measure of variation Flashcards
What is variation?
variation is the width of distribution of your data set. There are different measures of variation- range, interquartile range, variance and standard deviation.
What is the range?
The range is the simplest measure of variation. It is largest to smallest. It is only based on 2 extreme points, and prone to bias outliners. The greater your sample size, the more likely to sample larger range.
What is the interquartile range?
This is the middle half of your data. Data is split into quarters from the median. Q1 is the lower 25%, and Q3 Is the higher 25% of your data. IQR is the difference between Q3 and Q1. To find the IQR, you have to fins the median value, split the data into 2 groups, lower and upper, and find the median of the lower and upper half, and then minus the lower half from the upper half.
What is the percentile range?
You can see other percentiles to measure variability. The range between 40th and 60th percentile, will cover 20% of your data, the range between the 10th and 90th will cover 80% of your data. Like the range, the broader the percentiles, the higher the variability.
How do you calculate deviance?
If the deviant is positive, the observation is bigger than the mean.
If the deviant is negative, the observation is smaller than the mean.
The sum of deviations is always =0. Positive values must be balanced with the negative.
Why is using variance better than using the range?
Usually better to measure variability than range. Both describe the typical distance of how far data falls, or deviates from the mean. Deviation of an observation- different between the observation and the sample mean.
What is variance?
The average of the squares of deviations from the mean. Then work out the total sum of the squares, divide by n-1.
What is standard deviation?
The square root of the variance. The larger the standard deviation, the greater the variability in the data.
The sum of squares: total of x-xbar, divide by n-1, and square root this value.
