Statistics – Measures of Central Tendency
If a person is given a large pile of numbers then, there is no hope of understanding the numbers unless a way to work the numbers out is figured out. For example if a pizza parlor managers is trying to keep track of the daily sales figures of different types of pizza.Suppose, if the values for daily sales of pizzas for a period of 9 days is taken:
40, 56, 38, 38, 63, 59, 51, 50, 46
A list of numbers like this is called raw data. One useful thing to do would be to calculate the average of all the numbers.
40 +56 + 38 + 38 + 63 + 59 + 51 + 50 + 46/9 = 441/9 = 49
Therefore, one can say that on an average, the pizza parlor has sold 49 pizzas per day.
Mean = Σx/n,
where Σx is the group of numbers and n is the number or count of the numbers.
Median is the halfway point of the data, that is half of the numbers are above it and half are below. To compute median, we must put the list of numbers in order. Here, we can take the above example
1. 40 38
2. 56 38
3. 38 40
4. 38 46
5. 63 50
6. 59 51
7. 51 56
From this list the median value is 50. Four values are greater than 50 and four values are below 50.
Mode is the value that occurs most frequently. If there is more than one value that occurs the greatest number of times, all such values are called modes. In the pizzas example, the value of the mode is 38, because the number 38 occurs twice in the list while none of the other numbers occur more than once. Many distributions that arise in practice are reasonably symmetric with most of the values concentrated near the middle, in which case the mean, median and mode are all close together. However, a distribution can have more than one mode. A distribution with two modes is called bimodal distribution.
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