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In left-skewed distributions, which of the following is the correct statement?

A) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2.
B) The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.
C) The distance from the smallest observation to Q2 is less than the distance from Q2 to the largest observation.
D) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.

1 Answer

2 votes

Final answer:

The correct statement for a left-skewed distribution is that the distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation, indicating a larger spread on the left side of the median.

Step-by-step explanation:

In a left-skewed distribution, we expect to see the bulk of the data values falling towards the right side, with a tail extending to the left. Considering the properties of quartiles in distributions, we can make some observations. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2 or median) is the 50th percentile, and the third quartile (Q3) is the 75th percentile. The interquartile range (IQR) is the distance between Q1 and Q3 and represents the middle 50% of the data.

Answering the student's question, the correct statement is Option B: "The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation." This is typical for a left-skewed distribution since the longer "whisker" of the box plot (which stretches from the minimum to Q1) indicates a larger spread on the left side of the median, reflecting more variability in the lower half of the data set.

User Reena Shirale
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