Find the range of the following sets of scores:
10,\, 7,\, 2,\, 14,\, 13,\, 15,\, 11,\, 4
15,\, - 2 ,\, - 8 ,\, 8,\, 15,\, 6,\, - 16 ,\, 15
- 0.5537,\, 1.7444,\, - 0.3381 ,\, 0.7200,\, - 0.3381,\, 1.0435
Consider the data provided in the table:
Find the range of the scores.
Find the mode.
| Score | Frequency |
|---|---|
| 68 | 16 |
| 69 | 41 |
| 70 | 30 |
| 71 | 31 |
| 72 | 49 |
| 73 | 29 |
Calculate the range for the data in the following histogram:
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?
A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in the following stem plot:
What was the difference between his slowest and fastest heart rate?
For each extra heartbeat per minute, it takes 10 seconds longer for him to recover. How much longer would it take to recover when he finishes with the fastest heart rate than when he finishes with the slowest heart rate?
| Leaf | |
|---|---|
| 16 | 0\ 3\ 4\ 4\ 6\ 7\ 8 |
| 17 | 1\ 2\ 2\ 3\ 5\ 5\ 5\ 6 |
| 18 | 4\ 4\ 6\ 8 |
| 19 | 0\ 1\ 3\ 6 |
\text{ Key: } 13|2=132
Find the range of fuel prices shown in the following graph:
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?
For each set of scores, find:
The total number of scores
The median
The range
The first quartile
The third quartile
The interquartile range
13,\, 15,\, 5,\, 16,\, 7,\, 20,\, 12
- 3 ,\, - 3 ,\, 1,\, 9,\, 9,\, 6,\, - 9
33,\, 38,\, 50,\, 12,\, 33,\, 48,\, 41
1.2,\, 2.9,\, 3.5,\, 1.6,\, 3.2,\, 4.8,\, 1.9
| Leaf | |
|---|---|
| 2 | 2\ 5\ 6\ 7\ 9 |
| 3 | 0\ 0\ 5\ 6\ 8 |
| 4 | 0\ 0\ 1\ 8\ 9 |
| Score | Frequency |
|---|---|
| 5 | 3 |
| 13 | 3 |
| 16 | 2 |
| 28 | 2 |
| 31 | 3 |
| 38 | 4 |
| 48 | 2 |
For each data set represented by a dot plot below, find:
The median
The first quartile
The third quartile
The interquartile range
For each set of data, find the following:
The first quartile
The third quartile
The interquartile range
| Leaf | |
|---|---|
| 6 | 2\ 7 |
| 7 | 1\ 2\ 2\ 4\ 7\ 9 |
| 8 | 0\ 1\ 2\ 5\ 7 |
| 9 | 0\ 1 |
The data below 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:
Find the interquartile range for the international venue.
Find 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 |
A group of students were asked how many phone calls they had made the previous day. The information was collected in the given frequency table:
How many students were surveyed?
Find the range of the data.
Find the interquartile range.
| Phone calls | Frequency |
|---|---|
| 0 | 8 |
| 1 | 5 |
| 2 | 10 |
| 3 | 6 |
| 4 | 6 |
| 5 | 7 |
| 6 | 3 |
| 7 | 2 |
A sample of boxes of matches were selected for quality control and the number of matches in each box recorded in the given frequency table:
How many matchboxes were sampled?
Find the range of the data.
Find the interquartile range.
| Matches | Frequency |
|---|---|
| 45 | 1 |
| 46 | 2 |
| 47 | 5 |
| 48 | 3 |
| 49 | 7 |
| 50 | 25 |
| 51 | 6 |
| 52 | 2 |
Edward records the number of fish he catches for each fishing trip over a period of time:
How many fishing trips did he go on?
Find the range in the number of fish caught.
Find the interquartile range.
Consider the given column graph:
| Class | Class centre | Frequency |
|---|---|---|
| 1-5 | ||
| 6-10 | ||
| 11-15 | ||
| 16-20 |
Complete the given frequency table.
Use the class centres to estimate the:
Range
Interquartile range
The histogram below displays the speeds of balls delivered by a bowler in cricket:
Create a frequency table for the data and include a column for class centres.
Use the class centres to estimate the:
Range
First quartile
Third quartile
Interquartile range
The following histogram shows the heights of tomato plants in a greenhouse.
Create a frequency table for the data and include a column for class centres.
Use the class centres to estimate:
The range
The interquartile range
In a survey the mass (in grams) of 30 individual apples from an orchard were noted and recorded in the following list:
86,\quad 87,\quad 91,\quad 93,\quad 94,\quad 95,\quad 96,\quad 96,\quad 98,\quad99
100,\quad 101,\quad 102,\quad 103,\quad 103,\quad 104,\quad 104,\quad 105,\quad 106,\quad 106
106,\quad 107,\quad 107,\quad 107,\quad 108,\quad 108,\quad 109,\quad 109,\quad 109,\quad 109
Find the following statistics:
The smallest value
The largest value
The range
The first quartile
The third quartile
The interquartile range
Complete the given frequency table.
Using the class centres, find an estimate for:
How much less was the approximation for the interquartile range than the actual interquartile range?
| \text{Weight (g)} | \text{Class} \\ \text{centre} | \text{Frequency} |
|---|---|---|
| 85\leq x \lt 90 | 87.5 | |
| 90\leq x \lt 95 | 3 | |
| 95\leq x \lt 100 | ||
| 100\leq x \lt 105 | ||
| 105\leq x \lt 110 |
A data set has the following known statistics:
| Median | Mode | Range | Interquartile range |
|---|---|---|---|
| 12 | 8 | 18 | 7 |
Find the new value for each of the statistics above, given each value of the data set was:
Increased by 6.
Multiplied by 3.
In competition, a diver must complete 8 rounds of dives. Her scores for the first 7 rounds are:
7.3,\, 7.4,\, 7.7,\, 8.4,\, 8.7,\, 8.9,\, 9.4
Find her score in the 8th round if the upper quartile of all of her 8 scores is 8.85.
In a competition, a contestant must complete 12 challenges earning as many points as possible. Her scores for the first 11 challenges are:
32,\, 38,\, 45,\, 55,\, 66,\, 86,\, 94,\, 98,\, 106,\, 108,\, 117
Find her score in the 12th round if the lower quartile of all of her 12 scores is 47.5.
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.
From the information given, find:
The maximum
The second number in the data set
The fourth number in the data set
List the five numbers in the data set.
Four numbers have a range of 5, a median of 9 and a mode of 11. Write the four numbers of this data set.