Find the mean of each of the following data sets:
56,\, 89,\, 95,\, 71,\, 75,\, 84,\, 65,\, 83
- 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
Consider the following histogram:
Find the total number of scores.
Calculate the sum of the scores.
Calculate the mean, correct to two decimal places.
The mean of a set of scores is 35 and the sum of the scores is 560. Calculate the number of scores in the data set.
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 increase or decrease?
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.
Five numbers have a mean of 7. If four of the numbers are 10, 10, 8 and 7 and the last number is x, find the value of x.
Find the median of the following sets of scores:
6, 8, 9, 11, 16, 17, 18
| Score | Frequency |
|---|---|
| 11 | 24 |
| 12 | 9 |
| 13 | 21 |
| 14 | 9 |
| 15 | 6 |
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
Consider the following histogram:
Find the number of scores.
Find the median.
Find four 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
Each of the following data sets are missing one score. Find the missing score if:
Find the range of the following sets of scores:
10, 7, 2, 14, 13, 15, 11, 4
0.1575, 0.1575, 1.3363, - 0.0833 , - 0.7586 , - 0.0833 , 1.3363, 0.7983
A group of students had a range in marks of 14 and the lowest score was 9. What was the highest score in the group?
The range of a set of scores is 8, and the highest score is 19. What is the lowest score in the set?
Calculate the range for the data in the following histogram:
For each of the following sets of scores:
Find the median.
Find the first quartile.
Find the third quartile.
Find the interquartile range.
33, 38, 50, 12, 33, 48, 41
13, 15, 5, 16, 7, 20, 12
| Score | Frequency |
|---|---|
| 5 | 3 |
| 13 | 3 |
| 16 | 2 |
| 28 | 2 |
| 31 | 3 |
| 38 | 4 |
| 48 | 2 |
| Leaf | |
|---|---|
| 2 | 2\ 5\ 6\ 7\ 9 |
| 3 | 0\ 0\ 5\ 6\ 8 |
| 4 | 0\ 0\ 1\ 8\ 9 |
Key: 2\vert 4=24
Describe the difference between the median and the mode.
Consider the data provided in the table:
Calculate the range.
Find the mode.
| Score | Frequency |
|---|---|
| 68 | 16 |
| 69 | 41 |
| 70 | 30 |
| 71 | 31 |
| 72 | 49 |
| 73 | 29 |
For each of the given data sets, find the following to two decimal places if necessary:
Mean
Median
Mode
Range
| Leaf | |
|---|---|
| 6 | 2\ 7 |
| 7 | 1\ 2\ 2\ 4\ 7\ 9 |
| 8 | 0\ 1\ 2\ 5\ 7 |
| 9 | 0\ 1 |
Key: 6\vert 2=62
\text{ }
| 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
For the following data set:
27, 25, 24, 24, 24, 24, 24, 25, 23, 24, 26, 23, 27, 23, 24, 27, 23, 23, 27, 25, 24, 24, 27, 25, 23
Complete the given frequency distribution table:
Construct a histogram of the data.
Find the mean, correct to one decimal place.
Find the range.
Find the mode.
| \text{Score }(x) | \text{Frequency }(f) | fx |
|---|---|---|
| 23 | ||
| 24 | ||
| 25 | ||
| 26 | ||
| 27 | ||
| \text{Total} |
Consider the following data set:
1, 2, 2, 4, 4, 5, 6, 6, 8, 8, 8, 9, 9If one score of 8 is changed to a 9, which measure(s) of centre or spread would be altered?
Consider the following set of data that represents the number of apps on six people’s mobiles:
10, 13, 14, 17, 20, 20
If each person downloads another 9 apps, which measure(s) of centre or spread would be altered?
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: 0 \vert 2\vert 4=20 \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 the value of x.
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?
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.
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.
The following stem plot shows the ages of 20 employees in a company:
How many of the employees are in their 30s?
What is the age of the oldest employee?
What is the age of the youngest employee?
What is the median age of the employees?
What is the modal age group?
| Leaf | |
|---|---|
| 2 | 0\ 3\ 5\ 6\ 7\ 7\ 9 |
| 3 | 0\ 2\ 2\ 2\ 7 |
| 4 | 4\ 4\ 5\ 7\ 8 |
| 5 | 2\ 3\ 7 |
Key: 2\vert 0=20
As part of a fuel watch initiative, the price of petrol at a service station was recorded each day for 14 days. The frequency table shows the findings:
| Price (in cents per litre) | Frequency |
|---|---|
| 130.0-134.9 | 4 |
| 135.0-139.9 | 5 |
| 140.0-144.9 | 2 |
| 145.0-149.9 | 3 |
What is the modal class (price range which has more scores than any other)?
What percentage of instances was the petrol price in the modal class? Round your answer to two decimal places.
In a study, a group of people were shown 30 names, and after 1 minute they were asked to recite as many names by memory as possible. The results are presented in the dot plot:
What does each dot represent?
How many people took part in the study?
What is the largest number of names someone remembered?
What was the smallest number of names someone remembered?
What is the range?
The stem plot shows the age of people who enter through the gates of a concert in the first 5 seconds:
How many people passed through the gates in the first 5 seconds?
What was the age of the youngest person?
What was the age of the oldest person?
What is the age difference between the youngest and oldest person?
| Leaf | |
|---|---|
| 1 | 2\ 3\ 4\ 5\ 5\ 6\ 6\ 7\ 7\ 9 |
| 2 | 1\ 2\ 4\ 4 |
| 3 | 0\ 2\ 9\ 9 |
| 4 | |
| 5 | 5 |
Key: 1\vert 2=12
The stem plot shows the results of a survey conducted on the price of concert tickets locally and the price of the same concerts at an international venue:
Determine the interquartile range for the international venue.
Determine the interquartile range for the local venue.
At which venue is there the least spread in the middle 50\% of prices?
| International | Local | |
|---|---|---|
| 9\ 9\ 9 | 6 | 8 |
| 8\ 5\ 5\ 5\ 3\ 0 | 7 | 5\ 6\ 6\ 9\ 9 |
| 8\ 4\ 3\ 2\ 1\ 0 | 8 | 2\ 2\ 6\ 6 |
| 5\ 3\ 2\ 0 | 9 | 0\ 0\ 1\ 4\ 5\ 6\ 8 |
| 5 | 10 | 0\ 3\ 5 |
Key: 9 \vert 6\vert 8=69 \text{ and } 68