Q: Given the SAT scores: 1100, 1130, 1190, 1200, 1220, 1240, 1280, 1320, 1360, 1420, 1480, 1550, what is the percentile of a score of 1280?

Using $$\frac{\text{number of values less than 1280}}{\text{total number of values}} \times 100$$, the percentile is $$\frac{6}{12} \times 100 = 50\%.$$

Q: What is the formula for calculating the percentile of a value $$x in a $$dataset?

$$\frac{\text{number of values less than } x}{\text{total number of values}} \times 100$$

Q: A playlist with 15 songs is in which percentile in the dataset: 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26?

Percentile is $$\frac{12}{28} \times 100 = 42.9\%$$

Question 1

Which of the following best describes the percentile of a value in a dataset?

Accepted Answer

The percent of responses in a dataset less than it.

Question 2

The 1st quartile (Q1) corresponds to which percentile?

Accepted Answer

25th percentile

Question 3

Given the SAT scores: 1100, 1130, 1190, 1200, 1220, 1240, 1280, 1320, 1360, 1420, 1480, 1550, what is the percentile of a score of 1280?

Accepted Answer

Using $$\frac{	ext{number of values less than 1280}}{	ext{total number of values}} 	imes 100$$, the percentile is $$\frac{6}{12} 	imes 100 = 50\%.$$

Question 4

What is the formula for calculating the percentile of a value $$x in a $$dataset?

Accepted Answer

$$\frac{	ext{number of values less than } x}{	ext{total number of values}} 	imes 100$$

Question 5

The Interquartile Range (IQR) is defined as:

Accepted Answer

$$Q_3$$ - $$Q_1$$

Question 6

If the first quartile (Q1) of SAT scores is 1195 and the third quartile (Q3) is 1390, what is the interquartile range (IQR)?

Accepted Answer

$$1390 - 1195 = 195$$

Question 7

Which value in the SAT score dataset is at the 75th percentile ($$P_{75}$$)?

Accepted Answer

Q3, which is 1390

Question 8

Given the dataset: 20, 23, 24, 25, 25, 40, 41, 42, 45, 47, what is the value of Q1?

Accepted Answer

Q1 is the 25th percentile, which is 24.5

Question 9

A playlist with 15 songs is in which percentile in the dataset: 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26?

Accepted Answer

Percentile is $$\frac{12}{28} 	imes 100 = 42.9\%$$

Question 10

What is the Five Number Summary displayed in a boxplot?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 11

Which statistic is NOT directly shown in a boxplot?

Accepted Answer

Mean

Question 12

If a boxplot for SAT scores shows a median of 1260, Q1 of 1195, and Q3 of 1390, what can you infer about the distribution?

Accepted Answer

The distribution is skewed right if the distance from median to Q3 is greater than from Q1 to median.

Question 13

Which class has a greater range of SAT scores if the juniors' scores range from 1100 to 1550 and the seniors' scores range from 1150 to 1500?

Accepted Answer

Juniors, because $$1550 - 1100 = 450 is $$greater than $$1500 - 1150 = 350$$

Question 14

Which value is at the 50th percentile in a dataset?

Accepted Answer

The median

Question 15

If the maximum value in a boxplot is much higher than Q3, what does this suggest about the data?

Accepted Answer

There may be outliers or a long right tail.

Question 16

In a real-world scenario, why might the interquartile range (IQR) be preferred over the range as a measure of spread?

Accepted Answer

IQR is less affected by extreme values and outliers.

Question 17

A boxplot for the number of songs in playlists shows a minimum of 9, Q1 of 12, median of 16, Q3 of 22, and maximum of 26. What is the IQR?

Accepted Answer

$$22 - 12 = 10$$

Question 18

If a dataset has a median of 25, Q1 of 20, and Q3 of 40, which value is at the 75th percentile?

Accepted Answer

Q3, which is 40

Question 19

Which of the following is a correct interpretation of the 25th percentile in a dataset?

Accepted Answer

25% of the data values are less than or equal to this value.

Percentiles, Quartiles, and Boxplots: Step-by-Step Statistics Guidance

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