# Statistics

Statistics is the study of the patterns and relationships of numbers and data. There are four main concepts that may appear on the test:# Median

*median*is the middle number.

For example, the median of the set {8, 9, 10, 11, 12} is 10 because it is the middle number.

In this case, the median is also the mean (average). But this is usually not the case.

If a set contains an even number of elements, then the median is the average of the two middle elements.

*What is the median of 0, â€“2, 256 , 18, ?*

Arranging the numbers from smallest to largest (we could also arrange the numbers from the largest to smallest; the answer would be the same), we get â€“2, 0, , 18, 256.

The median is the middle number, .

# Mode

*mode*is the number or numbers that appear most frequently in a set. Note that this definition allows a set of numbers to have more than one mode.

*What is the mode of 3, â€“4, 3 , 7, 9, 7.5 ?*

The number 3 is the mode because it is the only number that is listed more than once.

*What is the mode of 2, Ï€, 2 , â€“9, Ï€, 5 ?*

Both 2 and Ï€ are modes because each occurs twice, which is the greatest number of occurrences for any number in the list.

# Range

*range*is the distance between the smallest and largest numbers in a set. To calculate the range, merely subtract the smallest number from the largest number.

*What is the range of 2, 8, 1 , â€“6, Ï€, 1/2 ?*

The largest number in this set is 8, and the smallest number is â€“6.

Hence, the range is 8 â€“ (â€“6) = 8 + 6 = 14.

# Standard Deviation

*Standard deviation*measures how far the numbers in a set vary from the setâ€™s mean. If the numbers are scattered far from the setâ€™s mean, then the standard deviation is large. If the numbers are bunched up near the setâ€™s mean, then the standard deviation is small.

*Which one of the following sets has the larger standard deviation?*

*A = {1, 2, 3, 4, 5}
B = {1, 4, 15, 21, 34}*

All the numbers in Set A are within 2 units of the mean, 3. All the numbers in Set B are greater than 5 units from the mean, 15 (except, or course, the mean itself).

Hence, the standard deviation of Set B is greater.