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

$Marge$ grows two different types of bean plants. She records the number of beans that she picks from each plant for $10$10 days. Her records show:

Plant $A$A: $10,4,4,5,7,10,3,3,9,10$10,4,4,5,7,10,3,3,9,10

Plant $B$B: $8,7,5,5,9,7,8,7,5,6$8,7,5,5,9,7,8,7,5,6

What is the mean number of beans picked per day for Plant $A$A? Leave your answer to one decimal place if needed.
What is the mean number of beans picked per day for Plant $B$B?
What is the range for Plant $A$A?
What is the range for Plant $B$B?
Which plant produces more beans on average?
$Plant B$
A
$Plant A$
B
Which plant has a more consistent yield of beans?
Plant A
A
Plant B
B

Question 2

The residents of two blocks of townhouses were asked the number of pets they own. The frequency of various responses are presented in the line plots.

According to the data, which of the following statements are true?

Pet ownership is a little lower in block $A$A.
True
A
False
B
In block $A$A, most households have zero or one pet.
True
A
False
B
In block $B$B, most households have three or more pets.
True
A
False
B
In block $A$A, pet ownership is skewed negatively.
True
A
False
B
Pet ownership ranges from $0$0 to $3$3 pets in block $A$A.
True
A
False
B
There is more variability in the block $B$B distribution.
True
A
False
B
Both sets of scores have an outlier.
True
A
False
B

Question 3

Student X scored $86,83,86,88,98$86,83,86,88,98 and

Student Y scored $61,83,50,85,83$61,83,50,85,83 across 5 exams.

Find the mean score of Student X, writing your answer as a decimal.
Find the mean score of Student Y
Find the standard deviation of the scores for Student X, correct to two decimal places.
Find the standard deviation of the scores for Student Y, correct to two decimal places.
Which student performed better?
Student X
A
Student Y
B
Which student performed more consistently?
Student X
A
Student Y
B

Outcomes

12D.D.2.5

Interpret statistical summaries to describe the characteristics of a two-variable data set and to compare two related two-variable data sets; describe how statistical summaries can be used to misrepresent two-variable data; and make inferences, and make and justify conclusions, from statistical summaries of two-variable data orally and in writing, using convincing arguments

Comparing Sets of Data (includes boxplot)