Calculating Standard Deviation (10A)

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.
Know:

  • How to calculate the mean of a set of data
  • The definition of an outlier
  • How to square a number
  • How to find the square root of a number

Understand:
That calculating the standard deviation shows us how much the data differs from the average value of a set of data

Do:

  • I can calculate the standard deviation from a set of data
  • I can use the standard deviation to compare different sets of data
  • I can identify outliers and eliminate them to calculate the standard deviation of a set of data.

Visual Representations

Notes

Standard Deviation is the calculation of 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

  1. Find the mean for your set of data (add all data values then divide the total by the number of items)

  2. Then find the difference between the data value compared to the mean

  3. Then calculate the variance (difference value squared) 

  4. Divide the variance by number of items.

  5. Then square root the total variance to find the standard deviation.

Standard Deviation Videos

Practise Questions

My Maths 10/10A

Exercise 10C pg. 495 Q. 1-13