Revise the statistical measures

mean, median, mode range, upper and lower quartiles, interquartile range

displays (graphs) which are good for showing these measures

Learning Intention

Please write this in your notes book

Find the mean of the numbers 4, 0, 3, 11 and 6.

x5

611304

524

8.4

Add up and divide by the number of scores.

Find the median of these sets of numbers:a 4, 8, 3, 11, 6b 3, 5, 7, 4, 9, 2c 4, 7, 7, 3, 9, 8

a 3, 4, 6, 8, 11 First put the numbers in order.Work in from the ends to find the middle.

The median is 6

b First put the numbers in order.Work in from the ends to find the middle.The median is half way between 4 and 5.

2, 3, 4, 5, 7, 9

The median is 4.5

c First put the numbers in order.Work in from the ends to find the middle.

The median is 7

3, 4, 7, 7, 8, 9

There are two middle numbers, both of which are the same.

There are two modes, 8 and 9.

Find the mode of these sets of numbers:a 6, 9, 4, 5, 7, 2, 7, 5, 7, 3b 8, 9, 3, 8, 9, 4, 7c 6, 12, 11, 9, 10

a 6, 9, 4, 5, 7, 2, 7, 5, 7, 3 Which number is most common?

b 8, 9, 3, 8, 9, 4, 7 Which number is most common?

Which number is most common?c 6, 12, 11, 9, 10

There is no mode.

The mode is 7.

Calculate the range of the numbers 10, 20, 2, 25, 11, 18, 23.

The largest value

The smallest value

Range

= 25

= 2

= 25 – 2

= 23

Find the lower and upper quartiles for each of 12 14 17 20 21 21 21 26

20.5The median is

12 14 17 20 21 21 21 26

12, 14, 17, 20The low group is which has a median of 15.5

Find the median.

Find the median of the lower group.

21, 21, 21, 26The high group is which has a median of 21Find the median of the high group.

LQ = 15.5

UQ = 21The interquartile range

= 5.5

= 21 – 15.5

Find the lower and upper quartiles for each of 0 2 3 5 6 8 9 9 10 12

7The median is

0, 2, 3, 5, 6The low group is which has a median of 3

Find the median.

Find the median of the lower group.

8, 9, 9, 10, 12The high group is which has a median of 9Find the median of the high group.

LQ = 3

UQ = 9

0 2 3 5 6 8 9 9 10 12

IQR

= 6

= 9 - 3

Find the lower and upper quartiles for each of 45 47 52 61 77

52The median is

45, 47The low group is which has a median of 46

Find the median.

Find the median of the lower group.

61, 77The high group is which has a median of 69Find the median of the high group.

LQ = 46

UQ = 69

45 47 52 61 77

Discard 52 so that the remaining numbers form two equal groups.

IQR

= 23

= 69 - 46

What display types (graphs) could you use to display the

Median, Range, UQ, LQ and IQR ?

Think, pair, share

Box Plot vs Dot Plot per FT p.129 RHS

Geogebra

Box plots (comparison)

Mean vs median vs spread

Box Plot vs Histogram per FT p.128 RHS not really covered

This exercise is to be completed on refill and handed in for marking.

Using the Graphics Calculator to find statistics 

Use the Graphics calculator to find the median, range, upper quartile, lower quartile and inter-quartile range. Main menu: StatDelete lists: (F6), DEL-A (F4), YES (F1) (just in case there is already data there)

Enter data into list: data value, EXE (after each data value)

Calculate statistics: > (more options) (F6), CALC (F2), SET (F6) (check for top option 1VAR XList: List 1) 1VAR (F1) The symbols for:Median = Med Range = maxX—minXlower quartile = Q1 upper quartile = Q3inter-quartile range = Q3—Q1

 

Using the Graphics Calculator to graph statistics 

Once you have the five point summary, use the GC to graph  Main menu: Stat The data and stats are is still there

Graph Statistics GRPH (F1), SET (F6), down arrow to Graph Type Select Box (may need to > for more options) EXE GPH1 will display box and whisker