Calculating Variance from Data Sets

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| By Thames
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Quizzes Created: 7116 | Total Attempts: 9,522,086
| Questions: 20 | Updated: Oct 31, 2025
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1) What is the mean of Data set A?

Explanation

Mean = (6 + 8 + 7 + 9 + 10) / 5 = 40 / 5 = 8.

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About This Quiz
Calculating Variance From Data Sets - Quiz

Ever wondered how we turn raw numbers into something that shows us consistency? This quiz is your chance to calculate variance from scratch using real data sets. From finding the mean to squaring those deviations, you’ll see how variance works as the "spread-o-meter" for data. Plus, you'll compare different sets... see moreto see which one is more predictable. By the end, you'll be an expert at understanding data consistency through variance! see less

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2) What is the deviation of the value 6 from the mean of Data set A?

Explanation

Deviation = value - mean = 6 - 8 = -2.

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3) What is the squared deviation of the value 10 from the mean of Data set A?

Explanation

Deviation = 10 - 8 = 2; squared deviation = 2 * 2 = 4.

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4) What is the sum of the squared deviations for Data set A?

Explanation

Deviations from 8: (6→-2, 8→0, 7→-1, 9→1, 10→2). Squares: 4, 0, 1, 1, 4. Sum = 4 + 0 + 1 + 1 + 4 = 10.

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5) What is the population variance of Data set A?

Explanation

Population variance = (sum of squared deviations) / n = 10 / 5 = 2.

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6) Which data set has the larger variance?

Explanation

Given sums of squared deviations (next question) show C has a larger total, so its variance is larger.

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7) If both data sets have the same mean, which statement best explains why one has a larger variance?

Explanation

Variance increases when values are farther from the mean (greater spread).

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8) Using the actual sums of squared deviations (populations with n = 4): for Data set B the sum is 20, and for Data set C the sum is 24. Which variance is correct?

Explanation

Population variance = (sum of squared deviations) / n. Var(B) = 20 / 4 = 5; Var(C) = 24 / 4 = 6.

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9) Which data set likely has more consistent values?

Explanation

Smaller variance means more consistency. Data set B has variance 5 vs. 6 for C.

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10) What is the mean number of complaints per day?

Explanation

Mean = (0 + 1 + 0 + 2 + 1 + 3 + 0) / 7 = 7 / 7 = 1.

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11) What is the population variance of complaints per day?

Explanation

Deviations from mean 1: -1, 0, -1, 1, 0, 2, -1. Squares: 1, 0, 1, 1, 0, 4, 1. Sum = 8. Population variance = 8 / 7.

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12) Which statement best interprets this variance?

Explanation

8/7 is approximately 1.14. Variance is in squared units and reflects average squared deviation from the mean.

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13) What is the mean?

Explanation

Mean = (30 + 30 + 30 + 30 + 30) / 5 = 150 / 5 = 30.

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14) What is the population variance?

Explanation

All values equal the mean; deviations are all 0; variance = 0.

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15) What does this variance tell you about the consistency of study time?

Explanation

Variance 0 means no variation from day to day.

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16) Which set has the larger variance?

Explanation

Both means are 6, but Data set F has larger deviations from 6 (for example, -5 and +5), so its variance is larger.

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17) If both sets have the same mean of 6, which calculation step most strongly increases the variance for Data set F compared to E?

Explanation

Larger deviations in F become much larger after squaring, which boosts the variance.

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18) Which statement about consistency is correct based on the variances?

Explanation

Smaller variance means more consistent values; E has the smaller variance.

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19) Which player has a higher variance in points per game?

Explanation

Player A’s scores are all the same (variance 0). Player B’s scores vary widely, so variance is higher.

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20) What does a higher variance imply in this context?

Explanation

Higher variance indicates greater game-to-game fluctuation, i.e., lower consistency.

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What is the mean of Data set A?
What is the deviation of the value 6 from the mean of Data set A?
What is the squared deviation of the value 10 from the mean of Data...
What is the sum of the squared deviations for Data set A?
What is the population variance of Data set A?
Which data set has the larger variance?
If both data sets have the same mean, which statement best explains...
Using the actual sums of squared deviations (populations with n = 4):...
Which data set likely has more consistent values?
What is the mean number of complaints per day?
What is the population variance of complaints per day?
Which statement best interprets this variance?
What is the mean?
What is the population variance?
What does this variance tell you about the consistency of study time?
Which set has the larger variance?
If both sets have the same mean of 6, which calculation step most...
Which statement about consistency is correct based on the variances?
Which player has a higher variance in points per game?
What does a higher variance imply in this context?
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