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
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.
Find the median of the following set of scores: 6,\, 8,\, 9,\, 11,\, 16,\, 17,\, 18
For each of the following sets of scores:
Sort the scores in ascending order.
Find the median.
69.4, \,66.7,\, 46.6,\, 76.6,\, 52.8,\, 80.6,\, 63.9
44.9,\, 45.6,\, - 54.8 ,\, 74.7,\, - 77.6 ,\, - 42.6 ,\, 67.9,\, 40.6
State the position of the median in an ordered set of:
69 scores
152 scores
Six numbers 6, 2, 7, 18, 17 and an unknown number x have a median of 8.5. Find the missing value x.
Find 4 consecutive odd numbers whose median is 40.
Find the mode(s) of the following data sets:
2, 2, 6, 8, 8, 8, 8, 12, 14, 14, 14, 14, 18, 18
| Score | Frequency |
|---|---|
| 25 | 17 |
| 26 | 42 |
| 27 | 35 |
| 28 | 32 |
| 29 | 12 |
| 30 | 20 |
| Leaf | |
|---|---|
| 2 | 2\ 5\ 6\ 7\ 9 |
| 3 | 0\ 0\ 5\ 6\ 8 |
| 4 | 0\ 1\ 3\ 8\ 9 |
Key: 2\vert 4=2.4
A consumer group surveys the price of petrol per litre at six different petrol stations and the results are as follows:
\$1.68, \$1.64, \$1.64, \$1.71, \$1.64, \$1.57
State the mode petrol price.
Each of the following data sets are missing one score. Find the missing score if:
Consider the set of data:1,\, 2,\, 2,\, 4,\, 4,\, 5,\, 6,\, 6,\, 8,\, 8,\, 8,\, 9,\, 9
If one score of 8 is changed to a 9, which measure of centre or spread would be altered?
Consider this set of data that represents the number of apps on six people’s phones:
10,\, 13,\, 14,\, 17,\, 20,\, 20
If each person downloads another 9 apps, which measure of centre or spread would change?
State whether each of the following statements are true or false:
If two sets of data have the same median then the data sets must be the same.
If two sets of data have different modes then the highest values cannot be the same.
Two sets of data have the same highest and lowest values. This means they must have the same median.
Two sets of data that have the same highest and lowest values must have the same mean.
A real estate agent wanted to determine a typical house price in a certain area. He gathered the selling price of some houses (in dollars):
317\,000,\, 320\,000,\, 347\,000,\, 360\,000,\, 378\,000,\, 395\,000,\, 438\,000,\, 461\,000,\, 479\,000,\, 499\,000
Find the mean house price.
What percentage of the house prices exceeded the mean?
Find the median house price.
What percentage of house prices exceeded the median?
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.
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.
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
A diver measures how long she can hold her breath underwater over several dives. If the median time is 3.9 minutes, determine whether the following statements are true:
The longest she held her breath is 7.8 minutes.
Most of the time she held her breath for less than 3.9 minutes.
Half the dives she was able to hold her breath longer than 3.9 minutes.
The shortest time she held her breath is 1.95 minutes.
Most of the time she held her breath for longer than 3.9 minutes.
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 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.
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 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.
The dot plot shows the number of sit-ups achieved by students in a Physical education exam.
Find the following, correct to two decimal places if necessary:
Mean
Median
Mode
On Sunday, 20 planes were delayed at the airport. The dot plot shows the number of hours each departure was delayed:
What was the median number of minutes a plane was delayed?
What percentage of planes were delayed for longer than the median time?
If a plane is delayed for more than 30 minutes, the airline must pay \$5000. In total, how much were airlines fined that day?
Consider the dot plot given. From which score can a dot be removed so that the mean, median and mode remain unchanged?
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?
What is the average number of children in a family for a student in this class?
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?
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?
The following stem plot shows the number of hours students spent studying for a science exam.
Find the following, correct to two decimal places if necessary:
Mean
Median
Mode
| Leaf | |
|---|---|
| 6 | 0\ 2\ 3\ 6\ 7\ 7\ 8 |
| 7 | 3\ 6\ 9 |
| 8 | 0\ 5\ 6\ 7 |
| 9 | 2 |
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
The following stem plot shows the ages of 20 employees in a company:
How many of the employees are in their 30's?
What is the age of the oldest employee?
What is the age of the youngest employee?
Find the median age of the employees.
What is the modal age group?
| Leaf | |
|---|---|
| 2 | 0\ 2\ 3\ 4\ 6\ 6\ 7 |
| 3 | 1\ 5\ 6\ 7\ 8 |
| 4 | 0\ 3\ 4\ 6\ 7 |
| 5 | 0\ 0\ 8 |
Key: 1 \vert 2 \ = \ 12 years old
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} |
For each frequency distribution table, find the median of the scores.
| Score | Frequency |
|---|---|
| 23 | 2 |
| 24 | 26 |
| 25 | 37 |
| 26 | 24 |
| 27 | 25 |
| \text{Score }(x) | \text{Frequency }(f) |
|---|---|
| 10 | 6 |
| 14 | 9 |
| 18 | 6 |
| 21 | 7 |
| 24 | 8 |
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.
Construct a column graph of the data.
Calculate the mean, correct to one decimal place.
| \text{Score }(x) | \text{Frequency }(f) | fx |
|---|---|---|
| 38 | ||
| 39 | ||
| 40 | ||
| 41 | ||
| 42 | ||
| \text{Total} |
The luggage check-in weight (in kilograms) of passengers is given in the following frequency table:
Complete the table.
Find the median check-in weight.
Find the mean check-in weight, correct to two decimal places.
When one of the passengers sees that the weight of their luggage is 21 kilograms, they decide to add some items to the bag. This changes the mean or the median?
| \text{Weight }(x) | \text{Frequency }(f) | fx |
|---|---|---|
| 16 | 12 | |
| 17 | 17 | |
| 18 | 21 | |
| 19 | 10 | |
| 20 | 18 | |
| 21 | 22 | |
| \text{Total} |
For each of the following column graphs, find:
The total number of scores.
The median.
The total sum of the scores.
The mean, correct to one decimal place.
Some people were asked approximately how many of their high school friends they remained in contact with after high school. The results are presented in the column graph:
What is the average number of friends that people in the survey remained in contact with?
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.
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.
For each of the following sets of data:
Find an estimate for the mean, correct to one decimal place. Use the midpoint of each class interval.
State the modal group.
| Score | Frequency |
|---|---|
| 0 \leq x \lt 20 | 4 |
| 20 \leq x \lt 40 | 15 |
| 40 \leq x \lt 60 | 23 |
| 60 \leq x \lt 80 | 73 |
| 80 \leq x \lt 100 | 45 |
| Score | Frequency |
|---|---|
| 20-24 | 5 |
| 25-29 | 10 |
| 30-34 | 16 |
| 35-39 | 4 |
| 40-44 | 3 |
| 45-49 | 2 |
| 50-54 | 1 |
| Score | Frequency |
|---|---|
| 1-4 | 2 |
| 5-8 | 7 |
| 9-12 | 15 |
| 13-16 | 5 |
| 17-20 | 1 |
| Score | Frequency |
|---|---|
| 1-5 | 20 |
| 6-10 | 15 |
| 11-15 | 8 |
| 16-20 | 4 |
| 21-25 | 3 |
| 26-30 | 2 |
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 20 days. The frequency table shows the findings:
What is the modal price range?
What percentage of instances was the petrol price in the modal price range?
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.
| Price (in cents per litre) | Frequency |
|---|---|
| 130.0-134.9 | 5 |
| 135.0-139.9 | 6 |
| 140.0-144.9 | 3 |
| 145.0-149.9 | 4 |
| 150.0-154.9 | 2 |
One hundred students were asked to note the number of hours they study in the week prior to an examination. The given frequency table shows the results of this survey:
Find the modal class for the number of hours spent studying in the week.
Use the class centres to find an estimate for the mean time spent studying.
| Hours | Students |
|---|---|
| 0 \leq h \lt 10 | 3 |
| 10 \leq h \lt 20 | 5 |
| 20 \leq h \lt 30 | 10 |
| 30 \leq h \lt 40 | 22 |
| 40 \leq h \lt 50 | 25 |
| 50 \leq h \lt 60 | 12 |
| 60 \leq h \lt 70 | 10 |
| 70 \leq h \lt 80 | 8 |
| 80 \leq h \lt 90 | 3 |
| 90 \leq h \lt 100 | 2 |
As part of the process of assessing the value of a block of land, a real estate agent considers other blocks recently sold in the area. For 68 recent sales, the information was as follows:
| \text{Price }(\$ C) | \text{Class centre} | \text{Frequency} |
|---|---|---|
| 200 \, 000 \leq C \lt 210\, 000 | 205\, 000 | 3 |
| 210\,000 \leq C \lt 220 \, 000 | 215\,000 | 10 |
| 220\,000 \leq C \lt 230\,000 | 225\,000 | 11 |
| 230\,000 \leq C \lt 240\,000 | 235\,000 | 16 |
| 240\,000 \leq C \lt 250\,000 | 245\,000 | 7 |
| 250\,000 \leq C \lt 260\,000 | 255\,000 | 7 |
| 260\,000 \leq C \lt 270\,000 | 265\,000 | 5 |
| 270\,000 \leq C \lt 280\,000 | 275\,000 | 4 |
| 280\,000 \leq C \lt 290\,000 | 285\,000 | 3 |
| 290\,000 \leq C \lt 300\,000 | 295\, 000 | 2 |
Use the class centres to find an estimate for the median.
Use the class centres to find an estimate for the mean price (to the nearest \$1000).
The histogram shows the weights of preschool students in kilograms:
Use the class centres to find an estimate of the following, correct to one decimal place, if necessary:
Mean
Median
State the modal class.
The given histogram shows the number of hours that students in a particular class had slept for the night before.
How many students are in the class?
Use the class centres to find an estimate of the following:
Mean
Median
State the modal class.
The histogram below shows the speed of balls delivered by cricket bowlers:
Use the class centres to find an estimate of the following, correct to two decimal places, if necessary:
Mean
Median
State the modal class.
The histogram below shows the heights of 200 randomly selected rugby players:
Use the class centres to find an estimate of the following:
Mean
Median
State the modal class.