Descriptive Statistics

Question 0

How do you calculate the median of n numbers?

Answer 0

1. Order the numbers from least to greatest.
2. If n is odd, the median is defined as the middle number, while if n is even, the median is defined as the average of the two middle numbers.

Example:

For the numbers 4,4,6,7,10.

The median is 6.

For the numbers 4,6,7,8,9,12.

The median is 6+8/2=7.

Question 1

Define average or arithmetic mean.

Answer 1

The sum of the n numbers divided by n.

Example:

6+4+7+10+4/5=31/5=6.2

Question 2

Define mode.

Answer 2

A list of numbers that occurs most frequently on the list.

Example:

1,3,6,4,3,5, the mode is 3.

Question 3

Define range.

Answer 3

The simplest measure of dispersion, defined as the greatest value in the numerical data minus the least value.

Example:
11,10,5,13,21.

The range is 21-5=16.

Question 4

Define standard deviation. How is it calculated?

Answer 4

Measures the spread of the data away from the mean. It is calculated as follows:

1. Find the arithmetic mean.
2. Find the differences between the mean and each of the n numbers.
3. Square each of the differences.
4. Find the average of the squared differences.
5. Take the nonnegative square root of this average.

Question 5

Define frequency distribution.

Answer 5

Data that has values occurring in varying frequencies.