Which measure of central tendency is the value that appears most often in a set of data?
What Is the Mode?The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set. Show
Key Takeaways
Understanding the ModeIn statistics, data can be distributed in various ways. The most often cited distribution is the classic normal (bell-curve) distribution. In this, and some other distributions, the mean (average) value falls at the midpoint, which is also the peak frequency of observed values. For such a distribution, the mean, median, and mode are all the same values. This means that this value is the average value, the middle value, and also the mode—the most frequently occurring value in the data. Mode is most useful as a measure of central tendency when examining categorical data, such as models of cars or flavors of soda, for which a mathematical average median value based on ordering can not be calculated. Examples of the ModeFor example, in the following list of numbers, 16 is the mode since it appears more times in the set than any other number:
A set of numbers can have more than one mode (this is known as bimodal if there are two modes) if there are multiple numbers that occur with equal frequency, and more times than the others in the set.
In the above example, both the number 3 and the number 16 are modes as they each occur three times and no other number occurs more often. If no number in a set of numbers occurs more than once, that set has no mode:
A set of numbers with two modes is bimodal, a set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal. When scientists or statisticians talk about the modal observation, they are referring to the most common observation. Advantages and Disadvantages of the ModeAdvantages:
Disadvantages:
How Do I Calculate the Mode?Calculating the mode is fairly straightforward. Place all numbers in a given set in order; this can be from lowest to highest or highest to lowest, and then count how many times each number appears in the set. The one that appears the most is the mode. What Is Mode in Statistics With an Example?The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set. What Is the Difference Between Mode and Mean?The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set. The mean is also known as the average. Measures of central tendency are numbers that tend to cluster around the “middle” of a set of values. Three such middle numbers are the mean, the median, and the mode. For example, suppose your earnings for the past week were the values shown in Table 1.
Mean You could express your daily earnings from Table 1 in a number of ways. One way is to use the average, or mean, of the data set. The arithmetic mean is the sum of the measures in the set divided by the number of measures in the set. Totaling all the measures and dividing by the number of measures, you get $1,000 ÷ 5 = $200. Median Another measure of central tendency is the median, which is defined as the middle value when the numbers are arranged in increasing or decreasing order. When you order the daily earnings shown in Table 1, you get $50, $100, $150, $350, and $350. The middle value is $150; therefore, $150 is the median. If there is an even number of items in a set, the median is the average of the two middle values. For example, if we had four values—4, 10, 12, and 26—the median would be the average of the two middle values, 10 and 12; in this case, 11 is the median. The median may sometimes be a better indicator of central tendency than the mean, especially when there are outliers, or extreme values. Given the four annual salaries of a corporation shown in Table 2, determine the mean and the median.The mean of these four salaries is $275,000. The median is the average of the middle two salaries, or $40,000. In this instance, the median appears to be a better indicator of central tendency because the CEO's salary is an extreme outlier, causing the mean to lie far from the other three salaries.
where n is the number of values. Occasionally, you may have data that consist not of actual values but rather of grouped measures. For example, you may know that, in a certain working population, 32 percent earn between $25,000 and $29,999; 40 percent earn between $30,000 and $34,999; 27 percent earn between $35,000 and $39,999; and the remaining 1 percent earn between $80,000 and $85,000. This type of information is similar to that presented in a frequency table. Although you do not have precise individual measures, you still can compute measures for grouped data, data presented in a frequency table.The formula for a sample mean for grouped data is
where x is the midpoint of the interval, f is the frequency for the interval, fx is the product of the midpoint times the frequency, and n is the number of values. For example, if 8 is the midpoint of a class interval and there are ten measurements in the interval, fx = 10(8) = 80, the sum of the ten measurements in the interval. Σ fx denotes the sum of all the products in all class intervals. Dividing that sum by the number of measurements yields the sample mean for grouped data. For example, consider the information shown in Table 3.
Substituting into the formula:
Therefore, the average price of items sold was about $15.19. The value may not be the exact mean for the data, because the actual values are not always known for grouped data. As with the mean, the median for grouped data may not necessarily be computed precisely because the actual values of the measurements may not be known. In that case, you can find the particular interval that contains the median and then approximate the median.Using Table 3, you can see that there is a total of 32 measures. The median is between the 16th and 17th measure; therefore, the median falls within the $11.00 to $15.99 interval. The formula for the best approximation of the median for grouped data is
where L is the lower class limit of the interval that contains the median, n is the total number of measurements, w is the class width, f medis the frequency of the class containing the median, and Σ f bis the sum of the frequencies for all classes before the median class. Consider the information in Table 4.
As we already know, the median is located in class interval $11.00 to $15.99. So L = 11, n = 32, w = 4.99, f med = 4, and Σ f b= 14. Substituting into the formula:
Figure 1.For a symmetric distribution, mean, median, and mode are equal.
Figure 2 shows a negatively skewed curve. Figure 2.A negatively skewed distribution, mean < median < mode.
Figure 3 shows a positively skewed curve. Figure 3.A positively skewed distribution, mode < median < mean.
Which measure of central tendency is used most often?The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average. For data from skewed distributions, the median is better than the mean because it isn't influenced by extremely large values.
Which measure of central tendency is the value that appears most often in a set of data apex?The mode is the value that occurs the most frequently in your data set, making it a different type of measure of central tendency than the mean or median.
What measure of central tendency is also known as middle most value?Median Measure of Central Tendency
Median (a measure of central tendency) is the middle-most value in the data set when all of the values (observations) in a data set are arranged either in ascending or descending order of their magnitude.
What refers to the value that most frequently appears in a set of data?The mode or modal value of a data set is the most frequently occurring value. It's a measure of central tendency that tells you the most popular choice or most common characteristic of your sample.
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