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Concepts in Mean, Median, Standard Deviation, Variance

Basics of statistics including concepts of averages, mode, median, standard deviation and range, are often tested in both the GMAT Problems Solving section and in the GMAT Data Sufficiency section of the GMAT Quant Section. A good grasp of the fundamentals of these concepts will help you crack questions from this topic with relative ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Definition of average (arithmetic mean)
2. Weighted average
3. Median and mode
4. Mean and median of sequences in Arithmetic Progression
5. Variance and standard deviation
6. Geometric mean and harmonic mean
7. 15 solved examples with illustrations
8. 12 exercise problems with the answer key and explanatory answers

Here is an example of a typical solved example in this chapter.

Question
If x > 14, what is the median of the set consisting of the following numbers: 10, 12, 14, 7, 15, 19?

Explanatory Answer
Arranging the six terms in ascending order, we get 7, 10, 12, 14, 15, and 19.

When x is included, we have seven terms; the median will be the forth term.

Since x > 14, the median will be 14.