{"id":2840,"date":"2026-10-13T15:30:00","date_gmt":"2026-10-13T10:00:00","guid":{"rendered":"https:\/\/digitoolkit.in\/blog\/?p=2840"},"modified":"2026-10-13T15:30:00","modified_gmt":"2026-10-13T10:00:00","slug":"range-formula-in-statistics-explained-with-examples","status":"publish","type":"post","link":"https:\/\/digitoolkit.in\/blog\/range-formula-in-statistics-explained-with-examples\/","title":{"rendered":"Range Formula in Statistics Explained with Examples"},"content":{"rendered":"<div style=\"background:#f2f7fb;border-left:4px solid #2271b1;padding:16px 20px;margin:0 0 24px;border-radius:4px;\">\n<p><strong>Quick Answer:<\/strong> The range formula is Range = Largest value &#8211; Smallest value. For grouped data, use the upper limit of the last class minus the lower limit of the first. The coefficient of range, (L &#8211; S) \/ (L + S), compares spread across different units.<\/p>\n<p><strong>Key takeaways:<\/strong><\/p>\n<ul>\n<li>Range = largest value &#8211; smallest value.<\/li>\n<li>For grouped data, use upper limit of last class minus lower limit of first class.<\/li>\n<li>Coefficient of range is (L &#8211; S) \/ (L + S) and has no unit.<\/li>\n<li>Rearrange the formula to find a missing maximum or minimum.<\/li>\n<li>Outliers affect range, so combine it with median or standard deviation.<\/li>\n<\/ul>\n<\/div>\n<h2>Range Formula: Small Idea, Many Uses<\/h2>\n<p>Of all the formulas in statistics, the range formula is the shortest. It has just one subtraction. Yet it shows up in school exams, cricket analysis, weather reports, stock charts and business dashboards across India.<\/p>\n<p>In this article, we explain the range formula, its variations for grouped data, and a related idea called the coefficient of range. Each part has a worked example in Indian units and rupees. To check your answers, use the free range calculator.<\/p>\n<h2>The Basic Range Formula<\/h2>\n<p><code>Range = L - S<\/code><\/p>\n<p>Here, L is the largest value in the data and S is the smallest value. The result has the same unit as the data. If you measure in rupees, the range is in rupees. If you measure in kilograms, the range is in kilograms.<\/p>\n<h3>Why it works<\/h3>\n<p>Think of a number line. Mark all your data points on it. The distance from the leftmost point to the rightmost point is the range. It is the total width that the data covers.<\/p>\n<h2>All the Range Formulas at a Glance<\/h2>\n<table>\n<thead>\n<tr>\n<th>Situation<\/th>\n<th>Formula<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ungrouped data<\/td>\n<td>Range = Largest value &#8211; Smallest value<\/td>\n<\/tr>\n<tr>\n<td>Grouped data (class intervals)<\/td>\n<td>Range = Upper limit of last class &#8211; Lower limit of first class<\/td>\n<\/tr>\n<tr>\n<td>Coefficient of range<\/td>\n<td>(L &#8211; S) \/ (L + S)<\/td>\n<\/tr>\n<tr>\n<td>Percentage range<\/td>\n<td>((L &#8211; S) \/ L) x 100<\/td>\n<\/tr>\n<tr>\n<td>Finding the missing maximum<\/td>\n<td>L = S + Range<\/td>\n<\/tr>\n<tr>\n<td>Finding the missing minimum<\/td>\n<td>S = L &#8211; Range<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The coefficient of range is a relative measure. It has no unit, so you can use it to compare data sets measured in different units or at very different scales.<\/p>\n<h2>Worked Example 1: Ungrouped Data from Share Prices<\/h2>\n<p>The closing price of a company&#8217;s share on five days was Rs 412, Rs 428, Rs 405, Rs 439 and Rs 421.<\/p>\n<ul>\n<li>L = 439<\/li>\n<li>S = 405<\/li>\n<li>Range = 439 &#8211; 405 = Rs 34<\/li>\n<\/ul>\n<p>The price moved within a band of Rs 34 during the week. Traders often call this the weekly trading range, and they use it to judge how volatile a stock is. Remember this is an educational example and not investment advice.<\/p>\n<h2>Worked Example 2: Grouped Data from Monthly Income<\/h2>\n<p>A survey of 100 households in a small town groups monthly income (in Rs) as shown below.<\/p>\n<table>\n<thead>\n<tr>\n<th>Income class (Rs)<\/th>\n<th>Households<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>10,000 &#8211; 20,000<\/td>\n<td>18<\/td>\n<\/tr>\n<tr>\n<td>20,000 &#8211; 30,000<\/td>\n<td>32<\/td>\n<\/tr>\n<tr>\n<td>30,000 &#8211; 40,000<\/td>\n<td>29<\/td>\n<\/tr>\n<tr>\n<td>40,000 &#8211; 50,000<\/td>\n<td>21<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>Upper limit of last class = 50,000<\/li>\n<li>Lower limit of first class = 10,000<\/li>\n<li>Range = 50,000 &#8211; 10,000 = Rs 40,000<\/li>\n<\/ul>\n<p>This is an approximate range. The real richest household may earn a little less than Rs 50,000, and the poorest may earn a little more than Rs 10,000. For exact values, you need the raw data.<\/p>\n<h2>Worked Example 3: Coefficient of Range<\/h2>\n<p>Two schools compare the heights of their Class 9 students. School A has heights from 140 cm to 170 cm. School B measures in metres, from 1.45 m to 1.65 m. Their raw ranges are 30 cm and 0.20 m, which cannot be compared directly.<\/p>\n<ul>\n<li>School A: (170 &#8211; 140) \/ (170 + 140) = 30 \/ 310 = 0.097<\/li>\n<li>School B: (1.65 &#8211; 1.45) \/ (1.65 + 1.45) = 0.20 \/ 3.10 = 0.065<\/li>\n<\/ul>\n<p>School A has the larger relative spread, 0.097 against 0.065. The coefficient has no unit, so the comparison is fair even when the units differ.<\/p>\n<h2>Worked Example 4: Finding a Missing Value<\/h2>\n<p>The range of daily sales at a Pune sweet shop is Rs 8,500. The lowest sale of the week was Rs 6,200. What was the highest?<\/p>\n<ul>\n<li>L = S + Range = 6,200 + 8,500 = Rs 14,700<\/li>\n<\/ul>\n<p>It was probably a festival day, such as the day before Diwali. Rearranging the formula like this is a common type of question in school exams.<\/p>\n<h2>Worked Example 5: Percentage Range<\/h2>\n<p>A farmer in Punjab records wheat yield from five plots, in quintals per acre: 18, 20, 22, 24 and 26.<\/p>\n<ul>\n<li>Range = 26 &#8211; 18 = 8 quintals per acre<\/li>\n<li>Percentage range = (8 \/ 26) x 100 = 30.8 percent<\/li>\n<\/ul>\n<p>The lowest plot yields about 31 percent less than the best plot. That helps the farmer decide where to improve soil or irrigation.<\/p>\n<blockquote>\n<p><strong>Expert insight:<\/strong> Use raw range when you compare data in the same unit and scale. Use the coefficient of range when units or scales are different.<\/p>\n<\/blockquote>\n<h2>Where Range Fits Among Other Measures<\/h2>\n<p>Range is the simplest measure of dispersion. Others include the interquartile range, mean deviation, variance and standard deviation. The interquartile range uses the 25th and 75th <a href=\"https:\/\/digitoolkit.in\/calculators\/percentile-calculator\/\">percentile<\/a> values, so it ignores extreme values at both ends.<\/p>\n<p>As a rule, range is best for a first look. Use more advanced measures when you need to make a decision or write a report. The NCERT Class 11 statistics material covers these in a clear order, from range to standard deviation, if you want to study further.<\/p>\n<h2>Worked Example 6: Interquartile Range Compared with Range<\/h2>\n<p>The range formula is often compared with the interquartile range, so a short example is useful. A coaching class in Kota records the scores of 9 students out of 100: 38, 52, 55, 58, 60, 63, 66, 70, 98.<\/p>\n<ul>\n<li>Range = 98 &#8211; 38 = 60 marks<\/li>\n<li>Lower quartile (Q1) is about 53.5 and upper quartile (Q3) is about 68<\/li>\n<li>Interquartile range = 68 &#8211; 53.5 = 14.5 marks<\/li>\n<\/ul>\n<p>The range of 60 marks suggests a very wide spread, but most students are within a 14.5 mark band. The two extremes, 38 and 98, are pulling the range up. This shows why teachers and analysts do not rely on range alone. The simple formula gives a first look, and the interquartile range tells you how tightly the middle group is packed.<\/p>\n<h2>Worked Example 7: Range of Rainfall Data<\/h2>\n<p>Monthly rainfall in a town in Kerala over six monsoon and post-monsoon months was 620 mm, 740 mm, 510 mm, 380 mm, 290 mm and 150 mm.<\/p>\n<ul>\n<li>L = 740 mm<\/li>\n<li>S = 150 mm<\/li>\n<li>Range = 740 &#8211; 150 = 590 mm<\/li>\n<li>Coefficient of range = 590 \/ (740 + 150) = 590 \/ 890 = 0.66<\/li>\n<\/ul>\n<p>A coefficient of 0.66 is high, which shows strongly uneven rainfall across the months. Farmers use this kind of spread to plan irrigation, sowing dates and water storage. A coefficient close to 0 would mean steady rainfall through the period.<\/p>\n<h2>Benefits of the Range Formula<\/h2>\n<p>The formula is fast and easy to remember. It can be done mentally for short lists and needs no table or special notation. That makes it ideal as a first check on any data set.<\/p>\n<p>It also uses the same units as the data, so the answer is easy to explain. A range of Rs 34 or 6 degrees means something to everybody. In business, it gives managers a quick sense of best and worst results. And in school, it builds the base for learning variance and standard deviation later.<\/p>\n<h2>Challenges and Limitations<\/h2>\n<p>Range uses only two values, so it ignores the shape of the rest of the data. If one student scores 5 marks and all others score between 70 and 80, the range is large but misleading. A single outlier distorts it.<\/p>\n<p>It also grows as you add data. A list of 1,000 numbers will usually have a larger range than a list of 10 numbers from the same source, so you cannot compare ranges from very different sample sizes. For grouped data, the answer is only an estimate.<\/p>\n<h2>Common Mistakes to Avoid<\/h2>\n<ol>\n<li><strong>Using the average instead of an extreme value.<\/strong> Range needs the largest and smallest values, not the mean.<\/li>\n<li><strong>Using class midpoints for grouped data.<\/strong> Use the class limits, not the midpoints, when finding the range.<\/li>\n<li><strong>Adding instead of subtracting.<\/strong> The coefficient of range uses L + S in the denominator, but the numerator is still L &#8211; S.<\/li>\n<li><strong>Comparing raw ranges in different units.<\/strong> Convert to the same unit or use the coefficient of range.<\/li>\n<li><strong>Forgetting brackets with negatives.<\/strong> Write L &#8211; (S) carefully when S is negative.<\/li>\n<li><strong>Reporting range without noting outliers.<\/strong> A very high or low value can mislead the reader.<\/li>\n<\/ol>\n<h2>Best Practices and Expert Recommendations<\/h2>\n<ol>\n<li><strong>Check the data first.<\/strong> Look for typing errors such as an extra zero before you trust the maximum or minimum.<\/li>\n<li><strong>Report the maximum and minimum with the range.<\/strong> Saying &#8220;Rs 34 (from Rs 405 to Rs 439)&#8221; is more useful than Rs 34 alone.<\/li>\n<li><strong>Use the coefficient for comparison.<\/strong> It makes cross-unit comparisons fair.<\/li>\n<li><strong>Add a second measure.<\/strong> The median or standard deviation shows what range cannot, so use a <a href=\"https:\/\/digitoolkit.in\/calculators\/statistics-calculator\/\">statistics calculator<\/a> for the full set.<\/li>\n<li><strong>Keep the sample size in mind.<\/strong> Compare ranges only when the data sets have a similar number of values.<\/li>\n<li><strong>Practise rearranging.<\/strong> Being able to solve for L or S helps you in exams and quick checks.<\/li>\n<\/ol>\n<h2>Try It Yourself<\/h2>\n<p>Type your own list of numbers into the <a href=\"https:\/\/digitoolkit.in\/calculators\/range-calculator\/\">range calculator<\/a> and compare the answer with the formula L &#8211; S. Try a data set with an outlier and see how much the range changes.<\/p>\n<h2>Conclusion<\/h2>\n<p>The range formula is simply the largest value minus the smallest value. With small changes, it also handles grouped data, relative comparisons and missing values. It is a quick and useful first step, but pair it with the median or standard deviation whenever the data has extreme values or when you need a deeper understanding of spread.<\/p>\n<div data-dtk-related=\"1\" style=\"background:#f8f9fb;border:1px solid #e2e8f0;border-radius:6px;padding:16px 20px;margin:28px 0;\">\n<p style=\"margin:0 0 10px;\"><strong>Related tools &amp; guides on DigiToolkit<\/strong><\/p>\n<ul style=\"margin:0;padding-left:20px;\">\n<li><a href=\"https:\/\/digitoolkit.in\/calculators\/range-calculator\/\">Try the free Range Calculator &rarr;<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/blog\/how-to-calculate-range-in-statistics-step-by-step\/\">How to Calculate Range in Statistics: Step by Step with Examples<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/blog\/what-is-range-in-statistics-simple-guide-with-examples\/\">What Is Range in Statistics? A Simple Guide with Indian Examples<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/blog\/free-online-range-calculator-tool-and-guide-india\/\">Range Calculator: Free Online Tool and Guide for Students and Businesses<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/blog\/range-calculation-examples-for-beginners-with-indian-data\/\">Range Calculation Examples for Beginners with Indian Data<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/calculators\/statistics-calculator\/\">Try the free Statistics Calculator<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/calculators\/median-calculator\/\">Try the free Median Calculator<\/a><\/li>\n<li><a href=\"https:\/\/digitoolkit.in\/blog\/category\/statistics-data\/\">More Statistics &amp; Data guides<\/a><\/li>\n<\/ul>\n<\/div>\n<h2>FAQs<\/h2>\n<p><strong>What is the formula for range?<\/strong><br \/>Range equals the largest value minus the smallest value. For data of 405, 412, 421, 428 and 439, the range is 439 &#8211; 405 = 34.<\/p>\n<p><strong>What is the coefficient of range?<\/strong><br \/>It is (L &#8211; S) divided by (L + S), where L is the largest and S the smallest value. It has no unit, so it is good for comparing data sets with different units.<\/p>\n<p><strong>How do I find range for grouped data?<\/strong><br \/>Subtract the lower limit of the first class from the upper limit of the last class. The answer is an approximate range.<\/p>\n<p><strong>How do I find the maximum if I know the range and minimum?<\/strong><br \/>Add the range to the minimum. If the range is 8,500 and the minimum is 6,200, the maximum is 14,700.<\/p>\n<p><strong>Is range the same as standard deviation?<\/strong><br \/>No. Range uses only the two extreme values, while standard deviation uses every value. Standard deviation is more reliable but needs more calculation.<\/p>\n<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What is the formula for range?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Range equals the largest value minus the smallest value. For data of 405, 412, 421, 428 and 439, the range is 439 - 405 = 34.\"}},{\"@type\":\"Question\",\"name\":\"What is the coefficient of range?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"It is (L - S) divided by (L + S), where L is the largest and S the smallest value. It has no unit, so it is good for comparing data sets with different units.\"}},{\"@type\":\"Question\",\"name\":\"How do I find range for grouped data?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Subtract the lower limit of the first class from the upper limit of the last class. 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Standard deviation is more reliable but needs more calculation.\"}}]}<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Understand the range formula in statistics, including grouped data and coefficient of range, with worked Indian examples in rupees and simple steps.<\/p>\n","protected":false},"author":1,"featured_media":2940,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[35],"tags":[],"class_list":["post-2840","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-statistics-data"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Range Formula Explained with Examples<\/title>\n<meta name=\"description\" content=\"Understand the range formula in statistics, including grouped data and coefficient of range, with worked 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