Module 1 quiz: describing data

B. Sort first: 3, 4, 7, 9, 12. The middle value is 7. The mean is also 7 here, which is a coincidence; don't rely on it.

B. The median only cares about the middle position, so one extreme sale barely shifts it. The mean, the range and the standard deviation all chase the outlier.

B. A standard deviation of 0 means no value is any distance from the mean, so every value equals the mean. The mean itself can be anything.

B. Mean 4; distances −2, 0, 2; squares add to 8; 8 ÷ (3 − 1) = 4; √4 = 2. Choice A divides by n instead of n − 1.

B. A sample's values sit a little closer to their own mean than to the true mean, so the raw average of squared distances runs small. Dividing by n − 1 corrects that.

C. Q1 is the median of the lower half (1, 3, 5, 7): 4. Q3 is the median of the upper half (9, 11, 13, 15): 12. 12 − 4 = 8. Choice D is the range.

A. The square root at the end undoes the squaring, so the standard deviation is back in kilograms. The variance is the one in kilograms squared.

C. A long right tail of high incomes pulls the mean up, while the median stays at the middle person. That's why income reports usually quote the median.

C. Blood type sorts people into groups with no numeric order. Height and temperature are continuous; number of siblings is a count.

B. Shifting every value moves the center by the same amount but leaves every distance from the mean unchanged, so the spread doesn't move.