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 (𝑥̄𝑥) 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 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.

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
  • C 1,000, 2,000, 3,000, 4,000, 5,000, 6,000
  • D3, 31, 53, 63, 63, 63
  • E100, 200, 300, 400, 500, 500

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?

  • Astandard deviation
  • Bmedian
  • Carithmetic mean
  • Drange

Q7:

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.

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 1731215,,,,and. 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 {17,20,6,13}, {5,16,5,9}, or {1,6,20,1} has the largest dispersion.

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

Q13:

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

  • A0, 18, 37, 49, 49, 49
  • B 50, 50, 50, 50, 50, 1,000
  • C100, 200, 300, 400, 500, 600
  • D10, 20, 30, 40, 50, 60
  • E149, 149, 149, 149, 149, 150

Q14:

Without calculating exact standard deviation values, determine which of the following data sets has the highest standard deviation.

  • A144, 144, 144, 144, 144, 145
  • B 900, 1,800, 2,700, 3,600, 4,500, 5,400
  • C18, 31, 32, 55, 55, 55
  • D10, 20, 30, 40, 50, 50
  • E75, 75, 75, 75, 75, 75

Q15:

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.

  • A5
  • B10
  • C1
  • D2

Q16:

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
Daniel 3.02 2.85 0.29
William 2.37 2.88 0.59
  • ADaniel
  • BWilliam

Q17:

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 small.
  • BThe arithmetic mean of these values is zero.
  • CAll the values are equal.
  • DThe difference between the individuals is great.
  • EAll the values are negative.

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