11.04 Standard deviation
Consider the following graphs:
Which graph has the highest standard deviation?
Which graph has the lowest standard deviation?
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
81,\, 90,\, 90,\, 88,\, 73,\, 80,\, 86,\, 87,\, 75,\, 82,\, 70,\, 81,\, 71,\, 81,\, 79,\, 81,\, 80,\, 86,\, 88,\, 79
20,\, 44,\, 27,\, 25,\, 21,\, 28,\, 41,\, 24,\, 27,\, 39,\, 35,\, 43,\, 30,\, 17,\, 40
3,\, 14,\, 11,\, 17,\, 3,\, 18,\, 15,\, 6,\, 17,\, 15
Find the standard deviation for the data represented by the frequency table, correct to two decimal places.
| Score | Frequency |
|---|---|
| 15 | 13 |
| 16 | 9 |
| 17 | 23 |
| 18 | 19 |
| 19 | 8 |
| 20 | 13 |
Find the standard deviation for the data represented by the grouped frequency table, correct 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 |
Find the standard deviation for the data represented by the following dot plots, correct to two decimal places:
Find the standard deviation for the data represented by the following histograms, correct to two decimal places:
For each of the following histograms:
Find the range of the data set.
Find the mean of the data set, correct to two decimal places.
Find the standard deviation of the data set, correct to two decimal places.
For each of the following stem-and-leaf plots, calculate the following statistics, correct to two decimal places:
Mean
Standard deviation
| Leaf | |
|---|---|
| 1 | 3\ 7\ 7 |
| 2 | 0\ 2\ 5\ 7\ 8\ 9 |
| 3 | 7\ 8 |
| 4 | 0\ 5\ 7\ 9 |
| 5 | 1 |
| 6 | 4\ 6 |
| 7 | 3\ 3 |
Key: 1 | 2 = 12
| 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
The number of runs scored by Mario in each of his innings is listed below:
33,\enspace 32,\enspace 32,\enspace 32,\enspace 31,\enspace 32,\enspace 32,\enspace 32,\enspace 32,\enspace 32
Find his batting average.
Find his standard deviation, correct to two decimal places.
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 population standard deviation of the scores, correct to two decimal places.
On the sixth dive, the diver scores 8.8. What effect will this score have on the mean and standard deviation?
If each judge gave the same score for the 6th dive, state the standard deviation of the scores for this dive.
The trial times (in seconds) of a female 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, correct to two decimal places.
On her next attempt, she manages to run 100\text{ m} in 10.1 seconds. Determine if this time would increase or decrease the following statistics:
Mean
Standard deviation
Meteorologists predicted a huge variation in temperatures throughout the month of April. The temperature each day for the first two weeks of April were recorded as follows:16, \, 18, \, 20.5, \, 21, \, 21, \, 21, \, 21.5, \, 22, \, 22, \, 24, \, 24, \, 25, \, 26, \, 27
State the range of the temperatures.
Calculate the interquartile range of the temperatures.
Find the population standard deviation, correct to one decimal place.
Would the standard deviation or the interquartile range be the best measure of spread to support or counter the prediction of a huge variation in temperatures?
The table shows the number of goals scored by a football team in each game of the year:
In how many games were no goals scored?
Determine the median number of goals scored.
Calculate the mean number of goals scored each game, to two decimal places.
Find the population standard deviation, correct to two decimal places.
| \text{Score}\left(x \right) | \text{Frequency}\left(f \right) |
|---|---|
| 0 | 3 |
| 1 | 1 |
| 2 | 5 |
| 3 | 1 |
| 4 | 5 |
| 5 | 5 |