Describe what the mean measures for a set of scores.
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 the following five numbers have a mean of 3:
8, 4, 2, 3, 1
3, 2, 5, 1, 4
1, 3, 7, 5, 2
2, 4, 5, 4, 3
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
Find the sum of the following sets of scores:
A set of 29 scores with a mean of 37.7
A set of 10 scores with a mean of 4
Calculate the number of scores in the following sets:
The mean of a set of scores is 35 and the sum of the scores is 560.
The mean of a set of scores is 38.6 and the sum of the scores is 694.8.
The five numbers 16, 16, 17, 24, 17 have a mean of 18. If a new number is added that is bigger than 24, will the mean be higher or lower?
The five numbers 11, 13, 9, 13, 9 have a mean of 11. If a new number is added that is smaller than 9, will the mean be higher or lower?
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.
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. What is the new mean of the class, to two decimal places?
A rating system of 1 - 4 was used in a survey to determine the usefulness of a new feature. The 14 scores shown below are known to be bi-modal with values 2 and 4. Determine the value of the missing score:
2, 4, 3, 2, 3, 4, 4, 1, 1, 2, 3, ⬚Six numbers 6, 2, 7, 18, 17 and an unknown number x have a median of 8.5. Find the missing value x.
Find all the numbers in the following data sets:
Three numbers have a mode of 10 and a mean of 10.
Four numbers have a range of 5, a median of 9 and a mode of 11.
Five numbers have a range of 16, a mode of 2, a median of 7 and a mean of 8. The minimum number in the set is 2.
Consider the stem-and-leaf plot below:
Find the mean, to two decimal places.
Find the mode.
Find the median.
Find the range.
| Leaf | |
|---|---|
| 2 | 4 |
| 3 | 0\ 5\ 5\ 5 |
| 4 | 0\ 2 |
| 5 | 0\ 2\ 9\ 9 |
| 6 | 3\ 3 |
| 7 | 0\ 1 |
| 8 | 0\ 1 |
| 9 | 0\ 0\ 5 |
Key: 2 \vert 4 = 24
A statistician organised a set of data into the frequency table shown:
Complete the frequency distribution table.
Calculate the mean, correct to two decimal places.
Find the range of the scores in the table.
Find the mode of the set of scores in the table.
| \text{Score } (x) | \text{Frequency } (f) | f\times x |
|---|---|---|
| 31 | 12 | |
| 32 | 14 | |
| 33 | 7 | |
| 34 | 20 | |
| 35 | 15 | |
| \text{Totals} |
Consider the following histogram:
Find the total number of scores.
Calculate the sum of the scores.
Calculate the mean, correct to two decimal places.
Consider the following data set:
6,\, 4,\, 3,\, 3,\, 3,\, 3,\, 3,\, 4,\, 2,\, 3,\, 5,\, 2,\, 6,\, 2,\, 3,\, 6,\, 2,\, 2,\, 6,\, 4,\, 3,\, 3,\, 6,\, 4,\, 2
Complete the frequency distribution table.
Construct a histogram of the data.
Calculate the mean, correct to one decimal place.
Find the range of the data.
Find the mode of the data.
| \text{Score } (x) | \text{Frequency } (f) | f\times x |
|---|---|---|
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| \text{Total} |
Consider the frequency distribution table:
Complete the table.
Find the mean of the scores, correct to two decimal places.
Find the mode of the scores.
Find the range of the scores.
How many scores are less than the mode?
| \text{Score } (x) | \text{Frequency } (f) | f\times x |
|---|---|---|
| 4 | 11 | |
| 5 | 35 | |
| 16 | ||
| 14 | ||
| \text{Total} | 43 | 365 |
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 |
The Stem and Leaf 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
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 given dot plot:
What was the total number of points scored from three-point shots during the season?
What was the mean number of points scored 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.
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 x.
The frequency table below shows the resting heart rate of some people taking part in a study:
| \text{Heart Rate} | \text{Class Centre } (x) | \text{Frequency } (f) | f\times x |
|---|---|---|---|
| 30-39 | 13 | ||
| 40-49 | 22 | ||
| 50-59 | 24 | ||
| 60-69 | 36 |
Complete the table.
What is the mean resting heart rate? Round your answer to two decimal places.
As part of a fuel watch initiative, the price of petrol at a service station was recorded each day for 21 days. The frequency table shows the findings:
If the class centres are taken to be the score in each class interval, find the total of the prices recorded.
Hence, find the average fuel price. Round your answer to two decimal places.
| Price (in cents per litre) | Class Centre | Frequency |
|---|---|---|
| 130.9 - 135.9 | 133.4 | 6 |
| 135.9 - 140.9 | 138.4 | 5 |
| 140.9 - 145.9 | 143.4 | 6 |
| 145.9 - 150.9 | 148.4 | 4 |
A group of high school students wanted to convince their principal that the school needed air-conditioning. They measured the temperature in a classroom at 1 pm every day during February and recorded the results (in \degree \text{C}) below:
35,\, 26,\, 32,\, 29,\, 29,\, 32,\, 26,\, 29,\, 35,\, 23,\, 23, 32,\, 35,\, 26,\, \\26,\, 23,\, 26,\, 29,\, 32,\, 35,\, 23,\, 26,\, 29,\, 29,\, 29,\, 32,\, 23,\, 29
Complete the following frequency table:
| \text{Class} | \text{Class centre } (cc) | \text{Frequency } (f) | f \times cc |
|---|---|---|---|
| 22 - 24 | |||
| 25 - 27 | |||
| 28 - 30 | |||
| 31 - 33 | |||
| 34 - 36 | |||
| \text{Totals:} |
Find the modal class.
Find the average temperature, correct to two decimal places.
The masses (in \text{kg}) of a group of students are listed below:
59,\, 64,\, 61,\, 60,\, 66,\, 57,\, 57,\, 61,\, 67,\, 60,\, 65,\, 64,\, 59,\, \\ 57,\, 67,\, 60,\, 64,\, 60,\, 55,\, 55,\, 65,\, 55,\, 64,\, 61,\, 65,\, 61,\, 58
Complete the following frequency table:
| \text{Class interval (kg)} | \text{Class centre }(cc) | \text{Frequency }(f) | f \times cc |
|---|---|---|---|
| 55 - 59 | |||
| 60 - 64 | |||
| 65 - 69 | |||
| \text{Totals} |
Which is the modal class?
Using the class centres estimate the mean correct to one decimal place.
A journalist wanted to report on road speed cameras being used as revenue raisers. She obtained the following data that showed the number of times 20 speed cameras issued a fine to motorists in one month:
101,\, 102,\, 115,\, 115,\, 121,\, 124,\, 127,\, 128,\, 130,\, 130,\, \\ 143,\, 143,\, 146,\, 162,\, 162,\, 163,\, 178,\, 183,\, 194,\, 977
Determine the mean number of times a speed camera issued a fine in that month, to one decimal place.
Determine the median number of times a speed camera issued a fine in that month, to one decimal place.
Which measure is most representative of the number of fines issued by each speed camera in one month: the mean or the median? Explain your answer.
The journalist wants to give the impression that speed cameras are just being used to raise revenue. Which of the following statements should she make:
A sample of 20 speed cameras found that the median number of fines in one month was 136.5.
A sample of 20 speed cameras found that, on average, 182.2 fines were issued in one month.
In a countrywide census, information is gathered to determine the make up of the population. Some of the questions asked are:
How many people live in your household?
What is your gender?
How many cars are there in your household?
What is the income of each person in your household?
Is English your first language?
State whether the following would be a reasonable measure from the information collected:
The average income per capita (per person of the population)
The median number of people per household
The average number of females in the population
The average number of people whose first language is English
The column graph below shows the total rainfall received during each month of the year:
What measure of centre would be most appropriate to measure the average rainfall per month?
Find this measure of centre to the nearest whole number.