# Measure of Center

## Definition

A measure of center is a value at the center or middle of a data set. Graphically, the center can be viewed as the "balance point" of the display. Algebraically, the most common ways to find the center are with the mean, median, or mode.

## Other examples of Measure of center

The mean is the most common measure of center. It is what most people think of when they hear the word "average". However, the mean is affected by extreme values so it may not be the best measure of center to use in a skewed distribution.

Procedure for finding

1. Add all the data values together
2. Divide by the sample size

Properties

• The mean always exists
• The mean does not have to be one of the data values
• The mean uses all the data values
• The mean is affected by extreme values

Formula

The median is the value in the center of the data. Half of the values are less than the median and half of the values are more than the median. It is probably the best measure of center to use in a skewed distribution.

Procedure for finding

1. Rank the data so that it is in order from lowest to highest
2. Find the number in the middle.
• Assuming that n is the sample size, then the depth (position) of the median is found by taking 0.5n and either rounding up (if a decimal) or adding 0.5 (if a whole number).
• Once the depth of the median is found, the median is the value in that position. If the depth is not a whole number, then average the two adjacent values (if the depth=19.5, then average the 19th and 20th numbers).

Properties

• The median always exists.
• The median does not have to be one of the data values.
• The median does not use all of the data values, only the one(s) in the middle.
• The median is resistant to change, it is not affected by extreme values.

The mode is the most frequent value. If no value appears more than any other, then there is no mode. If two or more values appear more than the others, then the data is bimodal or multimodal.

Procedure for finding

1. Rank the data in order from lowest to highest. This is not necessary, but it makes it easier to count how many times a certain value appears when they are in order.
2. Find the frequency of each value.
3. The most frequent value is the mode.

Properties

• The mode may or may not exist. If it does exist, there may be one or several modes.
• The mode has to be one of the data values.
• The mode does not use all the data values.
• The is probably not affected by extreme values since it's unlikely the extreme values are not the most common.

The range is the point between the lowest annd the higtest value

Procedure for finding

1. Add the lowest and highest values together
2. Divide by 2
Properti

• The range always exists
• The range does not have to be one of the values
• The range does not use all of the values, only the lowest and highest
• The range is greatly affected by extreme values since it uses only the extreme

## Concluson

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