Worksheet: Variance and Standard Deviation

In this worksheet, we will practice finding and interpreting the variance and the standard deviation.

Q1:

Calculate the standard deviation of the values 45, 35, 42, 49, 39, and 34. Give your answer to 3 decimal places.

Q2:

If ( 𝑥 ̄ 𝑥 ) 2 for a set of 6 values equals 25, find the standard deviation of the set, and round the result to the nearest thousandth.

Q3:

The table shows the distribution of goals scored in the first half of a football season.

Number of Goals 1 2 4 5 6
Number of Matches 1 9 7 5 8

Find the standard deviation of the number of goals scored. If necessary, give your answer to three decimal places.

Q4:

The table shows the heights of some basketball players in centimeters. Calculate, to three decimal places, the standard deviation of the heights.

180 181 183 185 179
184 175 188 183 184

Q5:

Without calculating the exact standard deviations, determine which of the following datasets has the highest standard deviation.

  • A10, 10, 10, 10, 10, 11
  • B100, 100, 100, 100, 100, 100
  • C100, 200, 300, 400, 500, 500
  • D 1 000, 2 000, 3 000, 4 000, 5 000, 6 000
  • E3, 31, 53, 63, 63, 63

Q6:

What is the name of a quantity expressing by how much the members of a group differ from the mean value for the group?

  • Amedian
  • Barithmetic mean
  • Crange
  • Dstandard deviation

Q7:

Fady has gathered in the table below his last jogging times in minutes.

96 97 98 100 101 108 81 114 83 116
85 113 119 120 86 89 91 87 94

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.

Q8:

The table represents the time, in minutes, that several people took to finish a race.

100 101 104 106 109 110 112 113 82 115
116 117 86 119 120 87 90 91 89

If the data was instead given in hours, calculate its standard deviation to two decimal places.

Q9:

Calculate the standard deviation of the values . If necessary, give your answer to three decimal places.

Q10:

Find, to two decimal places, the variance of the following scores obtained in a quiz by 92 students.

Score 0–20 20–40 40–60 60–80 80–100
Frequency 26 10 24 5 27

Q11:

The data set shows the number of tomatoes growing on each tomato plant in a garden.

7 12 8 3 0 4 4 6 5

Calculate the range of the data.

Calculate the interquartile range of the data.

Calculate, to the nearest hundredth, the population standard deviation.

Q12:

By calculating the standard deviation, determine which of the sets { 1 7 , 2 0 , 6 , 1 3 } , { 5 , 1 6 , 5 , 9 } , or { 1 , 6 , 2 0 , 1 } has the largest dispersion.

  • A { 1 , 6 , 2 0 , 1 }
  • B { 5 , 1 6 , 5 , 9 }
  • C { 1 7 , 2 0 , 6 , 1 3 }

Q13:

Determine (without calculating the standard deviation exactly) which of the following data sets has the lowest standard deviation.

  • A100, 200, 300, 400, 500, 600
  • B50, 50, 50, 50, 50, 1 000
  • C10, 20, 30, 40, 50, 60
  • D149, 149, 149, 149, 149, 150
  • E0, 18, 37, 49, 49, 49

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