8/8/2023 0 Comments Range in math termWe could rearrange them if we wanted from smallest to largest, but that’s not necessary. Overall, they did pretty well, scoring the following: You have a class of 12 students, and after you give them their weekly exam on Friday, you look at the scores. To find the range in a data set, simply identify the highest and lowest number, find the difference, and viola-you have the range. This latter part is where range comes in. It helps people make predictions about future events to a great degree, as well as describe large masses of data. Statistics is a discipline that involves the analysis and collection of data. If you’re trying to find the range of a data set (or you’re being asked to find it), all you need are the highest and lowest value in a set. In the following section on box and whisker plot, we will see a useful method to visualize this five-number summary.The range is a mathematical tool that’s used in finding the spread in a data set. The five-value series formed by the minimum, the three quartiles and the maximum is often referred to as “the five-number summary.” It is a well-known manner to summarize data sets. In this example, we might have expected that when adding an extreme value, the measure of dispersion would increase, but the opposite happened because there was a great difference between the values of data points of ranks 3 and 4. The second example demonstrated that the interquartile range is more robust than the range when the data set includes a value considered extreme. The more robust interquartile range went from 28 to 19.5, a decrease of only 8.5. In summary, the range went from 43 to 69, an increase of 26 compared to example 1, just because of a single extreme value. The upper quartile is the mean of the values of data point of rank 6 + 3 = 9 and the data point of rank 6 + 4 = 10, which is (43 + 47) ÷ 2 = 45. The lower quartile is the mean of the values of the data point of rank 6 ÷ 2 = 3 and the data points of rank (6 ÷ 2) + 1 = 4. Because it falls between ranks 6 and 7, there are six data points on each side of the median. The median would be the mean of the values of the data point of rank 12 ÷ 2 = 6 and the data point of rank (12 ÷ 2) + 1 = 7. What happens when the data set includes a data point whose value is considered extreme compared to the rest of the distribution? Example 2 – Range and interquartile range in presence of an extreme valueįind the range and interquartile range of the data set of example 1, to which a data point of value 75 was added. The semi-interquartile range is 14 (28 ÷ 2) and the range is 43 (49-6).įor 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. The interquartile range will be Q3 - Q1, which gives 28 (43-15). Once you have the quartiles, you can easily measure the spread. The rank of the upper quartile will be 6 + 3 = 9. The second half must also be split in two to find the value of the upper quartile. The lower quartile will be the point of rank (5 + 1) ÷ 2 = 3. Then you need to split the lower half of the data in two again to find the lower quartile. The rank of the median is 6, which means there are five points on each side. 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 find the rank of the median to split the data set in two. ![]() The information is grouped by Rank (appearing as row headers), Value (appearing as column headers). This table displays the results of Rank of data points. Example 1 – Range and interquartile range of a data set ![]() When the data set is small, it is simple to identify the values of quartiles. The semi-interquartile range is half the interquartile range. The interquartile range is the difference between upper and lower quartiles. The median is considered the second quartile (Q2). ![]() The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. To calculate these two measures, you need to know the values of the lower and upper quartiles. The interquartile range and semi-interquartile range give a better idea of the dispersion of data. It's used as a supplement to other measures, but it is rarely used as the sole measure of dispersion because it’s sensitive to extreme values. The range only takes into account these two values and ignore the data points between the two extremities of the distribution. To calculate the range, you need to find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum).
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