Measure of central tendency
A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as the median and the mode.
Formula to find MEAN, MEDIAN AND MODE
Mean, add up the values in the data set and then divide by the number of values that you added.
Median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
Mode, identify which value in the data set occurs most often.
Examples 1:
How to find Mean
Mean.
3, -7, 5, 13, -2
- The sim of these number is 3 -7 + 5 + 13 - 2 =12
- There are 5 numbers
- The mean is equal to 12 ➗ 5 = 2.4
here is how to do it one line:
Example 2:
Find the mean, median, mode, and range for the following list of values:
1, 2, 4, 7
The mean is the usual average:
(1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5
The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers. Because of this, the median of the list will be the mean (that is, the usual average) of the middle two values within the list. The middle two numbers are 2 and 4, so:
(2 + 4) ÷ 2 = 6 ÷ 2 = 3
So the median of this list is 3, a value that isn't in the list at all.
The mode is the number that is repeated most often, but all the numbers in this list appear only once, so there is no mode.
The largest value in the list is 7, the smallest is 1, and their difference is 6, so the range is 6.
mean: 3.5
median: 3
mode: none
range: 6
median: 3
mode: none
range: 6
The values in the list above were all whole numbers, but the mean of the list was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.
Example 3:
Find the mode of a numerical data set
109 112 109 110 109 107 104 104 104 111 111 109 109 104 104
Solution:
Given data,
109 112 109 110 109 107 104 104 104 111 111 109 109 104 104
Total number of element = 15
Among the 15 data elements the values 104 and 109 both occur five times which are hence the modes of the data set.
109 112 109 110 109 107 104 104 104 111 111 109 109 104 104
Solution:
Given data,
109 112 109 110 109 107 104 104 104 111 111 109 109 104 104
Total number of element = 15
Among the 15 data elements the values 104 and 109 both occur five times which are hence the modes of the data set.
Questions for Measure of Central Tendency
1) What is the mode of the following numbers?
Awesome, black! now I understand. thanks a lot.
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