It is important to be able to compare data sets because it helps us make conclusions or judgments about the data. For example, say Jim got $\frac{5}{10}$510 in a geography test and $\frac{6}{10}$610 in a history test. Which test did he do better in? Just based on those marks, it makes sense to say he did better in history.
But what about if everyone else in his class got $\frac{4}{10}$410 in geography and $\frac{8}{10}$810 in history? If you had the highest score in the class in geography and the lowest score in the class in history, does it really make sense to say you did better in history?
By comparing the means of central tendency in a data set (that is, the mean, median and mode), as well as measures of spread (range and standard deviation), we can make comparisons between different groups and draw conclusions about our data.
Practice questions
Question 1
The number of goals scored by Team 1 and Team 2 in a football tournament are recorded.
| Match | Team 1 | Team 2 |
|---|---|---|
| A | $2$2 | $5$5 |
| B | $4$4 | $2$2 |
| C | $5$5 | $1$1 |
| D | $3$3 | $5$5 |
| E | $2$2 | $3$3 |
| Match | Team 1 | Team 2 |
|---|---|---|
| A | $2$2 | $5$5 |
| B | $4$4 | $2$2 |
| C | $5$5 | $1$1 |
| D | $3$3 | $5$5 |
| E | $2$2 | $3$3 |
Find the total number of goals scored by both teams in Match C.
What is the total number of goals scored by Team 1 across all the matches?
What is the mean number of goals scored by Team 1?
What is the mean number of goals scored by Team 2?
QUESTION 2
The weights of a group of men and women were recorded and presented in a stem and leaf plot as shown.
| Men | Women |
|
|
|
| Key: | 4 | 2 | $=$= | 42 kg |
Calculate the standard deviation of the group of men, correct to two decimal places.
Calculate the standard deviation of the group of women, correct to two decimal places.
Find the range of the weights for the group of men.
Find the range of the weights for the group of women.
Which group, on average, has the higher variability in weight?
Men
AWomen
B