Question 1

Which of the following best describes the meaning of the 75th percentile in a data set?

Accepted Answer

75% of the measurements are less than this value, and 25% are greater.

Question 2

A newborn's weight is at the 90th percentile. What does this indicate?

Accepted Answer

The newborn weighs more than 90% of all newborns.

Question 3

Which of the following is NOT a quartile in a data set?

Accepted Answer

Extreme Quartile (100th percentile)

Question 4

In a box plot, what does the region between the hinges and the inner fences represent?

Accepted Answer

Values that are not outliers

Question 5

A data point falls between the upper inner and outer fences in a box plot. How is this point classified?

Accepted Answer

It is a potential outlier and requires further assessment.

Question 6

Which formula correctly calculates the z-score for a measurement $$x$$ given mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 7

A student scores 80 on a test where the mean is 70 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{80 - 70}{5} = 2$$

Question 8

If a data point falls outside the upper outer fence in a box plot, how is it classified?

Accepted Answer

It is an outlier.

Question 9

Which of the following statements about z-scores is TRUE?

Accepted Answer

A z-score tells you how many standard deviations a measurement is from the mean.

Question 10

Given the following measurements and their respective means and standard deviations, which measurement is furthest below its mean?

$$x = 100, \mu = 125, \sigma = 10$$
$$x = 5, \mu = 3, \sigma = 2$$
$$x = 0, \mu = -150, \sigma = 100$$
$$x = 10, \mu = 16, \sigma = 3$$

Accepted Answer

Measurement $$x = 100, \mu = 125, \sigma = 10$$

Question 11

A hospital tracks the birth weights of newborns. If a newborn's weight is at the 25th percentile, which quartile does this correspond to?

Accepted Answer

Lower quartile

Question 12

Which of the following best describes the median in terms of percentiles?

Accepted Answer

It is the 50th percentile.

Question 13

A box plot is constructed for the cholesterol levels of patients in a clinic. If a patient's cholesterol level is outside the lower outer fence, what does this indicate?

Accepted Answer

The patient's cholesterol is an outlier.

Question 14

If a student's SAT score is at the 90th percentile, what percentage of students scored lower than this student?

Accepted Answer

90%

Question 15

Which of the following is a measure of relative standing?

Accepted Answer

Percentile

Question 16

A measurement has a z-score of $$-2. $$What does this indicate about the measurement?

Accepted Answer

It is 2 standard deviations below the mean.

Question 17

Which of the following best describes the relationship between percentiles and quartiles?

Accepted Answer

Quartiles are specific percentiles: 25th, 50th, and 75th.

Question 18

A researcher wants to determine if a measurement is an outlier using a box plot. Which step should they take if the measurement falls between the inner and outer fences?

Accepted Answer

Assess it further as it is a potential outlier.

Question 19

A measurement $$x$$ has a z-score of $$3. If $$the mean $$\mu is$$ $$50$$ and the standard deviation $$\sigma is$$ $$5$$, what is the value of $$x$$?

Accepted Answer

$$x = \mu + 3\sigma = 50 + 3 	imes 5 = 65$$

Descriptive Statistics: Quartiles, Box Plots, and Z-Scores

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