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10.1 Calculating statistics

10.1 Calculating statistics

You can use statistics to summarise sets of data. The mode is the most common value or number.

You can also use them to compare di#erent sets The median is the middle value, when they are
of data. listed in order.
You should already be able to calculate three The mean is the sum of all the values divided by

di#erent averages: the mode, the median and the number of values.
the mean. The range is the largest value minus the smallest.
Remember that the range is not an average. It
measures how spread out a set of values or numbers is.
A frequency table is any table that
For a large set of data, it is not practical to list every number records how often (frequently) data
separately. Instead, you can record the data in a frequency table.
values occur.

Worked example 10.1
The table shows the number of beads Number of beads 25 30 35 40 45 50
on 200 necklaces. Frequency 34 48 61 30 15 12
a Find the mode.
b Find the mean.
c Find the range.

a The mode is 35. The mode is the number with the highest frequency.
b 6900 ÷ 200 = 34.5 (25 × 34 + 30 × 48 + 35 × 61 + 40 × 30 + 45 × 15 + 50 × 12) ÷ the
sum of all the frequencies. This is a reasonable answer because it is
near the middle of all the possible number of beads.
c 50 − 25 = 25 This is the difference between the largest and smallest number of
beads.

) Exercise 10.1

1 These are the times (in minutes) that eight students took to walk to school.
a Calculate: i the median time ii the mean time iii the range. 10, 12, 15, 18, 24, 25, 30, 35
There is an error in the times given in part a. The 35 should be 53.
b Correct the values for: i the median time ii the mean time iii the range.
2 Find the modal age for each set of data.
a The ages of the members of a fitness class

57, 56, 51, 59, 51, 56, 58, 58, 51, 53, 50, 51, 54, 51

b The ages of a group of children

Age (years) 10 11 12 13 14
Frequency 5 12 13 17 20

3 Find the median age for each group in question 2.

98 10 Processing and presenting data