Cost per No. of Applications

Measures of Central Tendency

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Getting Started	General Instructions \| Introduction to Your Study
Descriptive Statistics	Histograms \| Scatter Plots \| Central Tendency \| Standard Deviation \| Confidence Intervals
Relating Variables	Correlation
Important Concepts	The Normal Distribution \| Z Scores \| Probability Distributions
Levels	You are currently on Central Tendency at level 2. Level 1 \| Level 2 \| Level 3
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Explanation

Calculating Measures of Central Tendency
Level 1 showed how the three different measures of central tendency are each suited to different types of data. We will now see how the different measures can give different results depending on the pattern of values in your data. We will also show you how to calculate the values of the three different measures.

The mode is calculated by counting how often each value occurs. There is no formula, you just count the values and see which one occurs most often. That value is the mode;
The median is found by first sorting your data in order and then finding the middle value. If you have an even number of data points, there won't be a value right in the middle, so you take the two middle values, add them together and divide the answer by 2;
The mean is calculated using a formula which adds all the values together and then divides by the number of values there are.

Now we know how to calculate the values, we can see how each different measure performs with different patterns of data.

The mean is badly affected by extreme values. Imagine you had the data: 1,2,3,4,400. The mean is 410/5 = 82, which doesn't really reflect where any of the data lies
The mode can be misleading if several values all appear equally often. It is useless if all the values in your data are different, as they each appear once only!
The median can smooth out extreme values but can produce the least frequently occurring value, as in this example: 1,1,1,2,3,3,3

Exploration

Here is the formula for calculating the mean of a set of numbers. Hover over any part of the formula for an explanation of what it signifies.
The sum of all the values in the data

The whole formula means 'The mean of x (where x is any numeric variable, such as no. apps) is the sum of its values divided by the number of values there are.'

Application

Here is the data from your study:

Cost	No. Apps
71	5
663	62
980	110
138	12
861	83
145	41
493	46
548	75
251	23
1024	100
435	41
772	75
71	10
663	59
381	62
138	15
861	78
145	59
493	56
548	56
251	27
1009	110
435	46
772	110
493	46
548	72
251	23
988	100
435	41
663	59

Calculator
( You need to enable Java to see this applet. )
Help

The Mean
Now we will calculate the mean of cost.

Use the calculator to add up all the values in the cost column.
Enter that value here:
Count the number of values in the data (n). Enter that value here:
Now divide the sum from step 1 by n. Enter that value here using 2 decimal places:
Now repeat the process for the no. apps column and enter the mean here:

To calculate the median and the mode, it is much easier to sort your data into order first.
Here is your data sorted with the position of each value noted along the top row.

Position	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Cost	71	71	138	138	145	145	251	251	251	381	435	435	435	493	493	493	548	548	548	663	663	663	772	772	861	861	980	988	1009	1024
No. Apps	5	10	12	15	23	23	27	41	41	41	46	46	46	56	56	59	59	59	62	62	72	75	75	78	83	100	100	110	110	110

The Mode
Now we will calculate the mode, if we can, for cost.
Find the mode by counting how many times each value appears and noting which appears most often. Also check to see if more than one value appears equally most often.

Let's see if it makes sense to calculate a mode for this data. The mode is the value that appears more than any other value. Is there a single mode for your data?

The Median
The median is in the middle of the ordered list of values.

Looking at cost, how many values are there?
Is there an exact midway point, or does the middle span two values?
At what position is the mid point? Enter its position or the first position if it spans two.
Find the value in the cost row at that position. If the mid point spans two places, add the numbers at those two positions together and divide what you get by two. The number you get is the median of cost. Enter it to 2 decimal places:
Now enter the median of no. apps. Use 2 decimal places

Reporting Your Findings
Once you have calculated your measures of central tendency, you usually want to report them. The best way to do this is in a table.
Cost
Mean Mode Median
517.53 663 493

Frequency Histograms | Standard Deviation