Cambridge International Mathematics

Analysis of discrete data (Chapter 13) 279

Below is the table forBefore upgrade:

No. of accidents/month Tally Frequency

2 j 1

3 0

4 j 1

5 jjj 3

6 ©jjjj© 5

7 ©jjjj©jjj 8

8 ©jjjj©jj 7

9 ©jjjj© 5

10 ©jjjj© 5

11 j 1

Total 36

Avertical bar chartcould be used to display

this data:

DESCRIBING THE DISTRIBUTION OF A DATA SET

Themodeof a data set is the most frequently occurring value(s). Many

data sets showsymmetryorpartial symmetryabout the mode.

If we place a curve over the vertical bar chart we see that this curve shows

symmetry. We say that we have asymmetrical distribution.

The distribution alongside is said to benegatively skewedbecause, by

comparison with the symmetrical distribution, it has been ‘stretched’ on

the left (or negative) side of the mode.

So, we have:

EXERCISE 13B.1

1 20 students were asked “How many pets do you have in your household?” and the following data was

collected: 21031213400220110101

a What is the variable in this investigation?

b Is the data discrete or continuous? Why?

c Construct a vertical bar chart to display the data. Use a heading for the graph, and add an

appropriate scale and label to each axis.

d How would you describe the distribution of the data? Is it symmetrical, positively skewed or

negatively skewed?

e What percentage of the households had no pets?

f What percentage of the households had three or more pets?

0

1

2

3

4

5

6

7

8

234567891011

number of accidents/month

frequency

Before upgrade

negative side

is stretched

positive side

is stretched

symmetrical distribution negatively skewed distribution positively skewed distribution

mode

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_13\279IGCSE01_13.CDR Thursday, 25 September 2008 4:25:48 PM PETER