What is the measure of variability that is defined as the average squared difference of the scores from the mean?
What are measures of variation?Measures of variation describe the width of a distribution. They define how spread out the values are in a dataset. They are also referred to as measures of dispersion/spread. Show
In this article, we will look at 4 measures of variation.
We will also see examples of how to calculates these measures of variation and when to use them. But before we get started, let’s understand why we need measures of variation in addition to measures of centre when exploring data for visualization. Why do we need measures of variation?A single statistic – the mode, the median or the mean may not be a model that represents the entire dataset accurately. Anytime we use a single number to represent the data, we lose the sense of variability in the data. Do averages tell the whole story?An average is a good measure to compare performance of “a group” over time. One way to think of an average is like a snapshot of a movie. It does not tell the whole story, it just gives a snapshot of a frame. Averages ignore the impact of the inevitable variations that occur in the data. Here is an example of two sample populations with the same mean and different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50. What are the disadvantages of averages?
Understanding Measures of VariationRangeRange is the simplest measure of variation. The range of a dataset is the difference between the highest value and the lowest value in the dataset. Range is also the most affected by outliers as it uses only the extreme values. Interquartile Range (IQR)The Interquartile Range or IQR describes the middle 50% of the values when ordered from lowest to highest value. To calculate the IQR, we find the median of the lower and upper half of the data. These are Quartile 1 and Quartile 3. The IQR is the difference between Quartile 3 and Quartile 1. IQR is considered a good measure of variation in skewed datasets as it is resistant to outliers. VarianceVariance is the average squared difference of values from the mean. To calculate variance, we square the difference between each data value and the mean. We divide the sum of these squares by the number of items in the dataset. Because variance is a squared quantity, there is no intuitive way to compare variance directly to data values or mean. Standard DeviationStandard deviation is a measure of how much data values deviate away from the mean. Larger the standard deviation, greater the amount of variation. Standard deviation is calculated as the square root of variance. Standard deviation uses the original units of data which makes interpretation easier. Hence standard deviation is the most commonly used measure of variation. Calculate Range, IQR, Standard Deviation and Variance : ExampleLet’s consider a small dataset of heights of 10 people. Here is how we can calculate the range, variance, standard deviation and interquartile range. Calculating Range, Variance and Standard DeviationCalculating Interquartile RangeHere is a video tutorial to learn more about calculating interquartile range. When to use Range, IQR, Standard Deviation and Variance?
Which measure of variability is the average of the squared deviations from the mean?The variance is the average of squared deviations from the mean. A deviation from the mean is how far a score lies from the mean. Variance is the square of the standard deviation. This means that the units of variance are much larger than those of a typical value of a data set.
What measure of variability is the average square distance of the scores from the mean?The variance is the average squared distance to the mean. However, it is erroneous to think that the standard deviation (the square root of the variance) equals the average distance to the mean.
What is the measure of average variability?The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean.
What are the 3 measures of variability?Measures of Variability. Range.. Interquartile range (IQR). Variance and Standard Deviation.. |