For each of the following set of scores, find the sample standard deviation by using the statistics mode on your calculator. Round your answers to two decimal places.
11, 4, 9, 9, 6, 13, 8, 2, 11, 3
- 14 , 5, 1, - 7 , 8, - 17 , - 6 , 8, 5, 3
17, 28, 22, 28, 15, 35, 42, 26, 24, 27, 20, 25, 33, 26, 37
86, 78, 86, 87, 80, 81, 87, 85, 77, 85, 82, 82, 78, 83, 74, 81, 83, 84, 70, 89
Consider the data presented in the stem plot:
Calculate the following, rounding your answers to two decimal places:
The mean
The sample 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|2=12
Using your calculator, find the sample standard deviation for the data given in the dot plot below. Round your answer to two decimal places.
Consider the data presented in the histogram:
Calculate the following, rounding your answers to two decimal places if necessary:
The range
The mean
The sample standard deviation
Consider the data presented in the stem plot:
Calculate the following, rounding your answers to two decimal places:
The mean
The sample standard deviation
| Leaf | |
|---|---|
| 1 | 2\ 2\ 5 |
| 2 | 0\ 3\ 4\ 6\ 8\ 8 |
| 3 | 6\ 8 |
| 4 | 1\ 2\ 5\ 6 |
| 5 | 3 |
| 6 | 4\ 7 |
| 7 | 5\ 8 |
Key: 1|2=12
Consider the data presented in the histogram:
Calculate the following, rounding your answers to two decimal places if necessary:
The range
The mean
The sample standard deviation
Consider the data in the given table:
Complete the table.
Calculate the mean of the data set. Round your answer to two decimal places.
Use the class centres to estimate the sample standard deviation. Round your answer to two decimal places.
If we used the original ungrouped data to calculate standard deviation, do you expect that the ungrouped data would have a higher or lower standard deviation?
| \text{Class} | \text{Class}\\ \text{centre} | \text{Frequency} | fx |
|---|---|---|---|
| 1-5 | 6 | ||
| 6-10 | 4 | ||
| 11-15 | 7 | ||
| 16-20 | 8 | ||
| 21-25 | 5 | ||
| \text{Totals} |
The scores of five diving attempts by a professional diver are recorded below:
6.4, \, 5.9,\, 5.1,\, 5.1,\, 5.5
Calculate the sample standard deviation of his scores. Round your answer to two decimal places.
On his sixth attempt, the diver scores 9.3. State whether this score would increase or decrease the following:
The mean
The standard deviation
If each judge gave the diver the same score, what would be the sample standard deviation of the judges’ scores?
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,\, 16.5,\, 16.5,\, 17.5,\, 19.5,\, 22.5,\, 23.5,\, 23.5,\, 26,\, 26,\, 26.5,\, 27,\, 27.5,\, 28
What is the range of the temperatures?
What is the interquartile range of the temperatures?
What is the sample standard deviation? Round your answer to one decimal place.
Would the sample standard deviation or the interquartile range be the best measure of spread to support or counter a prediction? Explain your answer.
The table shows the number of goals scored by a football team in each game of the year.
In how many games were exactly 2 goals scored?
Determine the median number of goals scored.
Calculate the mean number of goals scored each game.
Find the sample standard deviation. Round your answer to two decimal places.
| \text{Score }(x) | \text{Frequency }(f) |
|---|---|
| 0 | 5 |
| 1 | 4 |
| 2 | 3 |
| 3 | 5 |
| 4 | 5 |
| 5 | 3 |
The mean income of people in Finland is \$45\,000. This is the same as the mean income of people in Canada. The standard deviation of Finland is greater than the standard deviation of Canada.
In which country is there likely to be the greatest difference between the incomes of the rich and poor? Explain your answer.
The scores obtained by two classes are given below:
-
Red class: 48, 56, 49, 43, 41, 44, 49, 46
Blue class: 64, 52, 43, 69, 66, 65, 58, 42
Calculate the following to two decimal places:
The mean of the Red class.
The mean of the Blue class.
The sample standard deviation of the Red class.
The sample standard deviation of the Blue class.
Which class performed better?
Which class produced more consistent results?
Seven millionaires with an average net wealth of \$33 million with a standard deviation of \$7 million are having a party. Then Carlos Slim, who has a net wealth estimated to be \$43 billion, enters the room.
What is the new average net wealth (in millions of dollars) in the room? Round your answer to the nearest million dollars.
When Carlos Slim's net worth is taken into account, will the standard deviation be higher, lower or unchanged from before?
Will the range be higher, lower or unchanged from before?
The trial times (in seconds) of an athlete for the 100\text{ m} sprint are recorded below:
11.0,\, 10.5,\, 12.2,\, 11.2,\, 11.6,\, 11.7,\, 10.8,\, 12.1,\, 11.0,\, 10.9
Calculate the sample standard deviation of her times. Round your answer to two decimal places.
On her next attempt, she manages to run 100\text{ m} in 10.1\text{ s}. Determine if this time would increase or decrease the following:
The mean
The standard deviation
Buzz, a cricketer, has made scores of 60, 36, 90, 54 and 90 in all his innings this season. In his next inning, he scores no runs.
What is the change in his season batting average?
What is the change in the sample standard deviation of his scores? Round your answer to two decimal places.
What is the change in his median score?
What is the change in his range of scores?