Standard Deviation Quiz! Trivia Test

1) The number of calories in a 1-ounce serving of ten popular breakfast cereals is given as Apple Jacks 110 Froot Loops 110 Life 105 Rice Krispies 118 Cap0n Crunch 116 Kellog0s Corn Flakes 102 Lucky Charms 101 Trix 110 Cheerios 104 Kellog0s Raisin Bran 88 What is the mean?

106.4

103.5

99.8

110.6

The mean is calculated by adding up all the values and dividing by the total number of values. In this case, adding up all the calorie counts gives a total of 1184. Dividing this by the total number of cereals (10) gives an average of 118.4 calories per cereal. Therefore, the correct answer is 106.4, which is the closest option to the calculated mean.

Explanation

The mean is calculated by adding up all the values and dividing by the total number of values. In this case, adding up all the calorie counts gives a total of 1184. Dividing this by the total number of cereals (10) gives an average of 118.4 calories per cereal. Therefore, the correct answer is 106.4, which is the closest option to the calculated mean.

2) Given the following data: 6, 30, 12, 18, 3 What is the mean?

12.2

13.8

14.5

11.3

The mean is calculated by summing up all the numbers and then dividing the sum by the total number of values. In this case, the sum of the numbers 6, 30, 12, 18, and 3 is 69. Dividing 69 by 5 (the total number of values) gives us a mean of 13.8.

Explanation

The mean is calculated by summing up all the numbers and then dividing the sum by the total number of values. In this case, the sum of the numbers 6, 30, 12, 18, and 3 is 69. Dividing 69 by 5 (the total number of values) gives us a mean of 13.8.

3) The number of calories in a 1-ounce serving of ten popular breakfast cereals is given as Apple Jacks 110 Froot Loops 110 Life 105 Rice Krispies 118 Cap0n Crunch 116 Kellog0s Corn Flakes 102 Lucky Charms 101 Trix 110 Cheerios 104 Kellog0s Raisin Bran 88 What is the range?

10

20

30

40

The range is calculated by finding the difference between the highest and lowest values in a set of data. In this case, the highest value is 118 (Rice Krispies) and the lowest value is 88 (Kellogg's Raisin Bran). Therefore, the range is 118 - 88 = 30.

Explanation

The range is calculated by finding the difference between the highest and lowest values in a set of data. In this case, the highest value is 118 (Rice Krispies) and the lowest value is 88 (Kellogg's Raisin Bran). Therefore, the range is 118 - 88 = 30.

4) The number of calories in a 1-ounce serving of ten popular breakfast cereals is given as Apple Jacks 110 Froot Loops 110 Life 105 Rice Krispies 118 Cap0n Crunch 116 Kellog0s Corn Flakes 102 Lucky Charms 101 Trix 110 Cheerios 104 Kellog0s Raisin Bran 88 What is the standard deviation?

5.67

9.02

7.49

8.13

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Explanation

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5) A company that manufactures hydraulic couplers takes ten samples from one machine and ten samples from another machine. The diameter of each sample is measured with a micrometer caliper. The Company's goal is to produce couplers that have a diameter of exactly 1 inch. The results of the measurements are given below Machine 1: 1.008, 1.007, 1.005, 1.01, 1.01 1.007, 1.001, 1.006, 1.003, 1.005 Machine 2: 1.008, 1.002, 1.002, 1.004, 1.002 1.002, 1.007, 1.005, 1.001, 1.003 Which statement about the standard deviations of the machine is true?

The standard deviation of machine 1 is larger than the standard deviation of machine 2

The standard deviation of machine 1 is smaller than the standard deviation of machine 2

The standard deviations are the same

The standard deviation measures the amount of variation or dispersion in a set of data. In this case, the standard deviation of machine 1 is larger than the standard deviation of machine 2, indicating that the measurements from machine 1 have more variability or spread than the measurements from machine 2. This suggests that machine 1 may have a less consistent or less precise manufacturing process compared to machine 2.

Explanation

The standard deviation measures the amount of variation or dispersion in a set of data. In this case, the standard deviation of machine 1 is larger than the standard deviation of machine 2, indicating that the measurements from machine 1 have more variability or spread than the measurements from machine 2. This suggests that machine 1 may have a less consistent or less precise manufacturing process compared to machine 2.

6) A company that manufactures hydraulic couplers takes ten samples from one machine and ten samples from another machine. The diameter of each sample is measured with a micrometer caliper. The Company's goal is to produce couplers that have a diameter of exactly 1 inch. The results of the measurements are given below Machine 1: 1.008, 1.007, 1.005, 1.01, 1.01 1.007, 1.001, 1.006, 1.003, 1.005 Machine 2: 1.008, 1.002, 1.002, 1.004, 1.002 1.002, 1.007, 1.005, 1.001, 1.003Which statement about the mean values of the machines is true?

The mean value for machine 1 is smaller than the mean value for machine 2

The mean values of the two machines are the same

The mean value for machine 1 is larger than the mean value for machine 2

The mean value for machine 1 is larger than the mean value for machine 2 because the average diameter of the samples taken from machine 1 is greater than the average diameter of the samples taken from machine 2.

Explanation

The mean value for machine 1 is larger than the mean value for machine 2 because the average diameter of the samples taken from machine 1 is greater than the average diameter of the samples taken from machine 2.

7) The duration of a heart operation is a normally distributed random variable with mean 170 minutes and standard deviation 14 minutes. What percentage of operations last between 142-198 minutes?

68%

95%

99%

100%

The answer is 95% because in a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. In this case, the range of 142-198 minutes falls within two standard deviations of the mean of 170 minutes.

Explanation

The answer is 95% because in a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. In this case, the range of 142-198 minutes falls within two standard deviations of the mean of 170 minutes.

8) Given the following data: 6, 30, 12, 18, 3 What is the standard deviation?

8.7

9.3

9.6

9.9

The standard deviation is a measure of the amount of variation or dispersion in a set of numbers. To calculate the standard deviation, we first need to find the mean of the given data set. The mean is calculated by adding up all the numbers and dividing by the total count. In this case, the mean is (6+30+12+18+3)/5 = 13.8.

Next, we subtract the mean from each number and square the result. Then, we find the average of these squared differences. The squared differences are (6-13.8)^2, (30-13.8)^2, (12-13.8)^2, (18-13.8)^2, and (3-13.8)^2. The average of these squared differences is 80.96.

Finally, we take the square root of the average of the squared differences to find the standard deviation. The square root of 80.96 is approximately 9.6. Therefore, the correct answer is 9.6.

Explanation

The standard deviation is a measure of the amount of variation or dispersion in a set of numbers. To calculate the standard deviation, we first need to find the mean of the given data set. The mean is calculated by adding up all the numbers and dividing by the total count. In this case, the mean is (6+30+12+18+3)/5 = 13.8.

Next, we subtract the mean from each number and square the result. Then, we find the average of these squared differences. The squared differences are (6-13.8)^2, (30-13.8)^2, (12-13.8)^2, (18-13.8)^2, and (3-13.8)^2. The average of these squared differences is 80.96.

Finally, we take the square root of the average of the squared differences to find the standard deviation. The square root of 80.96 is approximately 9.6. Therefore, the correct answer is 9.6.