Presentation of Data

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Statistics Units

Grouped and ungrouped data may be presented as :

Pie Charts
Frequency Histograms
Frequency Polygons
Ogives
Boxplots

This page will not attempt to introduce any other forms of statistical representation.

Examples

Example 1

Survey results of the ages of students in the Adult Basic Education maths classes are shown in this frequency table.

Age Interval(yrs) Frequency

15-19 13

20-24 15

25-29 20

30-34 10

35-39 8

40-44 4

Use this data to produce a frequency histogram.

Example 2

Use the chart above and include a cumulative frequency column. From this draw an ogive graph. Use the graph to find the median, lower quartile, upper quartile and lowest and highest value.
Draw a box-plot.

Age Interval(yrs) Frequency Cumulative frequency

15-19 13 13

20-24 15 28

25-29 20 48

30-34 10 58

35-39 8 66

40-44 4 70

Lowest Value: 15
Highest Value: 44

        Five-number summary
         Lowest value:    15
         25% Quartile:   21
         50% Quartile(median)   26
         75% Quartile:   36
         Highest value:    44

Box Plot

Have a Go

Problem 1

Pie Chart

Students in an Adult School were surveyed about the type of transport they use to travel to school.
The results were:
walking 9, train 10, tram 6, car 12, bicycle 3.
Construct a pie chart with this information.

Problem 2

Ogive

Age in years of twenty secondary school students visiting the zoo on a weekday were recorded.The results were:
12, 16, 10, 19, 17, 10, 10, 11, 11, 11, 11, 12, 12, 11, 12, 13, 12, 14, 15, 18
(i) Find the lowest and highest values.
(ii) Construct a frequency table           including a cumulative frequency column
(iii) Calculate the mean age of school students visiting the zoo.
(iv) Construct an ogive and find
        a) the median age
        b) the interquartile range of ages.

Practice Questions

Question 1

Consumers were asked to rate the taste of a new diet drink as being poor (P), good (G), excellent (E). The following data were obtained:

G	P	G	E	G	G	E	P	G	G
E	G	E	P	E	E	G	P	G	G
P	G	G	E	E

(i) Construct a frequency table.
(ii) Add a relative frequency table to the table.

Click to See Answer

Question 2

A doctor's office has studied the waiting times for patients who arrive at the office with a request for emergency service. The followong data were collected over a 1-month period (the waiting times are in minutes):
2, 5, 10, 12, 4, 4, 5, 17, 11, 8, 9, 8,12, 21, 6, 8, 7, 13, 18, 3

(i) Find the minimum value, first quartile, median, third quartile and maximum value for the data values.
(ii) What proportion of patients needing emergency service have a waiting time of less than 10 mniutes?

Click to See Answer

Question 3

The price of houses sold at auction on a particular day in two Melbourne suburbs is as follows:

Williamstown($'s)	Deerpark($'s)
165,000	120,000
365,000	98,000
265,000	102,000
150,000	95,000
180,000	89,000
245,000	105,000
398,000	130,000
234,000	108,000
195,000	96,000
155,000	110,000

(i) Compare the median house price in Williamstown with that in Deerpark.
(ii) Find the mean house price for both suburbs.
(iii) Which is a better measure of house prices: mean or median?

Click to See Answer

Question 4

Primary students from a northern Melbourne primary school were surveyed about which team in the AFL they support. The results were as follows:
Carlton 18, Collingwood 20, Essendon 30,
North Melbourne 12, other 10.
Construct a pie chart with this information.

Click to See Answer

Solution 1
Pie Chart

Transport
Type Number of
Students Percentage of students preferring transport type Angle size for PieChart

walking 9 22.5% of 360� = 81�

train 10 25 % of 360� = 90�

tram 6 15 % of 360� = 54�

car 12 30 % of 360� = 108�

bicycle 3 7.5 % of 360� = 27�

Total Student Population = 40

back to Have a Go

Solution 2
Ogive

Lowest value: 10 years
Highest value: 19 years

Age of students(years) attending zoo Tally Cumulative Frequency Total number of students

10 3 3 3 x 10 = 30

11 5 8 5 x 11 = 55

12 5 13 5 x 12 = 60

13 1 14 1 x 13 = 13

14 1 15 1 x 14 = 14

15 1 16 1 x 15 = 15

16 1 17 1 x 16 = 16

17 1 18 1 x 17 = 17

18 1 19 1 x 18 = 18

19 1 20 1 x 19 = 19

Total = 20 Total =237

Median age (50th percentile) = 11.2 years
25th percentile = 10.5 years
75th percentile = 14.0 years

Interquartile range = 14.0-10.5

back to Have a Go

Answer to Practice Question 1

Rating of Drink	Frequency	Relative Frequency
P	5	0.2
G	12	0.48
E	8	0.32
Total	25	1.0

Return to Practice Questions

Answer to Practice Question 2

        2 3 4 4 5 | 5 6 7 8 8   | | 8 9 10 11 12   | 12 13 17 18 21
                            Q1                     Q2                           Q3
         Minimum Value: 2
        Q1 25% quartile: 5
        Median 50% quartile: 8
        Q3 75% quartile: 12
        Maximum Value: 21

The number of patients with waiting time of less than 10 minutes is 12.

Return to Practice Questions

Suburb	Williamstown	Deerpark
Median	$214,500	$103,500
Mean	$235,200	$105,00