statistics year 9. note 1: statistical displays

StatisticsYear 9

Note 1: Statistical Displays


IWB Ex 31.01 Pg 859

3

Oliver

Sally and Mark (with 4 each)

Note 2: Dot PlotsA dot plot uses a marked scaleEach time an item is counted it is marked by a dot

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

Dot Plots - Skewness

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

Dot Plotse.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?

196

IWB Ex 31.02 Pg 863

Note 3: Pie Graphs

Note 3: Pie GraphsPie 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 Graphse.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?20

360= 18°

= 10 × 18°= 5 × 18°= 3 × 18°= 2 × 18°

= 180° = 90° = 54° = 36°

Note 3: Pie GraphsIWB Ex 31.03 Pg 870We 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.

500180

500300

50020

× 360°

× 360°

× 360°

= 129.6°

= 216°

= 14.4°

TV Providers of JMC students

OtherFreeviewSkyview

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

Note 4: Stem & Leaf GraphsDaily 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

Note 4: Stem & Leaf Graphs

IWB Ex 31.04 Pg 875

Note 5: Scatter Plot

Eg: this has a positive relationship – the taller the person the longer they can jump

IWB Ex 31.05 Pg 879Scatter Plots show the relationship between two sets of

data.

Note 6: Time Series GraphThis ‘line graph’ shows what happens

to data as time changesTime is always on the x-axisData values are read from the y axis

Time

# o

f adv

ertis

emen

ts What are some of the features of this graph?

Note 6: Time Series GraphEach week, roughly the same

amount of advertisements are soldThe 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 31.06 Pg 884

IWB Ex 31.05 Pg 879

Calculating Statistics - averagesMean (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: MeanMean (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

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 AveragesIn statistics, there are 3 types of averages:

• mean• median• mode

valuesofnumber total values theall of sum

Mean - x MedianThe 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 31.07 Pg 892 Ex 31.08 Pg 896 Ex 31.09 Pg 901

Starter1. Calculate the mean for each of the following:

a) 4, 8, 12, 4, 1, 1b) 40, 50c) 21, 0, 19, 20

2. Ten numbers add up to 89, what is their mean3. Calculate the mean to 2dp

a) 84, 31, 101, 6, 47, 89, 49, 55, 111, 39, 98b) 1083, 417, 37.8, 946

4. A rowing ‘eight’ has a mean weight of 86.375kg. 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.

824

56, # of houses

Note 8: Frequency Tables

How would you display this information in a graph?

Note 8: Frequency TablesTables are efficient in organising large amounts of data. If data is counted, you can enter directly into the table using tally markse.g 33 students in 10JI were asked how many times

they bought lunch at the canteen. Below is the tally of individual results.

0 4 0 3 5 0 5 5 0 2 10 5 2 3 0 0 5 5 1 2 55 3 0 0 1 5 0 5 1 3 0

# of times

Tally Frequency, f

0 IIII IIII I 111 IIII 42 III 33 IIII 44 I 15 IIII IIII 10

The data can be summarised in a frequency table

Note 8: Frequency TablesCalculate the mean =

# of times

Tally Frequency, f

0 IIII IIII I 111 IIII 42 III 33 IIII 44 I 15 IIII IIII 10

Why is this mean misleading?

valuesofnumber total values theall of sum

3310514433241110

=

Total 33

3376

= = 2.3

Most students either do not buy their lunch at the canteen or buy it there every day.

IWB Ex 31.11 Pg 910

Starter1. 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 numbersa) {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 coinsa) what is the median of the coinsb) 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.

22

10

9No 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: HistogramsWhen a frequency diagram has grouped data we use a histogram to display it

- measured data (e.g. Height, weight)


IWB Ex 31.12 Pg 916

Calculating StatisticsRange – 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

medianLQ UQ

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

minimumLower 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

5 1 2 6 3 3 18 4 4 1 7 2 4Find:

a.) the min and max number of geese sightedb.) the medianc.) the meand.) the upper and lower quartilese.) the IQRf.) extreme values

Min – 1Max - 18

Order the data - 4Add all the numbers and divide by 13 – 4.62 (2 dp)

LQ – 2 + 2 = 2

1 1 2 2 3 3 4 4 4 5 6 7 18LQ UQ

UQ – 5 + 6 = 5.52 25.5 – 2 = 3.518

Note 11: Quartilese.g. Calculate the median, and lower and upper quartiles for this set of numbers

Arrange the numbers in order 35 95 29 95 49 82 78 48 14 92 1 82 43 89

medianLQ UQ

Median – halfway between 49 and 78, i.e. = 63.5 LQ – bottom half has a median of 35

1 14 29 35 43 48 49 78 82 82 89 92 95 95

27849

UQ – top half has a median of 89

Starter

Summary: Data DisplayLine Graphs – identify patterns & trends over time

Interpolation - Extrapolation -

Reading in between tabulated valuesEstimating values outside of the rangeLooking at patterns and trends

0123456

0 1 2 3 4 5 6 7 8 9 10 11

Summary: Data DisplayPie Graph – show proportion

Scatter Graph – show relationship between 2 sets of data

Multiply each percentage of the pie by 360°

Sales

60%

60% - 0.6 × 360° = 216°

0.5 1 1.5 2 2.5 3012345Plot a number of coordinates

for the 2 variablesDraw a line of best fit - trendReveal possible outliers (extreme values)

Summary: Data DisplayHistogram – display grouped continuous data

– area represents the frequency

Bar Graphs – display discrete data – counted data

– draw bars (lines) with the same width

0246

freq

uenc

y

Distance (cm)

Blue Red Green White0

5

10

15 – 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

1011121314

3 3 4 82 3 6 7 81 9 90 25

Key: 10 3 means 10.3

Back to Back Stem & Leaf – useful to compare spread & shape of two data sets

59 8 8 3

4 2 03 3

2

statistics year 9. note 1: statistical displays

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