 # Math Book 2: Statistics

Mean, Median, Mode, Range, Weighted Average, Deviation

Descriptive Statistics is a topic from which you could expect 2 to 3 questions in the GMAT quant section. This topic is an important one.

### Concepts Covered

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. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Definition of average (arithmetic mean).
2. Weighted average.
3. Standard framework to solve questions involving arithmetic mean and weighted averages.
4. Median and mode.
5. Mean and median of sequences in Arithmetic Progression.
6. What is variance and standard deviation? How to compute standard deviation?
7. What happens to the average and standard deviation of a set of numbers when a constant k is added or subtracted to each term of the set?
8. What happens to the average and standard deviation of a set of numbers when a constant k is multiplied to each term of the set or when each term of the set is divided by a constant k?
9. Arithmetic mean - Geometric mean inequality for positive numbers.
10. 10 illustrative example and 19 solved examples.
12. A timed multiple choice test with 40 GMAT level questions in the work book. All questions have been provided explanatory answers.

Here is a typical solved example from this chapter.

### Sample Question

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

Arrange the six terms whose values are known in ascending order: 7, 10, 12, 14, 15, and 19.
When x is included, we have seven terms; the median will be the fourth term.
Because x > 14, x will appear to the right of 14 in the sequence.
The 4th term of the sequence, irrespective of where x appears to the right of 14, will be 14.
Therefore, the median is 14.

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details