10.07 Making statistical comparisons
Which of the following sets of data has the lowest mode:
-
Set A:\,3,\, 9,\, 18,\, 9,\, 65,\, 13
Set B:\,5,\, 12,\, 16,\, 16,\, 50,\, 3
Which of the following sets of data has the highest median:
Set A:\,3,\, 9,\, 13,\, 18
Set B:\,9,\, 16,\, 16,\, 65,\, 86
Which of the following sets of data has the lowest mean:
Set A:\,14,\, 15,\, 2,\, 15,\, 26
Set B:\,7,\, 5,\, 3,\, 2,\, 1,\, 5
Which of the following sets of data has the lowest median:
Set A:\,14,\, 15,\, 2,\, 15,\, 26
Set B:\,7,\, 5,\, 3,\, 2,\, 1,\, 5
The runs scored by each player in a cricket match are displayed below:
Team A: 70,\, 0,\, 73,\, 25,\, 31,\, 52,\, 1,\, 20,\, 2,\, 7,\, 8
Team B: 28,\, 33,\, 12,\, 60,\, 51,\, 24,\, 4,\, 19,\, 1,\, 5,\, 7
Find the mean runs for team A to one decimal place.
Find the mean runs for team B to one decimal place.
Which team scored more runs?
In a standardised test out of 100, the students in two classes got the results displayed below:
Class A: 66,\, 66,\, 100,\, 76,\, 74,\, 67,\, 68,\, 96,\, 61,\, 73,\, 61,\, 79,\, 83,\, 68,\, 66
Class B: 90,\, 62,\, 60,\, 74,\, 61,\, 85,\, 71,\, 85,\, 68,\, 72,\, 82,\, 76,\, 65,\, 72,\, 72
Find the median mark for Class A.
Find the median mark for Class B.
Which class did better on the test? Explain your answer.
The monthly rainfall for two cities across a year is displayed below:
City A: 140,\, 101,\, 120,\, 67,\, 71,\, 31,\, 11,\, 57,\, 23,\, 79,\, 83,\, 123
City B: 48,\, 75,\, 23,\, 64,\, 62,\, 90,\, 75,\, 97,\, 44,\, 68,\, 27,\, 57
Find the range in monthly rainfall for City A.
Find the range in monthly rainfall for City B
Which city had more consistent rainfall throughout the year? Explain your answer.
Which of the following histograms has the largest mode?
Which of the following histograms has the smallest median?
Consider the following histograms:
Which histogram has the smallest range?
Which histogram has the largest range?
The following histograms show the season results of two soccer groups, Group A and Group B, and the number of games (frequency) in which they scored a certain number of goals:
Find the mode for Group A.
Find the mode for Group B.
Find the range for Group A.
Find the range for Group B.
Which group scored the lowest total number of goals during the season?
Which group has the most varied results? Explain your answer.
The prices of sales at two locations of a shop are recorded in the histograms below:
Find the mean sale price for Location A.
Find the mean sale price for Location B.
Which location made more sales?
Which location has a higher average sale price?
An online shopping website records the user ratings for two similar products in the histograms below.
Find the median user rating for Product A.
Find the median user rating for Product B.
According to the website's rating system, a perfect rating is 5.0. Which product got more perfect ratings?
According to the website's rating system, a positive rating is greater than 3. Which product got more positive ratings?
Classes 7M and 9C were surveyed about whether they should receive more maths homework.
The results are displayed in the given table:
| Agreed | Disagreed | |
|---|---|---|
| 7M | 6 | 24 |
| 9C | 8 | 24 |
Are these results likely to be representative of the student population? Explain your answer.
What conclusion can we make from the data?
An online survey was run over two separate weeks to see if residents in a council area agreed with a new regulation. The results are shown in the given table:
Which week is more likely to be representative of the entire council area population? Explain your answer.
What conclusion can we make from the data?
| Agreed | Disagreed | |
|---|---|---|
| Week 1 | 19 | 30 |
| Week 2 | 178 | 80 |
Tricia wanted to find if students at her school believed that more school funding should go towards sports. She surveyed the students who took her bus as well as students on her athletics team. The results are shown in the given table:
Which group is more likely to be representative of the school population? Explain your answer.
Tricia determines that the opinion of students is evenly split. Is this a reliable conclusion? Explain your answer.
| Agreed | Disagreed | |
|---|---|---|
| Bus | 10 | 11 |
| Team | 22 | 3 |
The number of goals scored by Team 1 and Team 2 in a football tournament are recorded in the following table:
Find the total number of goals scored in Match C.
Find the total number of goals scored by Team 1 across all the matches.
Find the mean number of goals scored by Team 1.
Find the mean number of goals scored by Team 2.
Which team did better in the football tournament? Explain your answer.
| Match | Team 1 | Team 2 |
|---|---|---|
| \text{A} | 2 | 5 |
| \text{B} | 4 | 2 |
| \text{C} | 5 | 1 |
| \text{D} | 3 | 5 |
| \text{E} | 2 | 3 |
The following table shows the scores of Student A and Student B in five separate tests:
Find the mean test score of each student.
What was the highest score achieved and which student obtained that score?
What was the lowest score achieved and which student obtained that score?
Find the range of each student's scores.
Which student had more consistent test scores? Explain your answer.
| Test | Student A | Student B |
|---|---|---|
| 1 | 74 | 79 |
| 2 | 89 | 97 |
| 3 | 79 | 93 |
| 4 | 99 | 87 |
| 5 | 86 | 71 |
The beaks of two groups of bird are measured, in millimetres, to determine whether they might be of the same species. The measurements are shown below:
Group 1: \,33,\, 39,\, 31,\, 27,\, 22,\, 37,\, 30,\, 24,\, 24,\, 28
Group 2: 29,\, 44,\, 45,\, 34,\, 31,\, 44,\, 44,\, 33,\, 37,\, 34
Complete the following table:
Do you think the two groups of birds are the same species? Explain your answer.
| Mean | Range | |
|---|---|---|
| Group 1 | ||
| Group 2 |
Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are shown below:
Plant A: \,10,\, 4,\, 4,\, 5,\, 7,\, 10,\, 3,\, 3,\, 9,\, 10
Plant B: \,8,\, 7,\, 5,\, 5,\, 9,\, 7,\, 8,\, 7,\, 5,\, 6
Complete the following table:
Which plant produces more beans on average?
Which plant has a more consistent yield of beans?
| Mean | Range | |
|---|---|---|
| Plant A | ||
| Plant B |
The ages of employees at two competing fast food restaurants on a Saturday night are recorded. Some statistics are given in the following table:
Which restaurant likely has the oldest employee on the night the data is recorded?
Which restaurant has the most consistent ages among employees? Explain your answer.
Which restaurant has an older workforce? Explain your answer.
| Mean | Median | Range | |
|---|---|---|---|
| Berger's Burgers | 18 | 17 | 6 |
| Fry's Fries | 18 | 19 | 2 |
Two English classes, each with 15 students, sit a 10 question multiple choice test. Their class results, out of 10, are below:
Class 1: \,3,\, 2,\, 3,\, 3,\, 4,\, 5,\, 1,\, 1,\, 1,\, 4,\, 2,\, 2,\, 3,\, 3,\, 2
Class 2: \,8, \,9, \,9, \,8, \,8, \,6,\, 8,\, 10,\, 6,\, 8,\, 8,\, 9,\, 6,\, 9,\, 9
Complete the following table. Round values to one decimal place where necessary.
| Mean | Median | Mode | Range | |
|---|---|---|---|---|
| Class 1 | ||||
| Class 2 |
Which class was more likely to have studied for their test? Explain your answer.
The hours of sleep per night for two people over a two week period are shown below:
Person A: 8,\, 5,\, 10,\, 7,\, 9,\, 7,\, 6,\, 10,\, 6,\, 9,\, 7,\, 7,\, 10,\, 5
Person B: 8,\, 8,\, 8,\, 7,\, 7.5,\, 8,\, 7.5,\, 7,\, 7,\, 7,\, 7.5,\, 7,\, 7,\, 7.5
Complete the following table. Round values to one decimal place where necessary.
| Mean | Median | Mode | Range | |
|---|---|---|---|---|
| Person A | ||||
| Person B |
Which person is the least consistent in their sleep habits? Explain your answer.
Which person has the most sleep over the 14 nights? Explain your answer.
The salaries of men and women working the same job at the same company are given below:
Men: \$80\,000,\, \$80\,000,\, \$75\,000,\, \$80\,000,\, \$75\,000,\, \$70\,000,\, \$80\,000
Women: \$70\,000,\, \$70\,000,\, \$75\,000,\, \$70\,000,\, \$70\,000,\, \$80\,000,\, \$75\,000
Complete the following table:
| Mean | Median | Mode | Range | |
|---|---|---|---|---|
| Men | ||||
| Women |
Who seems to be getting the higher salary, the men or the women? Explain your answer.
Two friends compete in a game. They play 10 games and their scores for each game is shown below:
- Caitlin: \,37,\, 52,\, 47,\, 43,\, 55,\, 56,\, 10,\, 46,\, 59,\, 36
- Ben: \,38,\, 62,\, 12,\, 45,\, 72,\, 21,\, 125,\, 26,\, 62,\, 50
Complete the following table:
Whose scores are less consistent? Explain your answer.
If a person has inconsistent scores, what might this suggest about the player's strategy?
If a person has very consistent scores, what might this suggest about the player's strategy?
| Caitlin | Ben | |
|---|---|---|
| \text{Minimum} | 10 | |
| \text{Median} | 46.5 | 47.5 |
| \text{Maximum} | 59 | |
| \text{Mean} | 44.1 | |
| \text{Range} |