what is the median of the coins b) on Wednesday there were 24 coins in the box. The mean value of the coins was 25cents. Which gives better information about the number of bags sold – the mean or the median No mode Two modes are 0 and 1 The mean gives information about the total sold: 24 x 25cents = $6. 3 bags were sold 35 cents

Note 9: Histograms When a frequency diagram has grouped data we use a histogram to display it - measured data (e.g. Height, weight)

Note 9: Histograms When a frequency diagram has grouped data we use a histogram to display it

Note 9: Histograms When a frequency diagram has grouped data we use a histogram to display it IWB Ex Pg 916 IWB Ex Pg 916

Calculating Statistics Range – a measure of how spread out the data is. The difference between the highest and lowest values. Lower Quartile (LQ) – halfway between the lowest value and the median Upper Quartile (UQ) – halfway between the highest value and the median Interquartile Range (IQR) – the difference between the LQ and the UQ. This is a measure of the spread of the middle 50% of the data.

Example: e.g. 40, 41, 42, 43, 44, 45, 49, 52, 52, 53 medianUQ Range = Maximum – Minimum = 53 – 40 = 13 IQR (Interquartile Range) = UQ – LQ = 52 – 42 = 10

The five key summary statistics are used to draw the plot. Note 10: Box and Whisker Plots Minimum LQ Median UQ Maximum

Note 10: Box & Whisker Plot Comparing data Male Female minimum Lower quartile median Upper quartile maximum IQR x extreme value

e.g. The following data represents the number of flying geese sighted on each day of a 13-day tour of England Find: a.) the min and max number of geese sighted b.) the median c.) the mean d.) the upper and lower quartiles e.) the IQR f.) extreme values Min – 1 Max - 18 Order the data - 4 Add all the numbers and divide by 13 – 4.62 (2 dp) LQ – = LQUQ UQ – = – 2 =

Note 11: Quartiles e.g. Calculate the median, and lower and upper quartiles for this set of numbers Arrange the numbers in order median LQUQ Median – halfway between 49 and 78, i.e. = 63.5 LQ – bottom half has a median of UQ – top half has a median of 89

Starter

Summary: Data Display Line Graphs – identify patterns & trends over time Interpolation - Extrapolation - Reading in between tabulated values Estimating values outside of the range Looking at patterns and trends

Summary: Data Display Pie Graph – show proportion Scatter Graph – show relationship between 2 sets of data Multiply each percentage of the pie by 360° 60% × 360° = 216° Plot a number of coordinates for the 2 variables Draw a line of best fit - trend Reveal possible outliers (extreme values)

Summary: Data Display Histogram – display grouped continuous data – area represents the frequency Bar Graphs – display discrete data – counted data – draw bars (lines) with the same width frequency Distance (cm) – height is important factor

Summary: Data Display Stem & Leaf – Similar to a bar graph but it has the individual numerical data values as part of the display – the data is ordered, this makes it easy to locate median, UQ, LQ Key: 10 3 means 10.3 Back to Back Stem & Leaf – useful to compare spread & shape of two data sets