Worksheets for Data Analysis

Statistics - Some Common Terms.

“There are lies, damn lies and statistics.” (Mark Twain)
To illustrate the following terms we will consider the case where a die (singular of dice) is rolled ten times with the results: 6, 1, 2, 5, 6, 4, 3, 2, 1, 6.
The frequency of a score is the number of times that score occurs.
The frequency of 6 in the above example is 3 because 6 occurs 3 times.
A frequency distribution table is a table showing the scores in order of size and also the frequency of each score.

Score	Frequency
1	2
2	2
3	1
4	1
5	1
6	3

The cumulative frequency of a score is the total of all scores equal to or less than that score.
The cumulative frequency of 3 is 5 because there are 5 scores equal to 3 or less than three. (1 occurs twice, 2 occurs twice, three occurs once. Total = 5 scores)
The mode is the score that occurs most often.
6 occurs 3 times. This is more often than any other number. Mode = 6
The mean (sometimes called the “arithmetic mean”)is the sum of all the scores divided by the number of scores.
6+1+2+5+6+4+3+2+1+6 = 36 Mean = 3.6
The median is the middle score. Half the scores are above the median and half are below the median.
If there are an odd number of scores then the median is the middle score.
If there is an even number of scores then there are two middle scores. The median is the average of the two middle scores.
If we write the above scores in order we get: 1,1,2,2,3,4,5,6,6,6.
There are ten scores and so put a stroke after the fifth score.
1,1,2,2,3 / 4,5,6,6,6.
Taking the mean of the numbers to the left and right of the stroke gives = 3½
The median is 3½
The range is the difference between the highest and lowest score.
Range = highest score – lowest score.
Range = 6 – 1 = 5

Graphs & Statistics

1. In a particular class there are 30 students. Of these, 15 have brown eyes, 10 have blue eyes and 5 have hazel eyes.
Represent this information in a
(a) sector graph
(b) bar graph
(c) column graph
2. There are 150 students in year 9 at East Mountains Girls High School.
Of these, 50 play softball for sport, 30 play netball, 30 attend aerobics, 20 play tennis, 10 play basketball and 10, for medical reasons, do not play any sport at all.
Represent this information on a
(a) Pictogram
(b) Histogram
(c) Sector Graph
(d) Bar graph
3. Belinda rolled a die (singular of dice) 20 times and the results are shown below.
1 6 5 1 2 4 3 6 2 1 3 1 4 2 2 4 6 5 1 3
(a) Draw a frequency distribution table of these results showing the number on the die, the tally, the frequency and the cumulative frequency.
(b) Determine the mode, median, mean and range of these numbers.
(c) Draw a column graph to represent these results.
4. Kim recorded the maximum temperature (in degrees Celsius) on twenty consecutive days as: 20, 23, 20, 19, 17, 21, 17, 17, 18, 22, 24, 22, 21, 23, 19, 20, 19, 22, 21, 21
(a) Draw a frequency distribution table of these results showing the temperature, the tally, the frequency and the cumulative frequency.
(b) Determine the mode, median, mean and range of these temperatures.
5. Zara and Laura were heating some water during a science experiment.
Laura would call out the time at 1 minute intervals and Zara would read a thermometer that was immersed in the water and write down the temperature.
A table of their results is shown below.

Time in minutes	TemperatureoC
0	15
1	16
2	18
3	21
4	23
5	25
6	28
7	30

Plot these results on a line graph and draw a line of best fit.