Worksheet: Variance and Standard Deviation
In this worksheet, we will practice finding and interpreting the variance and the standard deviation.
The table shows the distribution of goals scored in the first half of a football season.
|Number of Goals||0||1||3||4||6|
|Number of Matches||5||2||7||7||4|
Find the standard deviation of the number of goals scored. Give your answer to three decimal places.
Without calculating the exact standard deviations, determine which of the following datasets has the highest standard deviation.
- A100, 200, 300, 400, 500, 500
- B3, 31, 53, 63, 63, 63
- C1,000, 2,000, 3,000, 4,000, 5,000, 6,000
- D10, 10, 10, 10, 10, 11
- E100, 100, 100, 100, 100, 100
What is the name of a quantity expressing by how much the members of a group differ from the mean value for the group?
- Astandard deviation
- Carithmetic mean
Michael has gathered in the table below his last jogging times in minutes.
If the jogging times were converted into hours, what would be the variance of the data set? Give your answer correct to two decimal places.
The table represents the time, in minutes, that several people took to finish a race.
If the data was instead given in hours, calculate its standard deviation to two decimal places.
Calculate the standard deviation of the values . Give your answer to three decimal places.
Find, to two decimal places, the variance of the following scores obtained in a quiz by 92 students.
By calculating the standard deviation, determine which of the sets , , or has the largest dispersion.
Determine (without calculating the standard deviation exactly) which of the following data sets has the lowest standard deviation.
- A100, 200, 300, 400, 500, 600
- B0, 18, 37, 49, 49, 49
- C50, 50, 50, 50, 50, 1,000
- D149, 149, 149, 149, 149, 150
- E10, 20, 30, 40, 50, 60
Without calculating exact standard deviation values, determine which of the following data sets has the highest standard deviation.
- A75, 75, 75, 75, 75, 75
- B900, 1,800, 2,700, 3,600, 4,500, 5,400
- C10, 20, 30, 40, 50, 50
- D18, 31, 32, 55, 55, 55
- E144, 144, 144, 144, 144, 145
The set of data 47, 51, 47, 51, 47, 51, 47, 51, 47, 51 has a mean of 49. Use this to decide (without calculating the exact answer) which of the following is closest to the standard deviation of the data.
Using the given table and assuming an approximate normal distribution of grades in both schools, determine which student has the higher grade when compared to his school peers.
|Student||GPA||School Mean GPA||Standard Deviation|
If the dispersion of a set of values is equal to zero, then which of the following are true?
- AThe difference between the individuals is great.
- BAll the values are equal.
- CThe difference between the individuals is small.
- DThe arithmetic mean of these values is zero.
- EAll the values are negative.