From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

Just an Average Worksheet

1. Given are two pieces of writing from different sources.

Writing Selection 1

(from The Three Little Pigs)

Writing Selection 2

(from a year 10 textbook)
The little pig makes a good house.

It has a red roof.

He is pleased with it.

I can play in this house he says.

The big bad wolf can not get me.

"Not I," said the pig.

 A train makes only two stops after its starting point.

At the first stop, one third of the passengers get off and twenty new passengers get on.

At the second stop, the remaining sixty passengers get off.

How many passengers were there originally?

One method of comparing the difficulty level in two pieces of writing is by comparing the word lengths (ie number of letters in each word).

a. Construct frequency tables from the data.
b. For each piece of writing construct a stemplot of the word length. Use the same scale for each stemplot to make comparisons easier.
c. Use your stemplot to decide if the mean or median is a better choice for locating the centre of the data. Justify your decision.
d. Calculate the centre of the data for each piece of writing. Briefly summarise your findings.

 

2. Another method of measuring the reading level of a piece of writing is counting the number of words per paragraph. On the right are two random samples of size n=27 from two different Queensland science textbooks, and on the left is some output on these datasets from NCSS Jr.

Use the stemplots to help you decide which measures of summary statistics to use. Justify your choice. Comment on the differences in the reading levels for these two books.
Year 9 Science

Mean: 42.3
Standard Deviation: 21.3
Median: 45
IQR: 34

Stem-Leaf Plot Section of Year 9 Science

1 | 3 4 7 8
2 | 1 2 2 3 7
3 | 0 1 9
4 | 0 5 5 5 5
5 | 1 1 3 6 6
6 | 0 8
7 |  
8 | 3 3 4

Unit = 1
Example: 1 |2 Represents 12

 Senior Biology

Mean: 81.4
Standard Deviation: 31.0
Median: 76
IQR: 41

Stem-Leaf Plot Section of Senior Biology

3 | 2 9
4 | 1 9
5 | 8
6 | 0 2 3 4
7 | 2 2 3 5 6
8 | 0 1 2 6 7 7
9 |  
10 | 3 6 7 8
11 |  
12 | 0
High | 146, 168

Unit = 1
Example: 1 |2 Represents 12

Year 9 Science

17
51
45
31
30
51
23
45
60
56
83
56
21
53
45
18
13
22
39
68
27
45
83
40
22
84
14

Senior Biology

63
82
120
87
73
64
108
32
49
41
72
80
106
62
103
60
75
39
58
86
76
107
146
81
72
168
87

 

3. The Australian Bureau of Meterology collects data on rainfall across Australia. Given below is the mean monthly rainfall in Broken Hill as well as the median monthly rainfall.

Average Monthly Rainfall in Broken Hill
(in millimetres) 1900 to 1990

Month

Mean

Median

Jan

23

9

Feb

24

10

Mar

18

9

Apr

19

9

May

22

13

Jun

22

15

Jul

17

15

Aug

19

17

Sep

20

12

Oct

25

15

Nov

19

10

Dec

20

7
a. Note that the median monthly rainfall is January is much smaller than the mean monthly rainfall. What does this imply about the shape of the distribution of the rainfall data for the month of January?
b. Which measure of central tendency, the mean or the median, is more appropriate for describing rainfall in Broken Hill? Justify your answer using knowledge of mean and median.
c. Use the above table to calculate the total yearly rainfall for Broken Hill.
d. In the north of Australia, the wet season occurs from November to April. Broken Hill, in central Australia, is to occasionally drenched by a northern storm during these months. These storms tend drop a large amount of rain in a comparatively short time. How does the table reflect this fact?