Measures of Central Tendency Part 1
In previous sections, you learned about measures of central tendency and variability, going through the basics of each concept as well as their applications in other concepts of statistics. Here, we’ll go through some more intermediate concepts involved in these descriptive statistics. That is, we’ll go through more practice problems and solutions involving these statistical measures
Changing the Units of Measures
The more you study the concepts involved in statistics, the more you’ll realize it requires a lot of data preparation. Meaning, the data that we receive from surveys and scientific studies isn’t always in the format we require to answer our questions. In higher levels of statistics, you will be able to learn about different methodologies, or processes for conducting studies, that can enable you to correct for issues in format before you even collect your data!
However, the majority of data preparation simply involves changing the units we have into another. This can be something like transforming centimetres into metres or changing a variable to follow a logarithmic scale. While changing units is a completely normal, and even routine, part of statistics, it’s important to keep in mind if and how changing units can also change certain measures of central tendency and variability.
For example, say you download the following information on a group’s weight before they join a particular exercise class.
Observation  Observation Value 
1  61 
2  64 
3  67 
4  71 
5  73 
6  73 
7  85 
8  91 
Here, our information is displayed in kilograms. From this information, we can determine all the measures we’ve learned in previous sections, rounding to the first decimal place.
Measure  Calculation 
Mean  73.1 
Median  72 
Mode  73 
Variance  104.7 
Standard Deviation  10.2 
Average Deviation  7.4 
Let’s say, however, that you also want to publish the information on these weights for an audience that uses the imperial system rather than the metric system of measurements. This means you will have to convert your units into pounds from kilograms, multiplying each observation value in your data by 2.2 to get an approximate weight. How will this affect what you’ve already measured?
Turns out, there’s a shortcut to calculating measures of central tendency and variability when the unit has been changed. Instead of changing all of the units in your data, you can simply follow the rules for changing units in the tables below.
When adding or subtracting a constant  Effect on the Measure 
Mean, Median, Mode  Add or subtract that constant 
Standard Deviation, Variance, Average Deviation, IQR  No effect, they stay the same 
When multiplying or dividing by a constant  Effect on the Measure 
Mean, Median, Mode, Standard Deviation, Average Deviation, IQR  Multiply or divide by that constant 
Variance  Multiply or divide by the square of that constant 
Looking back at our example, since we are multiplying our data by a constant, 2.2, we simply have to follow the rules above in order to get all the measures we desire, rather than multiplying the whole data set by 2.2 and recalculating everything.
Measure  Calculation in Kg  Calculation in Lbs 
Mean  73.1 

Median  72 

Mode  73 

Variance  104.7 

Standard Deviation  10.2 

Average Deviation  7.4 

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