Classification and Evolution Statistics

What is the meaning of mean, median, mode and anomaly?

• Mean - sum of data values divided by number of data values

• Median - middle value of data set (n+1/2)

• Mode - most frequent value

• Anomaly - value in dataset that is not part of inherent variation

Describe what is meant by ‘normal distribution’ and how variety is linked?

• When the mean, median and mode are the same

• 50% of values are = to or greater than mean and 50% of values are = to or less than mean

• The level of variation around mean value can vary when there is normal distribution

• For data showing continuous variation, the spread depends on sample size

What does standard deviation measure? What does a larger or lower SD mean? What does the symbols in the equation represent?

• Spread of data around the mean

• The greater the SD, the more variable or spread out data is

How do you calculate SD?

• Find mean

• Subtract mean from each individual value

• Square each result for each individual value

• Find the sum of the resulting values

• Substitute into SD formula

What do error bars show? Which results on a standard deviation graph would show the most variability? How would you know if there is a significant statistical difference between results from error bars?

• Number of SD either side of the mean e.g. a 95% of values for normal distribution lie within 2 SD of the mean

• Visual display on a graph of variation around the mean, usually shown as mean + and - 1 SD

• Longer error bars show more variability

• There is significant statistical difference if error bars do not overlap

How can you interpret SD?

• Can calculate the range of values that lie close to the mean

  • Empirical rule for normal distribution - 1 SD: 68% of values lie within mean + or - 1 SD

  • 2 SD: 95% within mean + or - 2 SD

  • 3 SD: 99.7% within mean + or - 3 SD