Find the standard deviation of the following set of scores correct to two decimal places:
8, 20, 16, 9, 9, 15, 5, 17, 19, 6
- 17 , 2, - 6 , 9, - 17 , - 9 , 3, 8, 5
Given the data in the stem and leaf plot, calculate the following correct to two decimal places:
The mean
The standard deviation
| Leaf | |
|---|---|
| 1 | 0\ 2\ 6 |
| 2 | 6\ 8 |
| 3 | 0 |
| 4 | 5\ 5\ 6 |
| 5 | 6\ 6 |
| 6 | 0 |
| 7 | 7 |
| 8 | 9 |
| 9 | 2 |
Key: 1 \vert 2 = 12
Consider the following histogram:
Find the range of the data set.
Find the mean of the data set correct to two decimal places.
Find the population standard deviation, correct to two decimal places.
Use your CAS calculator to determine the standard deviation for the data represented by the histogram. Round your answer to two decimal places.
Use your CAS calculator to determine the standard deviation for the data represented by the following dot plots:
Use your CAS calculator to determine the standard deviation for the data represented by the frequency table:
Round your answer to two decimal places.
| Score | Frequency |
|---|---|
| 15 | 13 |
| 16 | 9 |
| 17 | 23 |
| 18 | 19 |
| 19 | 8 |
| 20 | 13 |
Use your CAS calculator to determine the standard deviation for the data represented by the grouped frequency table, using the class centres. Round your answer to two decimal places.
| Class | Class centre | Frequency |
|---|---|---|
| 40\leq x < 45 | 42.5 | 4 |
| 45 \leq x < 50 | 47.5 | 11 |
| 50 \leq x < 55 | 52.5 | 16 |
| 55 \leq x < 60 | 57.5 | 17 |
| 60 \leq x < 65 | 62.5 | 7 |
| 65 \leq x < 70 | 67.5 | 12 |
| 70 \leq x < 75 | 72.5 | 11 |
| 75 \leq x < 80 | 77.5 | 5 |
Use your CAS calculator to determine the standard deviation for the data represented by the histogram, using the class centres. Round your answer to two decimal places.
Consider the frequency table below:
Complete the table.
Use the class centres to estimate the mean. Round your answer to two decimal places.
Use the class centres to estimate the standard deviation. Round your answer to two decimal places.
| \text{Class} | \text{Class Centre} | f | fx |
|---|---|---|---|
| 1-9 | 6 | ||
| 10- 18 | 7 | ||
| 19- 27 | 7 | ||
| 28- 36 | 6 | ||
| 37- 45 | 6 | ||
| \text{Totals} |
The 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?
Determine the median number of goals scored.
Calculate the mean number of goals scored each game, to two decimal places.
Use your calculator to find the standard deviation, to two decimal places.
| \text{Score, }x | \text{Frequency, }f |
|---|---|
| 0 | 3 |
| 1 | 1 |
| 2 | 5 |
| 3 | 1 |
| 4 | 5 |
| 5 | 5 |
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?
Two machines A and B are producing chocolate bars with the following mean and standard deviation for the weight of the bars:
| Machine | Mean (g) | Standard deviation (g) |
|---|---|---|
| A | 52 | 1.5 |
| B | 56 | 0.65 |
What does a comparison of the mean of the two machines tell us?
What does a comparison of the standard deviation of the two machines tell us?
Two friends compete in triple jump and the distance of 20 jumps were recorded. The mean and standard deviation for the jumps are shown below:
| Jumper | Mean (m) | Standard deviation (m) |
|---|---|---|
| \text{William} | 12.6 | 0.8 |
| \text{Kathleen} | 11.6 | 0.4 |
What does a comparison of the mean of the two friends tell us?
What does a comparison of the standard deviation of the two friends tell us?
Two friends compete in 100 \text{ m} sprints and the time to complete 50 sprints were recorded. The mean and standard deviation for the sprints are shown below:
| Runner | Mean (s) | Standard deviation (s) |
|---|---|---|
| \text{Derek} | 13.1 | 1.2 |
| \text{Sarah} | 14.5 | 0.75 |
What does a comparison of the mean of the two friends tell us?
What does a comparison of the standard deviation of the two friends tell us?
Two cricketers compare the mean and standard deviation of their runs made per match. They conclude that Tobias is a more consistent batter but Lucy generally scores more runs per match.
What can we say about the comparison of their means and standard deviations?
The scores obtained by two classes are given below:
Red Class: 48, 51, 50, 47, 51, 49, 58, 57
Blue Class: 44, 54, 58, 61, 66, 40, 51, 50
Calculate the mean of the scores obtained by the Red class, correct to two decimal places.
Calculate the mean of the scores obtained by the Blue class, correct to two decimal places.
Calculate the standard deviation of the scores obtained by the Red class, correct to two decimal places.
Calculate the standard deviation of the scores obtained by the Blue class, correct to two decimal places.
Which class performed better? Explain your answer.
Which class produced more consistent results? Explain your answer.
The scores of five diving attempts by a professional diver are recorded below:
5.6, \, 6.6, \, 6.3,\, 5.9, \, 6.4
Calculate the standard deviation of the scores to two decimal places.
On the sixth attempt, the diver scores 8.8. What affect will this score have on:
The mean
The standard deviation
If each judge gave the same score for the 6th dive, what would be the standard deviation of the judges’ scores for this dive?
The following table shows the heart rate 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 for stepping rate, giving all answers to one decimal place:
| \text{Height of step} | \text{Data} | \text{Slow} | \text{Medium} | \text{Fast} |
|---|---|---|---|---|
| \text{Short step} | \text{Average of heart rate} | 90.0 | ||
| \text{Short step} | \text{Standard deviation of heart rate} | 1.0 | ||
| \text{Tall step} | \text{Average of heart rate} | |||
| \text{Tall step} | \text{Standard deviation of heart rate} |
Which combination of step height and stepping rate generated the higher heart rate?
Which combination of step height and stepping rate showed the least variability?
In an entrance exam, applicants completed two papers as shown in the table.
On average, students performed better in Paper 1, but their marks were less spread out in Paper 2.
State the range of possible values for s.
| Mean | Standard Deviation | |
|---|---|---|
| \text{Paper } 1 | 77 | 13 |
| \text{Paper }2 | 57 | s |
The mean of a set of scores is 77 and the standard deviation is 29. Find the value of:
\text{Mean } - \text{Standard Deviation}
\text{Mean } + 2 \times \text{Standard Deviation}
\text{Mean } - \dfrac{\left( 2 \times \text{Standard Deviation}\right)}{3}
\text{Mean } + \dfrac{\left( 4 \times \text{Standard Deviation}\right)}{5}
\text{Mean } + 3 \times \text{Standard Deviation}
\text{Mean } - 2 \times \text{Standard Deviation}
The mean of a set of scores is \mu = 51, and the standard deviation is \sigma = 16. Find the value of:
\mu - \sigma
\mu + 2 \sigma
\mu + 3 \sigma
\mu - 2 \sigma
\mu + 0.5 \sigma
\mu - \dfrac{2 \sigma}{3}
The literacy rate of a population is used to help measure the level of development of a country. The mean literacy rate in a particular country is 59\%, and the standard deviation is 5\%. The literacy rate varies from place to place within the country.
Find the literacy rate that is 3 standard deviations above the mean. Write your answer as a percentage.
Find the literacy rate that is 2 standard deviations below the mean. Write your answer as a percentage.
The percentage of people in each country with internet access is averaged and found to be 30\%. In one particular country, the percentage is 67.5\%, which is 2.5 standard deviations above the mean. What is the standard deviation among the countries? Write your answer as a percentage.
The following table shows the mean and standard deviation of the marks obtained by a student in two subjects:
Find the mark in Science that is 2 standard deviations below the mean.
Find the mark in English that is 1.5 standard deviations above the mean
Find the mark in Science that is 0.5 standard deviations above the mean
Find the mark in English that is 1 standard deviation below the mean.
| Mean | Standard Deviation | |
|---|---|---|
| Science | 89 | 11 |
| English | 72 | 12 |
The following table shows the marks obtained by a student in two subjects:
How many standard deviations above the mean was the student's score in Science?
In which subject did the student perform better?
| Mark | Mean | Standard Deviation | |
|---|---|---|---|
| Science | 100 | 44 | 14 |
| Math | 98 | 68 | 15 |
A batsman’s mean number of runs is 62 and the standard deviation is 13. In the next match he makes 50 runs.
Explain how this latest match affected his mean and standard deviation.