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
A group of students had a range in marks of 14 and the lowest score was 9. Find the highest score in the group.
The range of a set of scores is 8, and the highest score is 19. Find the lowest score in the set.
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 one dot represent?
How many people took part in the study?
State the largest number of names someone remembered.
State the smallest number of names someone remembered.
Find the range of the data.
Calculate the range of the data in the given the bar chart:
The following stem and leaf plot shows the number of hours students spent studying for a science exam:
From the data in the stem and leaf plot, find the following:
Mean
Median
Mode
Range
| Number of hours | |
|---|---|
| 6 | 2\ 7 |
| 7 | 1\ 2\ 2\ 4\ 7\ 9 |
| 8 | 0\ 1\ 2\ 5\ 7 |
| 9 | 0\ 1 |
Consider the data provided in the table:
Calculate the range.
State the mode.
| Score | Frequency |
|---|---|
| 68 | 16 |
| 69 | 41 |
| 70 | 30 |
| 71 | 31 |
| 72 | 49 |
| 73 | 29 |
Consider the following set of scores:
13, 15, 5, 16, 7, 20, 12
Sort the scores in ascending order.
Find the total number of scores.
Find the median.
Find the range.
Find the first quartile.
Find the third quartile.
Find the interquartile range.
For each of the following data sets:
Find the number of scores.
Find the median.
Find the first quartile.
Find the third quartile.
Find the interquartile range.
33, 38, 50, 12, 33, 48, 41
- 3 , - 3 , 1, 9, 9, 6, - 9
| Leaf | |
|---|---|
| 2 | 2\ 5\ 6\ 7\ 9 |
| 3 | 0\ 0\ 5\ 6\ 8 |
| 4 | 0\ 0\ 1\ 8\ 9 |
Key: 1 | 2 = 12
| Score | Frequency |
|---|---|
| 5 | 3 |
| 13 | 3 |
| 16 | 2 |
| 28 | 2 |
| 31 | 3 |
| 38 | 4 |
| 48 | 2 |
Consider the set of scores in the following bar chart:
Organise the data into a frequency table that includes an fx column and a cumulative frequency column.
Find the median score.
Find the first quartile.
Find the third quartile.
Find the interquartile range.
Find the standard deviation of the following sets of scores correct to two decimal places by using the statistics mode on your calculator:
8, 20, 16, 9, 9, 15, 5, 17, 19, 6
- 17 , 2, - 6 , 9, - 17 , - 9 , 3, 8, 5
Consider the following dot plot:
Find the mean of the data. Round your answer to two decimal places.
Find the standard deviation of the data. Round your answer to two decimal places.
Find the percentage of data that lie within 1 standard deviation of the mean.
Find the percentage of data that lie within 2 standard deviations of the mean.
The dot plot shows the number of sit-ups achieved by students in a Physical Education exam:
Find the mean to two decimal places.
Find the standard deviation of the data. Round your answer to two decimal places.
Find the percentage of data that lie within 1 standard deviation of the mean. Round your answer to one decimal place.
Find the percentage of data that lie within 2 standard deviations of the mean.
For the given stem and leaf plot, find the following to two decimal places:
The mean
The standard deviation
Find the percentage of data that lie within 1 standard deviation of the mean.
Find the percentage of data that lie within 2 standard deviations of the mean.
| Leaf | |
|---|---|
| 1 | 3\ 3\ 9 |
| 2 | 3\ 8 |
| 3 | 4 |
| 4 | 4\ 7\ 9 |
| 5 | 5\ 8 |
| 6 | 8 |
| 7 | 5 |
| 8 | 3 |
| 9 | 7 |
Key: 1 | 2 = 12
Consider the following table:
| \text{Class} | \text{Class Centre} | \text{Frequency} | f x |
|---|---|---|---|
| 1 - 9 | 8 | ||
| 10 - 18 | 6 | ||
| 19 - 27 | 4 | ||
| 28 - 36 | 6 | ||
| 37 - 45 | 8 | ||
| \text{Totals} |
Complete the table.
Use the class centres to estimate the mean to two decimal places.
Use the class centres to estimate the standard deviation to two decimal places.
If we used the original ungrouped data to calculate the standard deviation, do you expect that the ungrouped data would have a higher or lower standard deviation? Explain your answer.
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. Round your answer to one decimal place.
At which venue is there the least spread in the middle 50\% of prices?
| Local price | International price | |
|---|---|---|
| 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: 1 |4 | 2 = \$41 \text{ and }\$ 42
A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in the following stem and leaf plot:
Find 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?
| Heart rate | |
|---|---|
| 16 | 0\ 1\ 4\ 4\ 6\ 7\ 8 |
| 17 | 1\ 2\ 2\ 3\ 5\ 5\ 5\ 6 |
| 18 | 4\ 4\ 6\ 8 |
| 19 | 0\ 1\ 3\ 6 |
Key: 13 | 2 = 132
The mean income of people in Country A is \$19\,069. This is the same as the mean income of people in Country B. The standard deviation of Country A is greater than the standard deviation of Country B.
In which country is there likely to be the greatest difference between the incomes of the rich and poor?
Seven millionaires with an average net wealth of \$41 million with a standard deviation of \$7 million are having a party. Suddenly Carlos Slim, who has a net wealth estimated to be \$31 billion, walks into the room.
Find the new average net wealth in the room. Give your answer rounded to the nearest million.
Will the new standard deviation be higher, lower or unchanged from before?
Will the new mode be higher, lower or unchanged from before if at least two of the original seven millionaires have the same net wealth?
Will the range be higher, lower or unchanged from before?
The following table shows the number of goals scored by a football team in each game of the year:
In how many games were 0 goals scored?
Find the median number of goals scored.
Calculate the mean number of goals scored to two decimal places.
Calculate the standard deviation to two decimal places.
Find the percentage of data that lie within 1 standard deviation of the mean.
Find the percentage of data that lie within 2 standard deviations of the mean.
| Score | Frequency |
|---|---|
| 0 | 3 |
| 1 | 1 |
| 2 | 5 |
| 3 | 1 |
| 4 | 5 |
| 5 | 5 |
Meteorologists predicted huge variation in temperatures throughout the month of April. The temperature each day for the first two weeks of April was recorded:
16, \quad 18, \quad 20.5, \quad 21, \quad 21, \quad 21, \quad 21.5, \quad 22, \quad 22, \quad 24, \quad 24, \quad 25, \quad 26, \quad 27
State the range.
Find the interquartile range.
Calculate the standard deviation to one decimal place.
Is the standard deviation or the interquartile range the best measure of spread to support or counter a prediction? Explain your answer.
The scores obtained by two classes are given below:
Red Class: 55, 57, 49, 58, 68, 57, 60, 53, 56, 51
Blue Class: 53, 57, 62, 51, 56, 62, 58, 55, 58, 51
Which class performed better on average? Use statistical calculations to justify your answer.
Which class produced more consistent results? Use statistical calculations to justify your answer.
Han, a cricketer, has achieved scores of 52, 20, 68, 70 and 150 in his first five innings this season. In his sixth innings, he scores 0.
Describe how his season batting average changed from before to after the sixth inning.
Describe how his standard deviation changed from before to after the sixth inning.
Describe how his median score changed from before to after the sixth inning.
Describe how his range changed from before to after the sixth inning.
The table shows the heart rate data of a group of people after exercise:
| Height of step | Stepping rate | Heart rate |
|---|---|---|
| \text{Short step} | \text{Slow} | 89 |
| \text{Short step} | \text{Slow} | 91 |
| \text{Short step} | \text{Medium} | 106 |
| \text{Short step} | \text{Medium} | 105 |
| \text{Short step} | \text{Fast} | 124 |
| \text{Short step} | \text{Fast} | 128 |
| \text{Tall step} | \text{Slow} | 100 |
| \text{Tall step} | \text{Slow} | 96 |
| \text{Tall step} | \text{Medium} | 125 |
| \text{Tall step} | \text{Medium} | 129 |
| \text{Tall step} | \text{Fast} | 132 |
| \text{Tall step} | \text{Fast} | 127 |
Complete the following table. Round all values to one decimal place.
| Height of step | Data | Slow | Medium | Fast |
|---|---|---|---|---|
| \text{Short step} | \text{Avg. heart rate} | 90.0 | ||
| \text{Standard deviation of heart rate} | 1.0 | |||
| \text{Tall step} | \text{Avg. heart rate} | |||
| \text{Standard deviation of heart rate} |
Which of the combinations of step height and stepping rate generated the higher heart rate?
Which combination of step height and stepping rate showed the least variability?