Take this Quiz: AP Statistics — exploring data | Zestly

Question 1

House prices in a small village are strongly skewed to the right: most houses cluster together and a handful of very large properties sit far out in the upper tail. Which measure of centre better describes what a typical house costs, and why?

Accepted Answer

The median, because it depends on the position of the middle value rather than on the size of the extreme ones, and so is not dragged into the tail

Answer

The mean, because it uses every observation and so wastes no information

Answer

The mean, because its sensitivity to the long tail makes it reflect the shape of the distribution more faithfully

Answer

The median, because in a skewed distribution the median and the mean coincide anyway

Question 2

Nine measurements, written in order, are $4, 6, 7, 8, 9, 10, 11, 13, 40$. A tenth value of $200$ is now added. Which statement describes what happens to the four summaries?

Accepted Answer

The mean rises sharply and the standard deviation rises sharply; the median moves only from $9$ to $9.5$ and the interquartile range is barely affected

Answer

The mean and the median both rise by the same amount, since every summary responds to a new observation

Answer

The mean falls, because dividing by a larger count outweighs the size of the new value

Answer

The standard deviation falls, because a wider set of values makes the distribution look more even

Question 3

The heights of a group of sunflowers have a mean of $150$ centimetres and a standard deviation of $10$ centimetres. What does the second figure tell you?

Accepted Answer

Roughly how far from $150$ centimetres a sunflower's height typically falls, measured in centimetres

Answer

The height of a sunflower exactly halfway up the group

Answer

The total of the squared differences between each height and the mean

Answer

The gap between the tallest and the shortest sunflower in the group

Question 4

In one class a pupil scores $85$ where the mean is $75$ and the standard deviation is $5$. In another class a pupil scores $90$ where the mean is $80$ and the standard deviation is $10$. Which pupil stands higher relative to their own class?

Answer

The second, whose raw score of $90$ exceeds the other's $85$

Answer

Neither — both are exactly ten marks above their class mean, so their standing is identical

Answer

The second, because a larger standard deviation means the marks were spread more widely and so the achievement counts for more

Answer

The first, whose standardised score is $2.0$ against the second's $1.0$

Question 5

A set of measurements has $Q_1 = 20$ and $Q_3 = 50$. Applying the rule that flags a value more than $1.5 	imes 	ext{IQR}$ beyond the nearer quartile, which of these values is an outlier?

Answer

$45$

Answer

$60$

Answer

$100$

Answer

$30$