AP STATISTICS
Quiz on Mean, Median, Standard Deviation, and Variance
Last 4 of ID____________________
Period______
1. The following is an ogive on the number of ounces of alcohol (one ounce is about 30 mL) consumed per
week in a sample of 150 students.
A study wished to classify the students as “light”, “moderate”, “heavy” and “problem” drinkers by the
amount consumed per week. About what percentage of students are “problem” drinkers, that is consume
between 12 and 18 ounces per week? 100-65=35
2. A distribution of 6 scores has a median of 21 and variance of 9.5. If each score increases 3 points, what
will be the value of the median? 21+3=24
3. A distribution of 6 scores has a median of 21 and variance of 9.5. If each score increases 3 points, what
will be the value of the variance? 9.5 (variance is resistant to addition or subtraction)
4. A distribution of 6 scores has a median of 21 and variance of 9.5. If each score doubles, what will be the
value of the median? 21x2=42
5. A distribution of 6 scores has a median of 21 and variance of 9.5. If each score doubles, what will be the
value of the variance? 9.5x22=9.5x4=38
6. Rainwater was collected in water collectors at 30 different sites near an industrial basin and the amount
of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10,
respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error.
The error can be corrected by adding 0.1 pH units to all of the values and then multiply the result by 1.2.
What are the mean and standard deviation of the corrected pH measurements?
Mean=(4.60+0.1)x1.2 =5.64
Standard Deviation=1.10x1.2=1.32
(Standard Deviation is resistant to addition and subtraction, so we just multiply)
7. Is it possible for a set of scores to have a variance of zero? Explain. Yes, if all of the scores are the same.
8. Is it possible for a set of scores to have a negative variance? Explain. No, the differences are squared
within the formula, so that wipes out any negatives. Also, variance describes a spread, which is a
distance between data and distance is never negative.
9. What are the different measures of center? Which is/are resistant to outliers? Mean, median, and mode.
Median and mode are resistant to outliers. Mean is not resistant to outliers.
10. What are the different measures of variability? Which is/are resistant to outliers?
Range, IQR, Standard Deviation, and Variance.
IQR is resistant to outliers.
Range is not resistant to outliers.
Standard Deviation is not resistant to outliers.
Variance is not resistant to outliers (some say moderately resistant to outliers).