Finding the central tendency of a numerical data set is necessary to know in all calculations. Mean, median, and mode are the most common ways to find it. Moreover, every student wants to learn the most exciting and easiest math formulas to find various values. In this article, you will learn about these and also how to calculate these three values in statistics.
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Mean is one of the ways to find the central tendencies in statistics. The arithmetic mean is the arithmetic average of a given data set or list of numbers.
To find the mean, add all the numbers in the data set and divide that value by the total number of values in the data set. This method will give you the average value of the given data.
Many other mean types include the geometric mean, the harmonic mean, and the Pythagorean mean. These are different statistical measures that have slightly different ways and strengths of calculating the mean value.
For example, there are numbers like 10, 12, 13, 14, 14, 16, 17, 18, and 21. The mean comes by the sum of the values (135) divided by the total number of values given in the data set (9), which equals 15.
There is another measure to find the central tendency that gives the information about where the data center lies. The median is the central number or the number that lies in the middle; the median is the numeric value in the middle of a data set.
To find the median, you will first have to arrange your set of numbers in the numerical value starting from the lowest or the smallest to the highest or largest value. Then, you can find out the middle value. If there is no exact middle number or midpoint in the set and two numbers comprise the middle of the data set, the median number will be the average of these two values. For example, in a data set of {13, 2, 3, 27, 47, 34, 11, 17}, the sorted order will become {2, 3, 11, 13, 17, 27, 34, 47}.
The median is the average of the two numbers in the middle(13, 17), which will give the median as:
(13+17 / 2) = 15
Moreover, the median in a data set of 12,13,14,15,16,17,18,20,22 is 16
The value in a set of data points that occurs most frequently is called the mode. The mode can be two or more than two values if there is a tie for the number occurring the most in the given data.
In order to find the mode, you first have to arrange the values in ascending order and then find out the value with the highest frequency.
For numbers 10,12,13,14,15,15,15,16,17,18 and 19, the mode is 15.
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1. Find the mean, median, and mode for these values: 7, 9, 10, 10, 10, 11, 11, 11, 12, 14
Solution:
The mean is the usual average, so you will add it up and then divide it,
=(7 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 14) ÷ 10
= 105 ÷ 10
= 10.5
The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5-th value; that formula reminds me, with that "point-five," that I'll need to average the fifth and sixth numbers to find the median. The fifth and sixth numbers are the last 10 and the first 11. So, to find the median, we will add the two numbers and divide by 2:
(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5
The mode is the number repeated most often. This list has two values that are repeated three times; namely, 10 and 11, each repeated three times.
Mean: 10.5
Median: 10.5
Modes: 10 and 11
2. Ashley’s math teacher said that their final class grade is based on the average of all exam grades. Ashley has gotten 93,87,71, and 97 on her math exams. What measure of central tendency will she use to calculate her average score? What will be the average?
Solution:
When we see the word average, we're talking about the mean! So, we will be using mean to solve this problem.
Mean= (93 + 87 + 71 + 97)/4
= 348/4
= 87
So, we know that Ashley's average score on her math exams was 87
PRACTICE WORD PROBLEMS
=> The average of three numbers is 6. When one number is removed from the list, the average is 5. What is the number that was removed from the list?
=> 30 students took a test. 15 students got an average (arithmetic mean) score of 80. 10 of them got an average score of 75. And the remaining 5 students got an average score of 55. What is the average score of the 20 students?
=> The following data show the number of kilometers joggers ran in a month 4,6,12,12,18,19,25,30,31,40,40,40,40,47,49,60. Find the median of the data.
👉 Mean, median, and mode are different measures of center in a numerical data set. They all summarize a dataset in their own way, with a single number to represent a "typical" data point from the dataset.
👉 Yes, absolutely. Mean represents typical values in our daily lives and serves as a yardstick for many observations. For example, mean will tell about how many average hours of training an employee has spent on training in a year. By this, we can find the mean training hours of a group of employees.
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This article benefits everyone who wants to learn about finding the central tendencies. We have discussed the mean, median, and mode in the simplest way. Whether directly, or indirectly, these mathematical terms are used in most mathematical calculations at higher levels.
