Measure of Spread

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Measure of Spread

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Measure of Spread- How similar or different a set of values are to one another
1. Range- The difference between the lowest and highest values in a data set.
  1. Range= maxValue – minValue
2. Spread- How far the values in a data set are from the mean.
3. Variance- The average of the squared differences from the mean.
  1. Subtract the mean from each value in the data set.
  2. Square each of those values (so they are a + value)
  3. Add all of the above squared together.
  4. Divide the sum total of the squares by the number of values in the data set.
4. Standard Deviation- How spread out the values are in a data set. Calculated by taking the square root of the variance.

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Today we’re going to be talking about measure of spread.

So the measure of spread is how similar or different a set of values are from one another. So if you take a look at this graph, you might say the red data set is different from blue set. And in stats we want to analyze data and measure just how different data sets are. So one of variables we would consider is the range, or what is the actual difference in the biggest value and the smallest value in a data set. Additionally we could look at the mean or the average of the values in a data set. We could also consider how far each of the data points are from the mean (spread).

Another statistical variable we could use is variance.Variance tells us how spread out a data set is… but these values are calculated in square units. Variance is the average of the squared difference from the mean. variance is calculated by subtracting the mean from each value in the data set, squaring each of those values and then adding them all together then divide that total sum by the total number of values in the data set.

Standard deviation is a common value used in statistics which is calculated by just taking the square root of the variance. This puts the value in the same units as the mean (not a squared value). So we can add this or subtract this value from the mean. So once you calculate the std dev of a data set you can add and subtract that value from the mean and that is range in which 68% of you data falls. Add /subtract 2 STD EV to the mean and that means 95% of your data is in that range. and 3 STD DEV is the range for 99.7% of your data. The rule to remember here is 68-95-99.7 Of course this is only for data that follows normal distribution.

So in review, we can take a data set and analyze it in such a way that we can tell how similar or different those values are from one another. We can calculate the Range by subtracting the maximum value from the minimum value. We can calculate the Mean or the average by adding the numbers together and dividing by the number of data points there are. We can also calculate the spread which is how far data points are from the mean, by subtracting the mean from each data point.Variance tells us how spread out a data set is and these values are in squared units. And we can also calculate the standard deviation by talking the square root of the variance and adding and subtracting that to the average to calculate where 68% of the data lies.

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