Unit 18 Section 4 : Comparing Data

In this section we consider how averages and the range can be used to compare sets of data.

Example Questions

Example Question 1
The two line diagrams below illustrate data that was collected about the scores of two groups of children in a short test.

(a) What is the mode for group A?

(b) What is the mode for group B?

(c) What is the range for group A?

(d) What is the range for group B?

(e) Which class did worse in the test?

(f) Which class had more varied results?


 
Example Question 2
Kathryn plants two different types of tomato plant. She records the number of tomatoes that she picks from each plant every day for 10 days. Her records are shown below:

(a) Calculate the mean for Plant A

(b) Calculate the mean for Plant B

(c) Calculate the range for Plant A

(d) Calculate the range for Plant B

(e) Which plant produces more tomatoes on average?

(f) Which plant has the more consistent yield of tomatoes?

Exercises

Question 1
Calculate the mean and range of these two data sets, and use them to make a comparison between the two sets.

(a) Mean of set A
(b) Mean of set B
(c) Range of set A
(d) Range of set B
(e) Which set has higher values on average?	Set A Set B Both are the same
(f) Which set has more varied data?	Set A Set B Both are the same

Question 2
Calculate the mean and range of these two data sets, and use them to make a comparison between the two sets.

(a) Mean of set A
(b) Mean of set B
(c) Range of set A
(d) Range of set B
(e) Which set has higher values on average?	Set A Set B Both are the same
(f) Which set has more varied data?	Set A Set B Both are the same

Question 3
Calculate the mean and range of these two data sets, and use them to make a comparison between the two sets.

(a) Mean of set A
(b) Mean of set B
(c) Range of set A
(d) Range of set B
(e) Which set has lower values on average?	Set A Set B Both are the same
(f) Which set has more consistent data?	Set A Set B Both are the same

Question 4
Roy and Frank are second-hand car salesmen. The following vertical line diagrams show how many cars they have sold per week over a period of time.

(a) What is the mode for Roy?
(b) What is the mode for Frank
(c) What is the range for Roy?
(d) What is the range for Frank?
(e) Who has sold most cars overall?	Roy Frank Both are the same
(f) Which salesman is more consistent?	Roy Frank Both are the same

Question 5
Miss Sharp's class decide to have a spelling competition with Mr Berry's class.
They have a test and the scores for each class are listed below.

(a) What is the mean for Miss Sharp's class?
(b) What is the mean for Mr. Berry's class?
(c) What is the range for Miss Sharp's class?
(d) What is the range for Mr. Berry's class?
(e) Whose class was better at spelling?	Miss Sharp Mr. Berry Both are the same
(f) Whose class produced more consistent results?	Miss Sharp Mr. Berry Both are the same

Question 6
A bus company keeps records of the number of buses that were late each day in February and in July in the same year:

Calculate the mean, median, mode and range for each of the two months, and fill in the table below.
Give the mean accurate to 1 decimal place.

	Mean (1dp)	Median	Mode	Range
February
July

In which month was the service better in general?	February July Both are the same
Which of these is most likely to explain the improvement?	More people travelling in July Better weather conditions in July The buses were repainted in March None of the above