Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days.
Plant A: 10, 4, 4, 5, 7, 10, 3, 3, 9, 10
Plant B: 8, 7, 5, 5, 9, 7, 8, 7, 5, 6
Find the mean number of beans picked per day for Plant A.
Find the mean number of beans picked per day for Plant B.
Find the range for Plant A.
Find the range for Plant B.
Which plant produces more beans on average? Explain your answer.
Which plant has a more consistent yield of beans? Explain your answer.
The residents of two blocks of townhouses were asked the number of pets they own. The frequency of various responses are presented in the dot plots below:
In which block is pet ownership lower?
How many pets do most households have in block A?
How many pets do most households have in Block B?
Describe the shape of the data for Block A.
Find the range for Block A.
Which block has more variability in the number of pets per household?
Do either blocks have an outlier?
Across five exams two students achieved the following scores:
-
Student X: 86, 83, 86, 88, 98
-
Student Y: 61, 83, 50, 85, 83
Find the mean score of Student X.
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? Explain your answer.
The pulse rates of two groups are given below:
Group 1: 82, 85, 88, 65, 73, 89, 79, 90, 76, 68, 88, 65, 63, 62, 88, 82
Group 2: 75, 88, 74, 73, 80, 76, 67, 81, 71, 83, 89, 62, 63, 80, 71, 78
Find the mean pulse rate of Group 1, correct to two decimal places.
Find the mean pulse rate of Group 2, correct to two decimal places.
Find the standard deviation of Group 1, correct to two decimal places.
Find the standard deviation of Group 2, correct to two decimal places.
What is the range for Group 1?
What is the range for Group 2?
Which group has the greater spread?
The beaks of two groups of bird are measured, in mm, 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
Calculate the range for Group 1.
Calculate the range for Group 2.
Calculate the mean for Group 1.
Calculate the mean for Group 2.
Do you think the two groups of birds are the same species? Explain your answer.
The median house price in the suburb of Humbleton is \$950\,000 with a mean price of \$1\,000\,000 and the median house price in the suburb of Brockway is \$950\,000 with a mean price of \$880\,000.
Which suburd is more likely to have very expensive houses? Explain your answer.
The ages of employees at two competing fast food restaurants on a Saturday night are recorded. Some statistics are given in the following table:
If the data for Berger's Burgers was represented using a histogram, would it be positively or negatively skewed?
Which restaurant has the oldest employee on the night the data is recorded?
| Mean | Median | Range | |
|---|---|---|---|
| Berger's Burgers | 18 | 17 | 6 |
| Fry's Fries | 18 | 19 | 2 |
Which restaurant has the most consistent ages among employees? Explain your answer.
Which restaurant has an older workforce? Explain your answer.
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 |
Calculate the following (correct to one decimal place where necessary), for Class 1:
The mean
The median
The mode
The range
Calculate the following (correct to one decimal place where necessary), for Class 2:
The mean
The median
The mode
The range
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 |
Calculate the following (correct to one decimal place where necessary) for Person A:
The mean
The median
The mode
The range
Calculate the following (correct to one decimal place where necessary) for Person B:
The mean
The median
The mode
The range
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 |
Calculate the following for the men:
The mean
The median
The mode
The range
Calculate the following for the women:
The mean
The median
The mode
The range
Who seems to be getting the higher salary, the men or the women? Explain your answer.
The stem and leaf plot shows the batting scores of two cricket teams, A and B:
Find the median score of Team A.
Find the median score of Team B.
Find the range of Team A’s scores.
Find the range of Team B’s scores.
Find the interquartile range of Team A’s scores.
Find the interquartile range of Team B’s scores.
| Team A | Team B | |
|---|---|---|
| 7\ 6\ 2 | 6 | 2\ 6\ 8 |
| 8\ 6\ 6\ 5\ 2 | 7 | 1\ 5\ 7 |
| 8\ 4 | 8 | 1\ 4\ 7\ 9 |
| 9 | 4\ 7 |
Key: 6 \vert 1 \vert 2 = 12 \text{ and } 16
The stem and leaf plots show the number of books read in a year by a random sample of university and high school students. Which of the following statements are true?
Compare the medians of both groups.
Compare the range of both groups.
Which group of students read more books? Explain your answer.
| University | High school | |
|---|---|---|
| 7 | 0 | |
| 6\ 6\ 3 | 1 | 0\ 0\ 3\ 5 |
| 4\ 3\ 2\ 1 | 2 | 1\ 2\ 4\ 4\ 6 |
| 9\ 8\ 8\ 6 | 3 | 1\ 8\ 9 |
| 8\ 2 | 4 | 0\ 1 |
| 5 | ||
| 6 | ||
| 3 | 7 |
Key : 1 | 2 = 12\text{ books}
The stem and leaf plot shows the amount of cash (in dollars) carried by a random sample of teenage boys and girls:
Who carries more cash, boys or girls?
Find the median for the boys.
Find the median for the girls.
Describe the shape of the data for Girls.
Describe the shape of the data for Boys.
Which group had more variation?
Were there any outliers?
| Boys | Girls | |
|---|---|---|
| 7 | 0 | |
| 1 | 1 | 1 |
| 5\ 4\ 1 | 2 | 2\ 6\ 8 |
| 8\ 5\ 4 | 3 | 3\ 4\ 4\ 6\ 6\ 8\ 9 |
| 9\ 8\ 2\ 2\ 2\ 1 | 4 | 3\ 4\ 6 |
| 9\ 7\ 4\ 3 | 5 | 4 |
| 8\ 5\ 2 | 6 | |
| 3\ 1 | 7 |
Key : 1 | 2 = 12 \text{ dollars}
The stem and leaf plots show the length (in minutes) of a random sample of phone calls made by Sharon and Tricia:
Find Sharon's mean to one decimal place.
Find Sharon's median.
Find Tricia's mean to one decimal place.
Find Tricia's median.
Hence, who generally makes slightly longer phone calls?
| Sharon | Tricia | |
|---|---|---|
| 3 | 1 | 3\ 4 |
| 7\ 6\ 4\ 3\ 2 | 2 | 6\ 7\ 8 |
| 9\ 8 | 3 | 2\ 4 |
| 4\ 3 | 4 | 1\ 2 |
| 7\ 6 | 5 | 6\ 7\ 8 |
Key : 1 | 2 = 12\text{ minutes}
The back to back stem and leaf plots shows the number of pieces of paper used over several days by Charlie’s and Dylan’s students:
Did Charlie's students use 7 pieces of paper on any day?
Is Dylan's median higher than Charlie’s median?
Is the median greater than the mean in both groups?
| Charlie's students | Dylan's students | |
|---|---|---|
| 7 | 0 | 7 |
| 3\ 2\ 1 | 1 | 3 |
| 8 | 2 | 8 |
| 4\ 3\ 2 | 3 | 3\ 4 |
| 9 | 4 | 5\ 6\ 7 |
| 2 | 5 | 2\ 3 |
Key: 1 \vert 1 \vert 3 = 11 \text{ and } 13
The back to back stem and leaf plot shows the number of desserts ordered at Hotel A and Hotel B over several randomly chosen days:
Interpret the lowest score for Hotel A.
Which hotel's median is higher?
Is the mean greater than the median in both groups?
| Hotel A | Hotel B | |
|---|---|---|
| 3 | 0 | |
| 4\ 3\ 2 | 1 | 3\ 4 |
| 7\ 6 | 2 | 7 |
| 4\ 3 | 3 | 3\ 4 |
| 6 | 4 | 6\ 7 |
| 2 | 5 | 2\ 3\ 4 |
Key: 2 \vert 1 \vert 3 = 12 \text{ and }13
The weight (in kilograms) of a group of men and women were recorded and presented in a stem and leaf plot as shown:
Find the mean weight of the group of men.
Find the mean weight of the group of women.
Which group is heavier overall? Explain your answer.
| Men | Women | |
|---|---|---|
| 5 | 0\ 1\ 2\ 3\ 4\ 4\ 4\ 5\ 5\ 5\ 7 | |
| 9\ 8\ 8\ 7\ 6\ 6\ 6\ 5\ 3 | 6 | 0\ 2\ 2\ 3\ 4\ 7\ 7\ 8 |
| 6\ 4\ 3\ 2\ 2\ 1\ 0\ 0\ 0\ 0 | 7 | 0 |
| 0 | 8 |
Key: 4 | 2 = 42\text{ kg}
The test scores of 11 students in Drama and German are listed below.
Drama: \,75,\, 85,\, 62,\, 65,\, 52,\, 76,\, 89,\, 83,\, 55,\, 91,\, 77
German: \,82,\, 86,\, 76,\, 84,\, 64,\, 73,\, 89,\, 62,\, 54,\, 69,\, 78
Construct parallel box plots to represent both data sets.
The following box plots shows the number of points scored by two basketball teams in each of their matches:
What is the median score of Team A?
What is the median score of Team B?
What is the range of Team A’s scores?
What is the range of Team B’s scores?
What is the interquartile range of Team A’s scores?
What is the interquartile range of Team B’s scores?
The parallel box plots below shows the data collected by the manufacturers on the life-span of light bulbs, measured in thousands of hours:
Complete the following table. Write each answer in terms of hours.
| Manufacturer A | Manufacturer B | |
|---|---|---|
| Median | ||
| Lower quartile | ||
| Upper quartile | ||
| Range | ||
| Interquartile range |
Hence, which manufacturer produces light bulbs with the best lifespan? Explain your answer.
The box plots below represent the daily sales made by Carl and Angelina over the course of one month:
What is the range in Angelina's sales?
What is the range in Carl's sales?
By how much did Carl's median sales exceed Angelina's?
Considering the middle 50\% of sales for both sales people, whose sales were more consistent?
Which salesperson had a more successful sales month?
Cooper and Marion are racing go-karts. The times (in seconds) for the 12 laps of their qualifying race are shown below:
- Cooper: \,58.9,\, 46.5,\, 52.6,\, 66.6,\, 58.4,\, 53.1,\, 45.0,\, 52.1,\, 52.4,\, 52.7,\, 44.8,\, 51.7
- Marion: \, 47.8,\, 54.6,\, 68.5,\, 68.0,\, 62.8,\, 57.2,\, 54.8,\, 63.4,\, 58.1,\, 64.3,\, 66.2,\, 47.1
Construct the five-number summary for each set.
Identify any outliers and use statistical calculations to justify your answer.
Create a parallel box plot of the two sets of times with the outlier(s) displayed separately.
Which racer will be in pole position for the final race, if it is given to the racer with the fastest qualifying lap time?
Does spinning out on a lap, causing a high outlier, impact the selection for pole position? Explain your answer.
Two friends compete in hammer throw competitions and train together over a season. They compete in 15 competitions and their final throw for each competition is shown below:
- Tim: \,29.8,\, 37.4,\, 33.9,\, 38.8,\, 34.3,\, 36.5,\, 34.5,\, 30.0,\, 35.2,\, 38.4,\, 33.0,\, 33.2,\, 39.6,\, 35.0,\, 36.9
- Odi: \,32.2,\, 35.4,\, 34.8,\, 33.0,\, 38.4,\, 26.0,\, 40.0,\, 37.2,\, 39.5,\, 42.4,\, 38.6,\, 42.3,\, 38.4,\, 42.8,\, 37.2
Complete the following table of statistics:
| Tim | Odi | |
|---|---|---|
| \text{Minimum} | 29.8 | |
| Q_1 | 33.2 | |
| \text{Median} | 35.0 | |
| Q_3 | 37.4 | |
| \text{Maximum} | 39.6 | |
| \text{Mean (} 1 \text{ d.p.)} | 37.2 | |
| \text{Sample standard deviation (}2 \text{ d.p.)} | 2.93 | |
| \text{Range} | ||
| \text{Interquartile range} |
Which competitor throws more consistently? Explain your answer.
Identify any outliers and use statistical calculations to justify your answer.
Create a parallel box plot of the two sets of data with the outlier(s) displayed separately.
Who is the better hammer thrower? Explain your answer.
When considering Odi's average throw is it reasonable to remove the outlier before calculating the mean? Explain your answer.
Two groups of size twelve take a test to assess their reaction time. The participants clicked a button as soon as they heard a sound which was played at random intervals. The reaction time in milliseconds of each participant is shown below:
- Group A: \,220,\, 210,\, 220,\, 215,\, 180,\, 185,\, 190,\, 190,\, 195,\, 190,\, 195,\, 195
- Group B: \,210,\, 170,\, 200,\, 170,\, 190,\, 210,\, 180,\, 200,\, 180,\, 210,\, 190,\, 190
Complete the following table of statistics:
| Group A | Group B | |
|---|---|---|
| \text{Minimum} | 180 | |
| Q_1 | 190 | |
| \text{Median} | 195 | 190 |
| Q_3 | 212.5 | |
| \text{Maximum} | 220 | |
| \text{Mean (}2 \text{ d.p.)} | 198.75 | |
| \text{Sample standard deviation (}1 \text{ d.p.}) | 14.7 | |
| \text{Range} | ||
| \text{Interquartile range} |
Which group had more consistent reaction times?
Construct a parallel box plot, showing the reaction times of group A and group B.
What can we conclude from the value of group B's first quartile?
Using the box plot and table of statistics in part (a), which group generally has the faster reaction times?
If group A represent a number of 16 year old males, and group B represents a number of 16 year old females, state a valid conclusion from this data.
The following boxplots summarize results from a medical study. The treatment group received an experimental drug to relieve cold symptoms, and the control group received a placebo. The boxplots show the number of days each group continued to report symptoms:
Describe the shape of the data from the control group.
Describe the shape of the data from the treatement group.
Does the drug have a positive effect on patient recovery? Explain your answer.
The box plots drawn below show the number of repetitions of a 70\text{ kg} bar that Weightlifter A and Weightlifter B can lift. They both record their repetitions over 30 days:
Which weightlifter has the more consistent results? Explain your answer.
Which weightlifter can do the most repetitions of the 70\text{ kg} bar? Explain your answer.
Construct a box plot for the following histograms:
Match the histograms on the left to the corresponding box plots on the right:
Histogram A
Histogram B
Histogram C
Histogram D
Histogram E
Histogram F
State whether the following pairs of histograms and box plots match with respect to their shape:
Explain why the following pairs of histograms and box plots do not match:
