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In statistics, mode of a set of numbers is numbers appear most often in that population. A data set does not have to have only one mode - if two or more values ​​are considered to be the most common, then that data set can be called bimodal (two modes) or multimodal (multimode) - in other words, all the most common values ​​are the mode of the set. For details on determining a data set's mode, see Step 1 below to get started.

Steps

Method 1 of 2: Find the Mode of a data set

1. 

   List the numbers in your data set. Modes are often obtained from statistical data point sets or a list of numerical values. So to find a mode, you need to have a data set to look for. It's hard to calculate mode values ​​just by visualization except for the data sets that are too small, so in most cases the wisest way is to write (or type) your data set out. . If you work with paper and pencil, just write the values ​​in your data set in order, while using a calculator, you may need to use an Excel program.
   • The process of finding the mode of a data set is easier to understand when illustrated by an example. In this section, let's use the following set of values ​​as an example: {18, 21, 11, 21, 15, 19, 17, 21, 17}. In the next steps, we will find the mode of this collection.

2. 

   
   
   Sort the numbers from smallest to largest. It is wise to arrange the values ​​of the data set in ascending order. Although this is optional, it makes the process of finding the mode easier because it groups similar values ​​side by side. For large datasets this is really necessary, as it is difficult to categorize long lists and remember how many times each number appears in the list and can lead to errors.
   • If you work with paper and pencil, jotting down can save time in the long run. Go through the set of numbers to see which number is the smallest, and once you have found it, start the new data set with that smallest number, followed by the second, third smallest, and so on. Make sure you write each number equal to the number of times it appeared in the original data set.
   • With the calculator, you can sort lists of values ​​from small to large with just a few clicks
   • In the above example, after sorting, our new list would be: {11, 15, 17, 17, 18, 19, 21, 21, 21}.

3. 

   
   
   Count the number of times each number is repeated. The next step is to count the number of times each number appears in the set.Find the value that occurs most often in the data set. For relatively small datasets whose points are sorted in ascending order, finding "clusters" of similar values ​​and counting their occurrences is relatively simple.
   • If you are working with paper and a pencil, memorize your count, write down how many times each value occurs on each cluster of the same number. If you are using a desktop excel program, you can do the same by writing them in the box next to them, or using one of the program's functions to count 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. once, 19 appear once, and 21 appeared three times. 21 is the most frequent value in this data set.

4. 

   
   
   Determine the value that occurs most often. When you know how many occurrences each value occurs, find the value with the most occurrences. This is the mode of your data set. Note that There can be more than one mode in a data set. If two values ​​have equal most occurrences in the population then the set is bimodal (two modes), if there are three such values ​​then the set is trimodal (three modes), and so on.
   • In the example above, ({11, 15, 17, 17, 18, 19, 21, 21, 21}), since 21 occurs at most, 21 is the mode.
   • If one more value than 21 also appears three times, (such as there is an additional 17 in the set), then 21 and this number both will be the mode.

5. 

   Don't confuse the mode with the mean or the median. Three statistical concepts that are often mentioned together are mean, median, and mode. Because these concepts have similar sounding names, and because in a data set a value can sometimes be closed. more than one roles in these numbers, so it's easy to confuse them. However, regardless of whether your data set has modes or not, it always has a median or mean. It is important to understand that these three concepts are completely independent of each other. See below:
   • Mean of a data set is the mean of that set. To find the mean, add all the values ​​in the set together, then divide the sum by the number of terms in the set. For example the initial set of numbers ({11, 15, 17, 17, 18, 19, 21, 21, 21}), the mean will be 11 + 15 + 17 + 17 + 18 + 19 + 21 + 21 + 21 = 160/9 = 17.78. 9 means there are 9 digits in the set.

     

   • Median of a data set is the "middle number" that divides the small and large values ​​of that set into two equal halves. Take the example above, ({11, 15, 17, 17, 18, 19, 21, 21, 21}) 18 is median because it is the middle number - there are exactly four numbers greater than it and four numbers less than it. Note that if the number of values ​​in the set is even then the median is the arithmetic mean of the two middle numbers.

     

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Method 2 of 2: Find Mode in special cases

1. 

   In data sets where each value has an equal number of occurrences, there is no mode. If values ​​in a given set occur the same number of times, this data set has no mode because no number occurs more than any other. For example, data sets in which each value occurs only once have no mode. The same is true for datasets with values ​​occurring twice, thrice, and so on.
   • If we change the example data set to {11, 15, 17, 18, 19, 21} so that each value occurs only once, now this data set There is no mode. This is the same if we change the data set so that each value occurs twice: {11, 11, 15, 15, 17, 17, 18, 18, 19, 19, 21, 21}.

2. 

   Modes of non-numeric data sets can be found in the same way as for numerical data sets. In general, most data sets are Quantitative - they contain numerical data. However, some data sets contain information that is not represented as a number. In these cases, "mode" is still the most frequently occurring value in that data set just like in numeric data set. In these cases, finding the mode is possible while finding the median or mean is not possible.
   • Take, for example, the area's plant species identification. The data set for the species of trees in the region are {Bang, Phuong, Bang, Thong, Bang, Bang, Phuong, Phuong, Thong, Bang}. This type of data set is called a data set Name because data points are distinguished based on their name only. The mode of the data set is Bang because it appears the most (five times while Phuong appears three times and Thong twice).
   • In the example above, you cannot calculate the mean or median because the data points are not numeric.

3. 

   For symmetric distributions with a mode, the mode, mean, and median coincide. As noted above, the mode, the median, and / or the mean may be the same under certain circumstances. In cases if the data set's density function forms a perfectly symmetrical curve with one mode (eg, Gaussian Curve or "Bell-shaped" Curve) then the mode, mean, and median will be same value. Because the distribution function will plot the relative occurrence of data points, the natural mode will be in the middle of the symmetrical distribution curve, since this is the highest point of the graph and corresponds to the value. most popular. Because the data set is symmetrical, this point on the graph will correspond to the median (middle value of the data set) and mean (the mean of the data set).
   • Consider the following example {1, 2, 2, 3, 3, 3, 4, 4, 5}. If we plot the distribution of this data set, we get a symmetry curve of height 3 at x = 3 and down to 1 at x = 1 and x = 5. Since 3 is the price treatment most often, it is the mode. Since the mid 3 value of the set has 4 values ​​on either side, 3 also the median. Finally, the mean of the population is 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 = 27/9 = 3, which means that 3 is also a mean.
   • The exception to this rule is that symmetrical datasets have more than one mode - in this case, since there is only one median and mean for that data set, both modes will not coincide with the other points. .
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Advice

• You can have more than one mode.
• If all numbers appear only once, there is no mode.

What you need

• Paper, pencil, and eraser