When can we measure spread? The spread of the values can be measured for quantitative data, as the variables are numeric and can be arranged into a logical order with a low end value and a high end value. Why do we measure spread? Summarising the dataset can help us understand the data, especially when the dataset is large.
As discussed in the Measures of Central Tendency page, the mode, median, and mean summarise the data into a single value that is typical or representative of all the values in the dataset, but this is only part of the 'picture' that summarises a dataset. A score of 68 Q1 represents the first quartile and is the 25 th percentile. If the datapoint for Q1 is farther away from the median than Q3 is from the median, then we can say that there is a greater dispersion among the smaller values of the dataset than among the larger values.
The same logic applies if Q3 is farther away from Q2 than Q1 is from the median. Alternatively, if there is an even number of data points, the median will be the average of the middle two numbers. In our example above, if we had 20 students instead of 19, the median of their scores will be the arithmetic average of the 10 th and 11 th numbers. Quartiles are used to calculate the interquartile range, which is a measure of variability around the median.
The interquartile range is simply calculated as the difference between the first and third quartile: Q3—Q1. In effect, it is the range of the middle half of the data that shows how spread out the data is.
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I Accept Show Purposes. Your Money. Personal Finance. Your Practice. Popular Courses. What Is a Quartile? Key Takeaways The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. The semi-interquartile range is half the interquartile range. When the data set is small, it is simple to identify the values of quartiles.
You first need to arrange the data points in increasing order. As you do so, you can give them a rank to indicate their position in the data set. Rank 1 is the data point with the smallest value, rank 2 is the data point with the second-lowest value, etc. Then you need to find the rank of the median to split the data set in two.
As we have seen in the section on the median, if the number of data points is an uneven value, the rank of the median will be.
Then you need to split the lower half of the data in two again to find the lower quartile. The second half must also be split in two to find the value of the upper quartile. Once you have the quartiles, you can easily measure the spread. The interquartile range will be Q3 - Q1, which gives 28 For larger data sets, you can use the cumulative relative frequency distribution to help identify the quartiles or, even better, the basic statistics functions available in a spreadsheet or statistical software that give results more easily.
What happens when the data set includes a data point whose value is considered extreme compared to the rest of the distribution?
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