Five ways to describe data
Smallest, biggest, range, total and mean: they do not all say the same thing.
Boys or girls?
The heights of a Grade 5 class are measured: 17 boys and 11 girls. We want to know who is taller, the boys or the girls.
Which group do you think is taller?
What this lesson covers
The idea
Data can be described and compared by its minimum value, maximum value, total, average, and range (the difference between the maximum and minimum values).
Boys or girls?
The heights of a Grade 5 class are measured: 17 boys and 11 girls. We want to know who is taller, the boys or the girls.
Which group do you think is taller?
- The boys
- The girls
- Cannot say yet
Guess, then look
There are many ways to describe a group of numbers. For each one, guess which group has the bigger value. Then see the numbers.
Different measures, different stories
The smallest and biggest values show the two ends. The range is the difference between them: how spread out the data is. The total adds everything. The mean is the equal-share value.
The boys have the tallest student and the shortest one, and the biggest total, because there are more boys. But the mean says the girls are taller.
Data can be described and compared by its minimum value, maximum value, total, average, and range (the difference between the maximum and minimum values).
- Measure | Boys | Girls
- Minimum | 128 | 136
- Maximum | 158 | 156
- Range | 30 | 20
- Total | 2430 | 1616
- Mean | 142.9 | 146.9
Notes
Data can be described and compared by its minimum value, maximum value, total, average, and range (the difference between the maximum and minimum values).
Check yourself
Yaangba’s family has heights 169, 173, 155, 165, 160 and 164 cm. What is the range of the heights?
Answer: 18
The biggest is 173 and the smallest is 155. 173 − 155 = 18 cm.
One player’s scores range from 20 to 90. Another player’s scores range from 45 to 75. Whose batting is more consistent?
The boys’ total height is 2430 cm and the girls’ is 1616 cm. Why is the boys’ total bigger?
The 11 girls have a total height of 1616 cm. Find their mean height, correct to 1 decimal place.
Answer: 146.9 cm
1616 ÷ 11 = 146.909…, which is 146.9 cm to 1 decimal place.
- The second player: the range 75 − 45 = 30 is smaller than 90 − 20 = 70. — correct. Yes! A small range means the scores stay close together.
- The first player, because the highest score is 90.. The highest score alone does not show consistency. Look at how far apart the scores are.
- Both are equally consistent.. The ranges are different: 70 and 30.
- Boys are taller than girls on average.. The mean says the opposite: the girls’ mean is higher.
- Boys’ heights have a smaller range.. The boys’ range is bigger, 30 against 20. And range does not change the total.
- There are 17 boys but only 11 girls. — correct. Yes! More values give a bigger total, so totals are unfair when group sizes differ.