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Worksheet: Variance and Standard Deviation

Q1:

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.

Q2:

Michael 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.

Q3:

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

99 101 102 108 109 110 111 80 81 114
112 113 86 87 120 118 92 94 95

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.

Q4:

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

Q5:

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

  • A4, 4, 4, 4, 4, 5
  • B25, 25, 25, 25, 25, 25
  • C100, 200, 300, 400, 500, 500
  • D500, 1 000, 1 500, 2 000, 2 500, 3 000
  • E24, 49, 69, 74, 74, 74

Q6:

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

  • A150, 150, 150, 150, 150, 151
  • B100, 100, 100, 100, 100, 100
  • C100, 200, 300, 400, 500, 500
  • D100, 200, 300, 400, 500, 600
  • E0, 1, 16, 26, 26, 26

Q7:

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

Q8:

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.

Q9:

If ( 𝑥 ̄ 𝑥 ) 2 for a set of 4 values equals 900, find the standard deviation of the set, and round the result to the nearest thousandth.

Q10:

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

Q11:

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

  • Avariance
  • Barithmetic mean
  • Crange
  • Dstandard deviation

Q12:

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.