GRE Quant - Statistics Review (copy)

Covers median, mode and range, quartiles, percentiles, standard deviation, frequency distributions and graphs and tables.

Median

The middle term in a group of terms that are arranged in numerical order. The median of a group of numbers is often different from its average.

Mode

The term that appears most frequently in a set. A set may have more than one mode. If every element in the set occurs an equal number of times, then the set has no mode.

Range

The distance between thew greatest and least values in a group of data points.

Quartiles

When a set of data is divided into four equal sections.

Determining Quartiles

1. Arrange terms in data set in numerical order from least (L) to greatest (G)

2. Subdivide the set into two halves, each containing an equal number of terms

3. The median of the lower half represents the first quartile (Q1), and the median of the upper half is the third quartile (Q3). The median of the entire set is the second quartile (Q2).

Interquartile Range

Difference between the values of the third and first quartile values, Q3 - Q1. Outliers do not affect the interquartile range because they fall into the bottom and top quartiles.

Percentiles

Similar to quartiles but used for larger groups of numbers; there are 100 subdivisions instead of 4. Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile, and Q4 = 100th percentile.

Standard Deviation

A measure of the dispersion in a given data set. Found by calculating the mean of a group of values, then using a type of averaging to determine how far away the other values in the group are from the mean.

Low Standard Deviation

If the values in the group are all relatively close to the mean.

High Standard Deviation

If the values in the group are relatively spread out.

Calculating Standard Deviation

1. Find the group’s mean

2. Determine the difference between the mean & each value in the group

3. Square each of those differences

4. Find the mean of the squared differences

5. Take the non-negative square root of the mean of the squared differences

Frequency Distribution

Description of how often certain data values occur in a set and is typically shown in a table or histogram.

Relative Frequency Distribution/Probability Distribution

The frequency with which given values occur is given in decimal form rather than as percentages.

Random Variable X

The value of a randomly chosen value from a known distribution of data.

Normal Distribution

A distribution where the data are symmetrically distributed around the mean, so the curve to the left of the mean is a mirror image of the curve to the right. The mean, median and mode are always equal in this distribution.

Percentage of Area 1 SD from Mean in Normal Distribution

68%

Percentage of Area 2 SD from Mean in Normal Distribution

95%

Standard Normal Distribution

Mean is centered at 0 and the standard deviation is calibrated to 1.