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Statistics

Year 9

Kowhai are small, woody legume trees. Kowhaiwhai patterns are special Maori patterns that are used for decorations and beautiful paintings. The koru and pit au are the most famous sort of designs for kowhaiwhai patterns. At the end of stalks there is normally a circle that resembles a silver fern. Red, black and white is the most common colours in a kowhaiwhai pattern. There are also kowhai trees that are very cool. They have flower like leaves that are a very bright yellow.At the end of stalks there is normally a circle that resembles a silver fern.

Note 1: Statistical DisplaysDot Plots - Symmetry

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

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.

IWB Ex31.02

Pg 863

19

How many journeys were made altogether?

What was the most common number of passengers?

6

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

= 10 × 18°

= 180°

= 90°

= 5 × 18°

= 54°

= 3 × 18°

= 36°

= 2 × 18°

All 20 Students represent all 360°of a pie graph

How many degrees does each student represent?

= 18°

Note 3: Pie Graphs

IWB Ex31.03

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°

× 360°

= 216°

× 360°

= 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 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

What are some of the features of this graph?

# of advertisements

Time

Note 6: Time Series Graph

Each week, roughly the same amount of advertisements are sold

The most popular days to advertise are:

Wednesday & Saturday

The least popular days to advertise are:

Monday & Tuesday

What are some of the features of this graph?

IWB Ex31.06

Pg 884

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

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

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

- Mode – is the most common value, one that occurs most frequently

e.g. Find the mode of the following

Note 7: Calculating Averages

- In statistics, there are 3 types of averages:
- mean
- median
- mode

Mode

Median

Mean - x

The middle value when all values are placed in order

The most common value(s)

Affected by extreme values

Not Affected by extreme values

IWB Ex31.07 Pg 892

Ex31.08 Pg 896

Ex31.09 Pg 901

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 (IRQ) – the difference between the LQ and the UQ. This is a measure of the spread of the middle 50% of the data.

Note 8: Box & Whisker Plot

Comparing data

Male

Female

x

median

minimum

maximum

Upper

quartile

extreme value

Lower

quartile

IQR

Note 8: Frequency Tables

A frequency table shows how much there are of each item. It saves us having to list each one individually.

8

2

4

56, # 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.

0 4 0 3 5 0 5 5 0 2 1

0 5 2 3 0 0 5 5 1 2 5

5 3 0 0 1 5 0 5 1 3 0

The data can be summarised in a frequency table

Note 8: Frequency Tables

IWB Ex31.11

Pg 910

Calculate the mean =

=

=

= 2.3

Why is this mean misleading?

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

Total 33

Note 9: Histograms

When a frequency diagram has grouped data we use a histogram to display it

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

Each student will fit into one of these groups of data

Total 15

Note 9: Histograms

When a frequency diagram has grouped data we use a histogram to display it

Note 9: Histograms

IWB Ex31.12

Pg916

When a frequency diagram has grouped data we use a histogram to display it

Summary: Data Display

Line Graphs – identify patterns & trends over time

Interpolation -

Reading in between tabulated values

Extrapolation -

Estimating values outside of the range

Looking at patterns and trends

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

Summary: Data Display

Pie Graph – show proportion

Multiply each percentage of the pie by 360°

60% - 0.6 × 360° = 216°

Scatter Graph – show relationship between 2 sets of data

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

frequency

Bar Graphs– display discrete data

Distance (cm)

– counted data

– draw bars (lines) with the same width

– 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

3 3 4 8

5

10

9 8 8 3

11

2 3 6 7 8

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

4 2 0

12

1 9 9

3 3

13

0 2

2

14

5

Key: 10 3 means 10.3

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