Question

Given that the median is 270 and the interquartile range is 20, which of the following statements are true?

I. 50% of the data are greater than or equal to 270
II. 50% of the data are between 260 and 280
III. 75% of the data are less than or equal to 280.
A) I and III
B) II only
C) I only
D) III only

Answer 1

The interquartile range (IQR) is a measure of the spread of the middle 50 percent of the data. Given that the median is 270 and the IQR is 20, statement II is true while statements I and III are false.

Step-by-step explanation:

The interquartile range (IQR) is a measure of the spread of the middle 50 percent of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Given that the median is 270 and the IQR is 20:

1. Statement I: 50% of the data are greater than or equal to 270. This statement is true because the median is the value that divides the data into two equal halves.
2. Statement II: 50% of the data are between 260 and 280. This statement is true because the IQR is 20, which means that the range from Q1 to Q3 is 20, and Q1 is 10 units below the median and Q3 is 10 units above the median.
3. Statement III: 75% of the data are less than or equal to 280. This statement is false because the IQR only represents the middle 50% of the data, so it does not include the upper 25% of the data.

Therefore, the correct answer is Option B) II only.