Q: Given the concert attendance data, how do you check for outliers using the $$1.5 \times IQR$$ rule?

Calculate $$Q_1 - 1.5$$ \times IQR$$ and Q_3$ + 1.5 \times IQR$$ and check for values outside this range.

Question 1

A sample of 300 students has a mean number of days absent of 4.1, a median of 3.5, and a standard deviation of 2.8. If about 75 students were absent more than 6 days, which statistic best describes this group?

Accepted Answer

They are above the third quartile.

Question 2

Given the data set: 13, 23, 10, 3, 16, 5, 7 (mean = 11, standard deviation = 6.95). If an 8th value is added and the range stays the same but the standard deviation increases, which value could be the 8th value?

Accepted Answer

25

Question 3

A restaurant manager records the number of hours worked by 41 employees. If the interquartile range (IQR) is the difference between the third and first quartiles, which of the following could be the IQR for the number of hours worked?

Accepted Answer

$$19$$

Question 4

Raspberries have a mean weight of 4.5 grams and a standard deviation of 0.5 grams. Strawberries have a mean weight of 15 grams and a standard deviation of 1.67 grams. What is the weight of a raspberry with the same standardized score as a strawberry weighing 17.5 grams?

Accepted Answer

$$5.60$$ grams

Question 5

Akshita charges $12 per hour for babysitting. For which statistic will the value for hours spent babysitting be equal to the value for the amount of money earned?

Accepted Answer

The standardized score of the maximum

Question 6

The dotplot shows the number of goals scored in 24 matches. If the standard deviation is $$2.55$$ goals, what does this value represent?

Accepted Answer

The typical distance a match's goals scored is from the mean.

Question 7

If the value 13 is removed from the goals scored data set, what happens to the standard deviation?

Accepted Answer

It decreases because an extreme value is removed.

Question 8

All 82 students in Mrs. Gallas’ classes were asked how many concerts they attended. If the five-number summary is used, which values are included?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 9

Suppose students spent an average of $122.50 at each concert. If the median number of concerts attended is 1, what is the median amount spent?

Accepted Answer

$$122.50$$

Question 10

Given the concert attendance data, how do you check for outliers using the $$1.5 	imes IQR$$ rule?

Accepted Answer

Calculate $$Q_1 - 1.5$$ 	imes IQR$$ and Q_3$ + 1.5 	imes IQR$$ and check for values outside this range.

Question 11

The number of songs on Beyoncé's and Taylor Swift's albums are summarized. If Beyoncé's median is 15 and Taylor Swift's is 14.5, what does this indicate?

Accepted Answer

Beyoncé's albums tend to have slightly more songs than Taylor Swift's.

Question 12

If the mean and standard deviation of Beyoncé's albums are $$14.429$$ and $$1.813$$ respectively, and Taylor Swift's are $$14.7$$ and $$2.263$$, which artist has more variability in album length?

Accepted Answer

Taylor Swift

Question 13

If a data set is skewed right, which measure of center is likely to be greater?

Accepted Answer

Mean

Question 14

Which of the following is NOT affected by extreme values (outliers)?

Accepted Answer

Median

Question 15

A student calculates the z-score for a value using $$z = \frac{x - \mu}{\sigma}. $$What does a z-score of $$-2$$ mean?

Accepted Answer

The value is 2 standard deviations below the mean.

Question 16

If the IQR for a data set is $$4$$ and $$Q_1 = 10$, what is Q_3$?

Accepted Answer

$$14$$

AP Statistics: Descriptive Statistics, Distributions, and Data Analysis

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