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The Mean
The arithmetic mean is another name for the average
of a set of scores. The mean can be found by dividing the sum of the scores
by the number of scores.
For example, the mean of 5, 8, 2, and 1 can be found by first adding
up the numbers. 5 + 8 + 2 + 1 = 16. The mean is then found by taking this
sum and dividing it by the number of scores. Our data set 5, 8, 2, and
1 has 4 different numbers, hence the mean is 16 ÷ 4 = 4.
The Mode
The mode of a set of data values is the number in the set that appears most frequently. For example, the number 5 appears three times in 1, 2, 5, 5, 5, 8, 8, 9. Since the number 5 appears the most times, it is the mode. A set of numbers that can have more than one mode, as long as the number appears more than once. In the data set 1, 2, 2, 3, 3, 4, 5. The mode is 2 and 3. We also can say that this data set is bimodal.
If no number appears more than once, then the data set has no mode.
The Median
The median is the middle value in a set of values. Half of all values are smaller than the median value and half are larger. When the data set contains an odd (uneven) set of numbers, the middle value is the median value. When the data set contains an even set of numbers, the middle two numbers are added and the sum is divided by two. That number is the median value.
How do I calculate a median ?
In order to find the median, we list the numbers
from smallest to largest. For example, in the data set {4, 8, 2, 10, 6};
we first order the numbers by increasing frequency {2, 4, 6, 8, 10}. Since
there is an uneven set of numbers, we take the middle number. The third
value of 6 falls in the middle of the array. Two numbers fall before it
and two fall after it.
In the data set {2, 3, 4, 5}, the median value falls between the 2nd
and 3rd value. We add these two values (2 + 3) and divide by 2. The median
value of this data set is 2.5.
In both cases, the data set is divided so that half the observation
lie in front of the median and half the observations fall behind it.
Why is it important to know the median value?
The median value is a measure of central tendency. It is a summary statistic that provides us with a description of the entire data set and is especially useful with large data sets where we might not have the time to examine every single value.
The Range
Range is the difference between the highest number and the lowest number, in a set of data.
The range tells you how spread the entire data is. For example, given
the numbers -3, 5, -9, and 19. The highest number is 19. The smallest number
is -3. The range is therefore 19 - (-3) = 22.