How To Find The Mode Of A Set Of Numbers 8 Steps With Pictures

The process of finding a data set’s mode is easier to understand by following along with an example problem. In this section, let’s use this set of values for the purposes of our example: {18, 21, 11, 21, 15, 19, 17, 21, 17}. In the next few steps, we’ll find the mode of this set.

If you’re working with paper and a pencil, re-writing can save time in the long run. Scan the set of numbers for the lowest number and, when you find it, cross it off in the first data set and re-write it in your new data set. Repeat for the second-lowest number, third-lowest, and so on, being sure to write each number as many times as it occurs in the original data set. With a computer your options are more extensive - for instance, most spreadsheet programs will have the option to re-order lists of values from least to greatest with just a few clicks. In our example, after re-ordering, the new list of values should read: {11, 15, 17, 17, 18, 19, 21, 21, 21}.

If you’re working with a pencil and paper, to keep track of your counts, try writing the number of times each value occurs above each cluster of identical numbers. If you’re using a spreadsheet program on a computer, you can do the same thing by writing your totals in adjacent cells or, alternatively, using one of the program’s options for tallying data points. In our example, ({11, 15, 17, 17, 18, 19, 21, 21, 21}),11 occurs once, 15 occurs once, 17 occurs twice, 18 occurs once, 19 occurs once, and 21 occurs three times. 21 is the most common value in this data set.

In our example set, ({11, 15, 17, 17, 18, 19, 21, 21, 21}), because 21 occurs more times than any other value, 21 is the mode. If a value besides 21 had also occurred three times, (like, for instance, if there were one more 17 in the data set), 21 and this other number would both be the mode.

A data set’s mean is its average. To find the mean, add up all of the values in the data set, then divide by the number of values in the set. For instance, for our example data set ({11, 15, 17, 17, 18, 19, 21, 21, 21}), the mean would be 11 + 15 + 17 + 17 + 18 + 19 + 21 + 21 + 21 = 160/9 = 17. 78. Note that we divided the sum of the values by 9 because there are a total of 9 values in the data set. {“smallUrl”:“https://www. wikihow. com/images/thumb/f/f8/Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet1-Version-2. jpg/v4-460px-Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet1-Version-2. jpg”,“bigUrl”:"/images/thumb/f/f8/Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet1-Version-2. jpg/aid130521-v4-728px-Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet1-Version-2. jpg",“smallWidth”:460,“smallHeight”:345,“bigWidth”:728,“bigHeight”:546,“licensing”:"<div class="mw-parser-output">

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<br />\n</p></div>"} A data set’s median is the “middle number” separating the lower and higher values of a data set into two equal halves. For instance, in our example data set, ({11, 15, 17, 17, 18, 19, 21, 21, 21}) 18 is the median because it is the middle number - there are exactly four numbers higher than it and four numbers lower than it. Note that if there are an even number of values in the data set, there is no single median. In these cases, the median is usually taken to be the mean of the two middle numbers. {“smallUrl”:“https://www. wikihow. com/images/thumb/e/e1/Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet2-Version-2. jpg/v4-460px-Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet2-Version-2. jpg”,“bigUrl”:"/images/thumb/e/e1/Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet2-Version-2. jpg/aid130521-v4-728px-Find-the-Mode-of-a-Set-of-Numbers-Step-5Bullet2-Version-2. jpg",“smallWidth”:460,“smallHeight”:345,“bigWidth”:728,“bigHeight”:546,“licensing”:"<div class="mw-parser-output">

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If we change our example data set to {11, 15, 17, 18, 19, 21} so that each value occurs only once, the data set now has no mode. The same is true if we change the data set so that each value occurs twice: {11, 11, 15, 15, 17, 17, 18, 18, 19, 19, 21, 21}.

For example, let’s say that a biological survey determines the species of each tree in a small local part. The data set for the types of trees in the park is {Cedar, Alder, Cedar, Pine, Cedar, Cedar, Alder, Alder, Pine, Cedar}. This type of data set is called a nominal data set because the data points are distinguished only by their names. In this case, the mode of the data set is Cedar because it occurs the most often (five times as opposed to three for Alder and two for Pine). Note that, for the example data set above, it’s impossible to calculate a mean or median because the data points have no numerical value.

For example, let’s consider the data set {1, 2, 2, 3, 3, 3, 4, 4, 5}. If we were to graph the distribution of this data set, we’d get a symmetrical curve that reaches a height of 3 at x = 3 and tapers off to a height of 1 at x = 1 and x = 5. Because 3 is the most common value, it is the mode. Because the central 3 in the data set has 4 values on either side of it, 3 is also the median. Finally, the average of the data set works out to 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 = 27/9 = 3, meaning that 3 is also the mean. The exception to this rule is for symmetrical data sets with more than one mode - in this case, because there can be only one median and mean for the data set, both modes will not coincide with these other points.