11.8.1 Self-Check on Averages

Tick iconExercise 1: Finding the Mean and the Range

Ten children in a class measured how tall they were and want to work out their typical height.

Work out the mean height and range for these 10 children from these measurements:

134 cm, 140 cm, 164 cm, 136 cm, 143 cm, 152 cm, 150 cm, 155 cm, 149 cm, 160 cm.

Solutions icon

Answer

Mean equation left hand side equals right hand side sum of all values divided by number of values
Mean height equation left hand side equals right hand side left parenthesis 134 plus 140 plus 164 plus 136 plus 143 plus 152 plus 150 plus 155 plus 149 plus 160 right parenthesis cm divided by 10 postfix equals 148.3 cm left parenthesis to one d full stop p full stop right parenthesis

So the mean height of children in the class is 148.3 cm (to 1 d.p.).

Range = Highest value – lowest value

          = 164 cm – 134 cm

          = 30 cm

So the range of heights for the 10 children is 30 cm (about 1 foot)!

Tick iconExercise 2: Finding the Median Value

Using the data from exercise 1 work out the median height for the class.

Solutions icon

Answer

Arranging all the values in ascending order:

134, 136, 140, 143, 149, 150, 152, 155, 160, 164

We have 10 values so need to calculate the mean of the middle two to find the median.

So mean of middle two values = 149 cm plus 150 cm divided by two = 149.2 cm.

So the median height for the class is 149.2 cm.

In this case the values are quite close.

Tick iconExercise 3: Finding the Mode or Modal Value

The remaining 10 children in the class were then measured giving a complete set of values.  Find the mode or modal value/s for the height.

134 cm, 140 cm, 164 cm, 136 cm, 143 cm, 152 cm, 150 cm, 155 cm, 149 cm, 160 cm, 134 cm, 144 cm, 147 cm, 150 cm, 154 cm, 162 cm, 144 cm, 142 cm, 153 cm, 130 cm.

Solutions icon

Answer

Arranging the values in ascending order:

130, 134, 134, 136, 140, 142, 144, 144, 143, 147, 149, 150, 150, 152, 153, 154, 155, 160, 162, 164.

So the modal values in this data set are 134 cm, 144 cm and 150 cm since they all occur the most often, in this case twice each.

11.8.2 Self-Check on Bar Charts