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Lesson: Data Sufficiency Intermeddiate - 17

Properties of Sets In Data Sufficiency: Median, Mode, Range

[Page 17 of 21]

Median, Mode, and Range are often tested in conjunction in Data Sufficiency. Although the individual concepts are relatively simple, the questions can become complicated! Let's look at some examples.

Select an answer, and then click Continue.

What is the sum of 5 evenly spaced integers in a set?

  1. The median of the set of numbers is 0.
  2. The range of the numbers in the set is 4.
Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient.
Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient.
Both statements TAKEN TOGETHER are sufficient, but NEITHER statement BY ITSELF is sufficient.
EACH statement BY ITSELF is sufficient.
The two statements TAKEN TOGETHER are NOT sufficient.

Countinue

Focus on the question.

Don't get caught in the trap of assuming that "evenly spaced integers" must refer to consecutive numbers (1,2, 3, etc.). They could, but they could also refer to numbers at a different fixed interval, like (0,4,8,12).

For a statement to be sufficient, it must provide information that indicates either the actual numbers, or the position of the 5 numbers on the number line.

Evaluate each statement separately.

Statement (1) is insufficient. Although the statement tells us that zero is the middle number, which indicates where the numbers fall on the number line, we can't tell whether they're consecutive or at a different fixed interval. Eliminate Choices (A) and (D).

Statement (2) is insufficient. If the range equals 4, then the highest and lowest numbers are four units apart. So, the five numbers in the set must be consecutive.

But, the statement does not tell you where the numbers fall on the number line. For example the set could be:

{1, 2, 3, 4, 5} or {0, 1, 2, 3, 4} or any other set of five consecutive numbers.

Since there is more than one possible sum, the statement is insufficient and we eliminate Choice (B).

Combine the statements, if necessary.

Combining the statements tells us that the median of the set of numbers is 0 and the range of the numbers in the set is 4. When we add in the information from the question stem, we have:

  • 5 evenly spaced integers
  • the number in the middle is 0
  • the range is 4

The only numbers that meet all of the criteria are:

{-2, -1, 0, 1, 2}

Thus, together the statements are sufficient.

Continue

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