Q: Given a sorted data set of 40 values, what is the locator $$L$$ for the 30th percentile ($$P_{30}$$)?

$$L = \frac{30}{100} \times 40 = 12.0$$

Question 1

A hospital is analyzing the body temperatures of patients. The mean body temperature is 98.2°F with a standard deviation of 0.6°F. A patient has a body temperature of 99.4°F. What is the z score for this patient’s temperature?

Accepted Answer

$$z = \frac{99.4 - 98.2}{0.6} = 1.67$$

Question 2

Which of the following statements about z scores is TRUE?

Accepted Answer

A z score is the number of standard deviations a value is above or below the mean.

Question 3

A student scored 85 on a test with a mean of 80 and a standard deviation of 5. Another student scored 78 on a different test with a mean of 70 and a standard deviation of 4. Which student performed better relative to their class?

Accepted Answer

The second student, because their z score is higher.

Question 4

If a data value has a z score of $$-2.5$$, how would you classify this value?

Accepted Answer

It is a significantly low value.

Question 5

A set of earthquake magnitudes has a mean of 2.5 and a standard deviation of 0.7. Is a magnitude of 4.0 significantly high?

Accepted Answer

Yes, because $$z = \frac{4.0 - 2.5}{0.7} = 2.14$$, which is greater than 2.

Question 6

Which of the following best describes the 25th percentile (P25) in a data set?

Accepted Answer

It separates the lowest 25% of values from the highest 75%.

Question 7

Given a sorted data set of 40 values, what is the locator $$L$$ for the 30th percentile ($$P_{30}$$)?

Accepted Answer

$$L = \frac{30}{100} 	imes 40 = 12.0$$

Question 8

If the locator $$L$$ for a percentile is not a whole number, what should you do to find the corresponding data value?

Accepted Answer

Round $$L up to $$the next larger whole number.

Question 9

Which of the following is NOT part of the 5-number summary?

Accepted Answer

The mean

Question 10

A boxplot is constructed using which of the following values?

Accepted Answer

Minimum, Q1, median, Q3, maximum

Question 11

If a boxplot shows the median closer to Q1 than Q3 and the right whisker is longer than the left, what can you infer about the data?

Accepted Answer

The data is skewed to the right.

Question 12

Given Q1 = 20, Q3 = 50, and a data value of 100, is this value an outlier according to the 1.5 × IQR rule?

Accepted Answer

Yes, because 100 is greater than Q3 + 1.5 	imes IQR.

Question 13

What is the interquartile range (IQR) for a data set with Q1 = 15 and Q3 = 45?

Accepted Answer

$$IQR = Q3 - Q1 = 30$$

Question 14

Which of the following best describes a modified boxplot?

Accepted Answer

A boxplot that identifies outliers with a special symbol and shortens the whiskers to the most extreme non-outlier values.

Question 15

A data set has a minimum of 5, Q1 = 10, median = 15, Q3 = 20, and maximum = 50. Which value is most likely to be an outlier?

Accepted Answer

50

Question 16

Which of the following is true about quartiles?

Accepted Answer

Q1 is the same as the 25th percentile.

Question 17

A researcher wants to find the value at the 90th percentile in a data set of 60 values. What is the locator $$L$$?

Accepted Answer

$$L = \frac{90}{100} 	imes 60 = 54$$

Question 18

Which of the following is the correct interpretation of a value at the 80th percentile?

Accepted Answer

80% of the values are below this value.

Describing, Exploring, and Comparing Data: Measures of Relative Standing and Boxplots

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