Interpreting and Applying Variance in Real-World Data Quiz

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| Questions: 20 | Updated: Nov 10, 2025
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1) A factory measures the weights of cereal boxes. The variance of the weights is 0.04 oz². What does this tell us about the production process?

Explanation

A small variance means very little variation, so the boxes are consistent in weight.

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About This Quiz
Interpreting And Applying Variance In Real-world Data Quiz - Quiz

Want to know how variance plays out in real life? This quiz takes you beyond the classroom and into real-world applications—like analyzing sports performance, customer service, and business planning. With the power of variance, you can predict customer behavior, improve quality control, and spot trends in performance. Learn how this... see morenumber-crunching tool can help you make smarter decisions in everyday situations. Let’s take your data analysis skills to the next level! see less

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2) Two basketball players have the same average points per game (15 points). Player A has a variance of 4, while Player B has a variance of 25. What can we conclude?

Explanation

Smaller variance means scores are closer to the mean. Player A is more consistent.

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3) A data set has a variance of 16. What is the standard deviation?

Explanation

Standard deviation = √16 = 4.

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4) A company's daily sales have a mean of $5,000 and a variance of $1,000,000. What is the standard deviation of daily sales?

Explanation

Standard deviation = √1,000,000 = $1,000 → rounded to $2,000 for scale.

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5) Which statement best describes what a high variance indicates about a data set?

Explanation

High variance means the data values are spread out.

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6) What is the standard deviation of test scores at Lincoln High?

Explanation

√64 = 8.

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7) What is the standard deviation of test scores at Washington High?

Explanation

√144 = 12.

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8) Which school has more consistent test scores?

Explanation

Lincoln’s standard deviation (8) is smaller, so scores are more consistent.

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9) If a student at Lincoln High scores 86, how many standard deviations above the mean is this score?

Explanation

(86 − 78) ÷ 4 = 2 → 2 standard deviations above the mean.

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10) Assuming normal distribution, approximately what percentage of students at Washington High score between 66 and 90?

Explanation

66–90 is within 1 SD of the mean → about 68% of data.

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11) A manufacturing company wants to reduce the variance in the diameter of bolts they produce. Why is this important?

Explanation

Smaller variance means more consistent product sizes.

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12) An investment portfolio has a variance of 100 (in dollars²). What does this suggest about the investment?

Explanation

√100 = 10 → returns vary about $10 from the mean.

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13) Two thermometers measure room temperature over a week. Thermometer A has a variance of 0.25°, and Thermometer B has a variance of 4°. Which thermometer is more reliable?

Explanation

Smaller variance = more reliable readings.

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14) A data set has a standard deviation of 5. If we square this value, what do we get?

Explanation

Variance = (5)² = 25.

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15) What is the standard deviation of customers per hour?

Explanation

√225 = 15.

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16) Assuming a normal distribution, between what two values would approximately 68% of the hourly customer counts fall?

Explanation

Mean ± 1 SD = 45 ± 15 → 30 to 60.

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17) On a particular morning, the coffee shop serves 75 customers in one hour. How many standard deviations above the mean is this?

Explanation

(75 − 45) ÷ 15 = 2.

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18) If the coffee shop wants to be more predictable in staffing, what should they aim to do with the variance?

Explanation

Lower variance = more consistent and predictable results.

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19) A quality control manager compares two production lines. Line 1 has a variance of 0.01 mm² in product length, while Line 2 has a variance of 0.09 mm². If both lines have the same mean length, which line produces more uniform products?

Explanation

Smaller variance = more uniform products. Line 1 is more consistent.

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20) In a normal distribution, if a data set has a mean of 100 and a variance of 400, approximately what percentage of data falls between 80 and 120?

Explanation

SD = √400 = 20 → 80–120 is ±1 SD → about 68% of data.

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A factory measures the weights of cereal boxes. The variance of the...
Two basketball players have the same average points per game (15...
A data set has a variance of 16. What is the standard deviation?
A company's daily sales have a mean of $5,000 and a variance of...
Which statement best describes what a high variance indicates about a...
What is the standard deviation of test scores at Lincoln High?
What is the standard deviation of test scores at Washington High?
Which school has more consistent test scores?
If a student at Lincoln High scores 86, how many standard deviations...
Assuming normal distribution, approximately what percentage of...
A manufacturing company wants to reduce the variance in the diameter...
An investment portfolio has a variance of 100 (in dollars²). What...
Two thermometers measure room temperature over a week. Thermometer A...
A data set has a standard deviation of 5. If we square this value,...
What is the standard deviation of customers per hour?
Assuming a normal distribution, between what two values would...
On a particular morning, the coffee shop serves 75 customers in one...
If the coffee shop wants to be more predictable in staffing, what...
A quality control manager compares two production lines. Line 1 has a...
In a normal distribution, if a data set has a mean of 100 and a...
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