Describe what the mean measures for a set of scores.
When finding the mean, is it necessary to arrange the data items in order?
Find the mean of the following data sets:
8,\, 15,\, 6,\, 27,\, 3
56,\, 89,\, 95,\, 71,\, 75,\, 84,\, 65,\, 83
22.4,\, 25.4,\, 19.1,\, 24.3,\, 7.4
- 14,\, 0,\, - 2,\, - 18,\, - 8,\, 0,\, - 15,\, - 1
Determine whether each of the following data sets has a mean of 3:
8,\, 4,\, 2,\, 3,\, 1
3,\, 2,\, 5,\, 1,\, 4
1,\, 3,\, 7,\, 5,\, 2
2,\, 4,\, 5,\, 4,\, 3
Find the sum of the following sets of scores:
A set of 10 scores with a mean of 4.
A set of 29 scores with a mean of 37.7.
A set of five numbers has a mean of 10. Two of the numbers are 6 and 13. Determine whether the following 3 other numbers could be in the set:
15,\, 11,\, 8
10,\, 13,\, 8
13, \,5,\, 6
10,\, 6,\, 18
The mean of a set of scores is 35 and the sum of the scores is 560. Calculate the number of scores in the set.
Five numbers have a mean of 7. If 4 of the numbers are 10, 10, 8 and 7 and the last number is x, find the value of x.
The mean of four scores is 21. If three of the scores are 17, 3 and 8, find the fourth score.
Han wants to try out as a batsman for a cricket team. In his last three matches, he scored 61, 75 and 66 runs. In his last match before trying out, he wants to lift his mean to 70.
If x is the number of runs he needs to score to achieve this, find the value of x.
The mean of a set of 41 scores is 18.6. If a score of 71.8 is added to the set, find the new mean. Round your answer to two decimal places.
A teacher calculated the mean of 25 students’ marks to be 64. A student who later completed the assessment got a mark of 55. Find the new mean of the class, correct to two decimal places.
The dot plot shows the number of goals scored across each of Eileen's soccer games:
How many games were played in total?
How many goals were scored in total?
Find the average number of goals per game. Express your answer as fraction.
In each game of the season, a basketball team recorded the number of 'three-point shots' they scored. The results for the season are represented in the dot plot below:
What was the total number of points scored from three-point shots during the season?
What was the mean number of points scored from three-point shots each game? Round your answer to two decimal places.
What was the mean number of three point shots per game this season? Round your answer to two decimal places.
Each student in the class was asked to write down the number of siblings they had. The teacher recorded the results in the following dot plot:
How many students were there in the class?
If none of the students share the same siblings, then how many siblings are there in total?
What is the average number of siblings for a student in this class? Express your answer as a fraction.
What is the average number of children in a family for a student in this class? Express your answer as a fraction.
Luigi is a casual nurse. He used a dot plot to keep track of the number of shifts he did each week for a number of weeks:
How many weeks did he record data?
How many shifts in total has he completed?
What is the average number of shifts he completed in a week? Express your answer as a fraction.
If the following week he completes 7 shifts, will the average decrease, remain unchanged, or increase?
What will be his new average number of shifts per week? Express your answer as a fraction.
The scores for a recent history test, out of 100, are shown in the following stem plot:
How many students took the test?
Find the average test score for the class.
| Leaf | |
|---|---|
| 6 | 2\ 3 |
| 7 | 2\ 4\ 9 |
| 8 | 3\ 4\ 9\ 9 |
| 9 | 1\ 1\ 5 |
Key: 8|3 \ = \ 83
A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in a stem plot:
How many events did the cyclist compete in?
What is his mean post event heart rate?
| Leaf | |
|---|---|
| 16 | 2 |
| 17 | 3\ 8 |
| 18 | 4\ 5\ 6\ 9 |
| 19 | 5\ 5 |
Key: 12|3 \ = \ 123
The size of each earthquake that occurred in a region over a three year period, measured from 0 to 9.9, is recorded in a stem plot:
How many earthquakes in total were recorded?
Find the mean number of earthquakes per year in the region.
Find the mean size of an earthquake that occurred during the period.
| Leaf | |
|---|---|
| 1 | 0\ 0\ 2\ 3\ 5\ 6\ 6\ 7\ 9 |
| 2 | 3\ 8 |
| 3 | 3\ 5\ 7 |
| 4 | 1\ 2\ 2\ 3 |
| 5 | 8\ 9 |
| 6 | 5 |
| 7 | 3\ 6 |
| 8 | 7 |
Key: 5|2 \ = \ 5.2
The following stem plot shows the batting scores of two cricket teams, England and India:
What is the highest score from England?
What is the highest score from India?
Find the mean score of England.
Find the mean score of India.
Calculate the combined mean of the two teams.
| England | India | |
|---|---|---|
| 1\ 0 | 3 | 1\ 2\ 4\ 7 |
| 6\ 6\ 5\ 5\ 5\ 5 | 4 | 0\ 2\ 9 |
| 7\ 3 | 5 | 2\ 5 |
| 6 | 4 |
Key: 1 \vert 2 \vert 4 = 21 \text{ and }24
A statistician organised a set of data into the following frequency table:
Complete the frequency distribution table.
Calculate the mean, correct to two decimal places.
| \text{Score }(x) | \text{Frequency }(f) | fx |
|---|---|---|
| 5 | 14 | |
| 7 | 4 | |
| 9 | 2 | |
| 11 | 18 | |
| 13 | 6 | |
| \text{Totals} |
In a survey some people were asked approximately how many minutes they take to decide between brands of a particular product. The results are shown in the following table:
How many people took part in the survey?
Calculate the mean time most people took to choose between brands, rounded to the nearest whole number of minutes.
Create a column graph for the results from the table.
| Minutes Taken | Frequency |
|---|---|
| 1 | 13 |
| 2 | 17 |
| 3 | 12 |
For the following data set:
39, \, 42,\, 40,\, 39,\, 39,\, 40,\, 42,\, 38,\, 41,\, 42,\, 40,
39,\, 39,\, 42,\, 40,\, 39,\, 39,\, 38,\, 39,\, 38,\, 39,\, 40,\, 40
Complete the frequency distribution table.
Calculate the mean, correct to one decimal place.
| \text{Score }(x) | \text{Frequency }(f) | fx |
|---|---|---|
| 38 | ||
| 39 | ||
| 40 | ||
| 41 | ||
| 42 | ||
| \text{Total} |
The table shows the scores of Student A and Student B in five separate tests:
Find the mean score for Student A.
Find the mean score for Student B.
What is the combined mean of the scores of the two students.
What is the highest score overall? Which student obtained that score?
What is the lowest score overall? Which student obtained that score?
| Test | Student A | Student B |
|---|---|---|
| 1 | 97 | 78 |
| 2 | 87 | 96 |
| 3 | 94 | 92 |
| 4 | 73 | 72 |
| 5 | 79 | 86 |
Lucy counted the number of carrots she harvested from her garden over eight months and displayed the data in the column graph:
How many carrots were harvested in total?
In which month numbers did Lucy harvest the same number of carrots?
Calculate the mean number of carrots harvested per month, rounded to the nearest whole number of carrots.
Some people were asked approximately how many of their high school friends they remained in contact with after high school to the nearest 10 friends. The results are presented in the column graph:
What is the average number of friends that people in the survey remained in contact with?
Consider the following column graph:
Find the total number of scores.
Calculate the sum of the scores.
Calculate the mean, correct to two decimal places.
A group of families were surveyed on the number of children they have and the results are shown in the column graph:
What is the average number of children in a family from the survey? Round your answer to one decimal place.
Consider the graph of the daily maximum temperature recorded each day for a week:
Find the mean of the daily maximum temperatures for the week. Round your answer to the nearest degree Celsius.
The price of chocolate bars over a year has been presented in the following graph:
Find the average price over the 12 months shown.
