Chapter 15

15-1 Presenting Statistical Data

Frequency distribution: a table that shows how many times each data item occurs.

Histogram: a bar graph displaying a frequency distribution

Stem and leaf plot: A way of displaying the data in a frequency distribution.

Statistics: the methods used to describe a set of data.

Mode: the number that occurs most frequently

Median: the middle number in a distribution (which must be sorted in order) or the mean of the two middle numbers

Mean: the arithmetic average of the numbers in a deviation of a distribution. The sum of all the data items divided by the number of data items.

15-2 Analyzing statistical Data Part 1

First quartile: the median of the lower half of the data

Third quartile: the median of the upper half of the data

= The median between the minimum and the median

= The median between the median and the maximum

Range = Maximum – Minimum

Box and whisker plot: is used to show the median, the first and third quartiles, and the range of a distribution.

15-2 Analyzing Statistical Data part 2

Variance: one of the statistics used to measure the dispersion or “spread” of the data.

Standard deviation: the other statistic used to measure the dispersion or “spread” of the data. (The square root of the variance.)

Mean =

Variance =

Variance =

Standard deviation =

Statistical Symbols and Variables:

= The mean of the x values

= The sum of the x values

= The variance of the x values

= The number of elements in the distribution

15-5 Fundamental Counting Principles

Outcome: the result

Event: a subset of outcomes

Compound event: several events which occur together

The Fundamental Counting Principle

In a compound event in which the first event may occur in ways, the second event may occur in ways, etc. The event may occur in the different ways, so the total number of ways the compound event may occur is:

Mutually exclusive choices: you can do one or the other but not both at the same time. The outcome of mutually exclusive choices is the SUM of each outcome.

15-6 Permutations (order, arrange)

Permutation: An arrangement of the elements of a set of definite order.

Ordered Arrangement: A permutation of a set of objects

Where objects. n₁, n₂, etc., are repeated objects.

15-7 Combinations (choose, select)

The number of combinations of a set of n objects taken r at a time is: