# Calculating the Variance of a Discrete Random Variable

• 1.

At a fair, tickets are drawn to win or lose money. Here is the probability distribution that represents the situation.

X = amount won -$4-$1$0$2$5 P(X=x) 0.10.20.40.20.1 Find the variance of the amount won. Answers: •$5.57

• $2.24 •$2.36

• $5.01 • 2. The following table summarizes the results of a study of the number of children in families. X = number of children 01234 P(X=x) 0.30.20.250.20.05 What is the variance in the number of children? Choose the closest answer. Answers: • 1.24 • 2.25 • 2.5 • 1.55 • 3. The following table summarizes the results of a study of the number of shoes a group of students own. X = number of shoes 3891014 P(X=x) 0.30.20.290.20.01 Find the variance of the number of shoes. Select the best answer. Answers: • 2.89 • 15.7 • 3.96 • 8.39 • 4. One new board came is based on spinning a wheel to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel. X = spaces moved -2-1025 P(X=x) 0.250.20.30.20.05 Find the variance of the situation. Choose the closest answer. Answers: • 7.7 • 3.25 • 1.80 • 2.77 • 5. Some friends are taking part in a small lottery game where they can either win or lose money. Here is a summary of the outcomes. X = amount of money -$2.50$0.5$1$2 P(X=x) 0.20.150.30.20.15 Find the variance of the amount of money. Pick the best answer. Answers: •$2.10

• $1.45 •$1.68

• $2.82 • 6. At the front of the store is a cart with irregular shirts. The shirts are either missing buttons or have too many. Andy reaches into the cart and grabs a shirt at random. This table summarizes the probabilities for each incorrect number of buttons. X = buttons -5-3-201 P(X=x) 0.150.150.30.20.2 Which of the the values below is the variance of the number of buttons? Answers: • 1.98 • 2.39 • 5.70 • 3.94 • 7. When playing a football game, there are points assigned to each play. One one position, there can be negative or positive points. This is the probability distribution of the points: X = points -10367 P(X=x) 0.050.250.40.250.05 Find the variance of the situation. Choose the closest answer. Answers: • 12.5 • 6.1 • 3.54 • 2.47 • 8. The following table summarizes the results of a study of the number of pets live in American homes. X = number of pets 01234 P(X=x) 0.250.250.280.20.02 Find the variance of the number of children. Choose the closest answer. Answers: • 1.13 • 1.58 • 2.5 • 1.27 • 9. One new board came is based on spinning a wheel to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel. X = spaces moved -2-10235 P(X=x) 0.150.20.30.20.050.1 Calculate the variance for this distribution. Choose the closest answer. Answers: • 4.25 • 6.97 • 2.12 • 2.64 • 10. When hiring a new employee, a company researched the salaries of their current employees. Here is a distribution of salaries (in thousands). X = salary 1015305075 P(X=x) 0.150.20.30.20.15 Compute the variance of the salaries. Select the best answer. Answers: • 21.59 • 466.19 • 26.79 • 717.50 • 11. Over the holiday, Joe's family plays a lottery type game where people either lose or win money. Here is the probability distribution of the lottery. X = amount of money -$2-$1$1$2$7
P(X=x) 0.20.150.30.20.15

Find the variance of the amount of money. Pick the best answer.

• $12.30 •$3.51

• $7.96 •$2.77

• 12.

One new board came is based on rolling a weighted four sided die to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel.

X = spaces moved -2023
P(X=x) 0.30.20.30.2

What is the variance of spaces moved?

• 3.84

• 1.96

• 2.22

• 4.92

• 13.

Anna has several values of coins in her purse and pulls out one randomly. Here is a table of the probability distribution related to the amounts possible.

X = coin amount 151025
P(X=x) 0.150.250.350.25

Compute the variance of the amounts, and select the best answer below.

• 73.33

• 110.25

• 10.50

• 8.56

• 14.

A large family is having a dinner where each person is asked to bring at least one dish. To be fair, Grandma spins a wheel for each person in order to figure out the number of dishes to bring. Here is a summary of the possible outcomes.

X = number of dishes 1234
P(X=x) 0.250.250.30.2

Calculate the variance in number of dishes and choose the closest answer below.

• 1.15

• 1.67

• 1.29

• 1.07

• 15.

Each section of a dart board shows a different point amounts that a player can win or lose. Based on the sections of the board, the table below represents the probability distribution.

X = points amount -3-1014
P(X=x) 0.150.250.30.26.04

Find the variance in points and select the closest value below.

• 1.56

• 6.70

• 2.59

• 2.42

• 16.

Calculate the variance of the probability distribution given below.

 x 0 1 2 P(x) 0.3 0.5 0.2

• 0.59

• 0.49

• 0.45

• 0.55

• 17.

Using the probability distribution determine the variance.

 x 1 2 3 4 P(x) 0.3 0.2 0.2 0.3

• 1.65

• 1.75

• 1.45

• 1.55

• 18.

Identify the correct variance of the following probability distribution.

 x 0 1 2 3 P(x) 0.18 0.32 0.25 0.25

• 1.11

• 1.4

• 2.11

• 2.4

• 19.

Which of the following options represents the variance of the given probability distribution?

 x 1 2 3 4 5 P(x) 0.15 0.15 0.2 0.4 0.1

• 1.63

• 1.57

• 1.53

• 1.67

• 20.

Evaluate the variance of the probability distribution given below.

 x 1 2 3 4 P(x) 0.15 0.25 0.25 0.35

• 1.19

• 1.16

• 1.2

• 1.13

• 21.

Use the probability distribution to determine the variance.

 x 0 1 2 P(x) 0.1 0.45 0.45

• 0.42

• 0.43

• 0.41

• 0.44

• 22.

Choose the correct variance of the following probability distribution.

 x 0 1 2 3 4 5 P(x) 0.1 0.1 0.3 0.15 0.3 0.05

• 1.84

• 1.94

• 1.64

• 1.74

• 23.

Which of the following choices represents the variance of the given probability distribution?

 x 0 1 2 3 P(x) 0.25 0.25 0.3 0.2

• 1.13

• 1.17

• 1.15

• 1.19

• 24.

Find the variance of the probability distribution given below.

 x 1 2 3 4 P(x) 0.1 0.3 0.2 0.4

• 1.09

• 1.07

• 1.03

• 1.05

• 25.

With the help of the probability distribution determine the variance.

 x 1 2 3 4 5 P(x) 0.2 0.3 0.2 0.1 0.2

• 1.76

• 1.66

• 1.86

• 1.96

• 26.

Identify the correct variance of the following probability distribution.

 x 0 1 2 P(x) 0.15 0.35 0.5

• 0.53

• 0.83

• 0.73

• 0.63

• 27.

Which of the following options represents the variance of the given probability distribution?

 x 1 2 3 4 P(x) 0.25 0.25 0.1 0.4

• 1.23

• 1.43

• 1.53

• 1.33

• 28.

Calculate the variance of the probability distribution given below.

 x 0 1 2 3 P(x) 0.7 0.1 0.1 0.1

• 1.07

• 1.06

• 1.09

• 1.04

• 29.

Using the probability distribution determine the variance.

 x 1 2 3 4 5 P(x) 0.08 0.12 0.3 0.15 0.35

• 1.53

• 1.63

• 1.67

• 1.57

• 30.

Select the correct variance of the following probability distribution.

 x 1 2 3 4 P(x) 0.5 0.2 0.15 0.15