Starter

1. Find the median of 5 7 11 15 18 21 23

2. Find the median of 11 15 17 20 23 25

3. Calculate the range of 22 25 28 21 15 32

4. Calculate the mode of 5 5 8 1 4 2 1 4 1

Statistical Diagrams

Boxplots

Statistical Diagrams

Why do we use statistical diagrams?Statistical diagrams - are a good way to graphically summarise data - easy to read makes - easy to compare with other data

What types of statistical diagrams is there?Line graph, bar graph, stem and leaf diagram, pie charts, box plots

Box and Whisker Plot

Box and whisker plotsA box and whisker plot is used to display information about the range, the median and the quartiles. It is usually drawn alongside a number line, as shown -

                                                                                 

A box and whisker plot is used to display information about the range, the median and the quartiles

To plot a box plot we need: minimum value, lower quartile (Q1), median, upper quartile (Q3) and the maximum value.

Minimum and maximum Values

Example: What are the maximum and minimumvalues of the following data?

3 3 4 5 5 6 6 7 7 8 8 8 9

Maximum = 9 Minimum = 3

MedianWhen ordered in size the median is the centre number. You can find the placeusing the formula:

Example : Find the median of the data:

6 7 9 13 18 25 27

3 Values 4th term 3 Values

If there is an even number of data values find the average of the two centre valuesExample: Find the median of the data:

12 values

4 4 5 6 8 8 8 9 9 9 10 12

6 Values 6.5th term 6 Values

7 values

Lower Quartile

The lower quartile (Q1) is found by considering only the bottom half ofthe data, below the median. To Find the lower quartile you must findthe median value of this part of the data.

4 4 5 6 8 8 8 9 9 9 10 12

Median3.5th term

3 values 3 values

Upper Quartile

The upper quartile (Q3) is the median of the upper half of the data, above the median. To find the upper quartile it is similar to finding the lower quartile however, this time you use the upper half above the median.

4 4 5 6 8 8 8 9 9 9 10 12

Q1 Median Q3

Inter-quartile Range

Is another measure of the spread of values in the data set.

4 4 5 6 8 8 8 9 9 9 10 12

Inter quartile range = 9 – 5.5 = 3.5

Examples

Example: Find the median and quartiles for the data below.

4 4 5 6 8 8 8 9 9 9 10 12

Median = 8 Lower Quartile = 5.5 Upper Quartile = 9

4 5 6 7 8 9 10 11 12

Example : Find the median and quartiles for the data below.

3 4 4 6 8 8 8 9 10 10 15

3 4 5 6 7 8 9 10 11 12 13 14 15

Example 1: Find the median and quartiles for the data below

and draw the box plot.137 148 155 158 165 166 166 171 171 173 175 180 184 186 186

130 140 150 160 170 180 190cm

Example 2: Find the median and quartiles for the data below

and draw the box plot.2 5 7 11 15 18 21 23 25 25

2 4 6 8 10

12 14 16 18 20 22 24 26

Example 3: Find the median and quartiles and inter-quartile

range for the data below and draw box plot.

3 8 11 15 18 21 25 27 30

Median = 18 Lower Quartile = 9.5 Upper quartile = 26 min = 3 max = 30Semi-quartile range = 26 – 9.5 = 16.5

Example 4: Find the median and quartiles and inter-quartile

range for the data below and draw box plot.

10 15 9 2 12 8 7 1

Median = 8.5 Lower Quartile = 4.5 upper quartile = 11 min = 1 max = 15 Semi-quartile range = 11 – 4.5 = 6.5

1. 5 9 11 12 13 18 22 25

2. 36 35 42 31 28 25 27 21 26

3. 101 105 115 102 103 122 125 131

4. 6 5 2 4 7 9 11 15

5. 85 72 65 64 63 62 61 68