Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation(VCMSP372)
LO: To calculate and interpret the mean and standard deviation of a set of data.
How to calculate the mean of a given set of data.
The definition of an outlier.
How to square a number.
How to find the square root of a number.
That calculating the standard deviation shows us how much the data differs from the average value of a set of data
I can calculate the standard deviation from a set of data.
I can use the standard deviation to compare different numerical sets of data and to describe the spread of a set of data.
I can identify outliers and eliminate them to calculate the standard deviation of a set of data.
Standard Deviation is the calculationof how spread out a set of data is. In some cases the standard deviation can be very large, which means the data is very spread out or the standard deviation can be very small, which means the data is very tightly packed together.
If the data fits a normal distribution curve, then 68.1% of the data should be within 1 standard deviation of the mean. 95.4% of the data should be within 2 standard deviations of the mean and 99.7% of the data should be within 3 standard deviations of the mean.
Calculating the Standard Deviation Process
Find the mean for your set of data (add all data values then divide the total by the number of items)
Then find the difference between the data value compared to the mean
Then calculate the variance (difference value squared).
Divide the variance by number of items.
Thensquare root the total variance to find the standard deviation.