Find the mean of the following sets of scores:
9, \quad 5,\quad 2,\quad 3,\quad 1
3,\quad 2,\quad 5,\quad 1,\quad 4
1,\quad 3,\quad 7,\quad 5,\quad 2
4,\quad 5,\quad 6,\quad 7,\quad 3
56, 89, 95, 71, 75, 84, 65, 83
-14, 0, -2, -18, -8, 0, -15, -1
Consider the given 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.
There are five numbers with a mean of 7. If four of the numbers are 10, 10, 8, 7 \text{ and } x, find the value of x.
The five numbers 16, 16, 17, 24 \text{ and } 17 have a mean of 18. If a new number is added that is bigger than 24, state whether the mean will become higher or lower.
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.
The table shows the scores of Student A and Student B in 5 separate tests:
Find the mean of the scores for Student A.
Find the mean of the scores 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 |
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?
Considering the total number of points, 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 \text{ and } 66 runs. In his last match before trying out, he wants to lift his mean to 70. Find the number of runs he needs to score to achieve this.
For the following sets of scores:
Sort the scores in ascending order.
Find the median.
17, 8, 6, 11, 9, 18
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
A set of 69 scores is arranged in ascending order. In what position does the median score lie?
In a set of 152 scores between which two scores does the median lie?
Write down 4 consecutive odd numbers whose median is 40.
Calculate the median for the following frequency table:
| Score | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|
| Frequency | 24 | 9 | 21 | 9 | 6 |
For the given histogram:
Find the number of scores.
Find the median.
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?
The following stem-and-leaf plot shows the ages of 20 employees in a company:
How many of the employees are in their thirties?
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 mode age?
| 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: 1 | 2 = 12 years old
A diver measures how long she can hold her breath underwater over several dives. If the median time is 3.9 minutes, explain what this means for her other times.
Find the mode of the following data sets:
| Score | Frequency |
|---|---|
| 25 | 17 |
| 26 | 42 |
| 27 | 35 |
| 28 | 32 |
| 29 | 12 |
| 30 | 20 |
2, 2,6,8,8,8,8,12,14,14,14,14,18,18
State the difference between the median and the mode.
A consumer group surveys the price of petrol per litre at six different petrol stations. The prices are as follows:\$1.68,\quad \$1.64,\quad \$1.64,\quad \$1.71,\quad \$1.64,\quad \$1.57
State the mode petrol price.
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 below shows the findings:
| Price (cents per litre) | Class Centre | Frequency |
|---|---|---|
| 130.9 - 135.9 | 133.4 | 4 |
| 135.9 - 140.9 | 138.4 | 5 |
| 140.9 - 145.9 | 143.4 | 2 |
| 145.9 - 150.9 | 148.4 | 4 |
What is the modal class?
What percentage of prices were in the modal class? Round your answer to two decimal places.
State whether 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 range.
Two sets of data that have the same highest and lowest values must have the same mean.
Consider the set of data:
1,\quad 2,\quad 2,\quad 4,\quad 4,\quad 5,\quad 6,\quad 6,\quad 8,\quad 8,\quad 8,\quad 9,\quad 9
If one score of 8 is changed to a 9, which of the measures of centre would be altered?
Consider this set of data that represents the number of apps on six people’s phones:
10,\quad 13,\quad 14,\quad 17,\quad 20,\quad 20
If each person downloads another 9 apps, which of the measures of centre would change?
Determine the measure of centre that should be used for the following data sets. Explain your choice.
12,\quad 15,\quad 16,\quad 21,\quad 22,\quad 25
85,\quad 85,\quad 95,\quad 70,\quad 60,\quad 70,\quad 105
36,\quad 46,\quad 49,\quad 40,\quad 52,\quad 44,\quad 39,\quad 37
6,\quad 12,\quad 18,\quad 9,\quad 0,\quad 3,\quad 15, \quad 46
Find the most appropriate measure of centre for the following scenarios:
For a particular street in Sydney, house prices for houses sold in the last 36 months (in 1000's) were given:
920,\quad 920,\quad 709,\quad 694,\quad 667,\quad 657,\quad 630,\quad 610,\quad 584,\quad 567,\quad 555
The number of animal races that were won by a trainer over the years shown are listed in the table:
| Year | 2003 | 2004 | 2005 | 2006 | 2007 |
|---|---|---|---|---|---|
| Races won | 116 | 105 | 102 | 108 | 113 |
Carl has been recording his spelling test scores for the past semester:14,\quad 16,\quad 2,\quad 15,\quad 15,\quad 16,\quad 15
Calculate the median of Carl's scores.
Calculate the mean of Carl's scores. Round your answer to two decimal places.
Which measure of centre most accurately describes the centre of this data set? Explain your answer.
For each of the following data sets find the following measures of centre. Round your answer 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 |
