A list of numbers, or numerical data, can be described by various statistical measures. To evaluate data correctly, you need to know the central tendency of numbers and the dispersion of their values. A measurement of central tendency is a value that’s typical, or representative, of a group of numbers or other information. Common tools for describing a central tendency include average (arithmetic mean), median, mode, and weighted mean.

Mean (Average)

The mean is simply the average value of a set of numbers. It is also called the average (or arithmetic mean). To find the mean, sum the values of all the elements and divide by the number of elements. This also indicated sum of items equals the average multiplied by number of items.

For example, the mean of the set {99, 100, 100, 105, 106, 116, 123} is sum of elements 99 + 100 + 100 + 105 + 106 + 116 + 123 = 749 divided by 7. Thus, the mean is 107.

Median

The median is the middle value in a set. By the middle value, we mean the value that has just as many elements in the set that are less than it as it has elements in the set that are greater than it.

For example, the median of the set {99, 100, 100, 105, 106, 116, 123} is 105 because it is the middle number in a set of seven.

If there is an even number of elements in the set, then the median is the number halfway between the two middle numbers.

For example, in the set {105, 108, 110, 112, 114, 115}, the median value is 111, since this is halfway between the two middle values 110 and 112.

Mode

The mode is the most common element in a set.

For example, in the set {99, 100, 100, 105, 106, 116, 123}, the mode is 100, because this number appears twice (Maximum number of times), while all other elements appear only once.

Range

The range of a set is the difference between the largest and the smallest elements. Though the range is a measure of spread from the highest to the lowest value, it doesn't take the numbers in between.

For example, the range of the set {105, 106, 107, 108, 109, 110, 111, 112, 113} is 8, since 113 – 105 = 8.

Standard Deviation

The standard deviation expresses variation by measuring how spread out the distribution is from the mean. Although the range can give you an idea of the total spread, standard deviation is a more reliable indicator of dispersion because it considers all the data, not just the two on each end.