√ Definition of Mean, Median, Mode (Formulas, Example Questions)
Definition of Mean, Median, and Mode
In statistics, there is a measure of data concentration. Some measures of data centering that you need to know are the mean, median, and mode.
What are the mean, median, and mode?
Mean can be interpreted as the average value of a group of data. The median is the middle value of the data after sorting. Meanwhile, the mode is the value that often appears in a group of data.
Next, the application of the mean, median, and mode will be presented.
Application of the Mean, Median, and Mode
Mean, median, and mode are very necessary in analyzing a result or data collection.
After the data is obtained/collected, the next step is to process the data using statistical methods.
For example in the case of math test scores. The application of the mean can be shown when determining how many students score above the class average.
The median is used when the teacher wants to divide the class into two groups based on the order of scores.
The mode can be used by teachers to find out how many students get a certain value or determine the highest frequency of a data.
Next, we will explain the formulas related to the mean, median, and mode.
Mean, Median and Mode Formulas
In the section below, several formulas will be explained, namely those relating to the mean, median, and mode.
Formula Means
In the previous section it was explained that the mean is the average value of a data. The average value is the quotient between the total value and the amount of data processed. Mathematically, the mean (average value) can be written as
The formula above is the formula for determining the mean (average value) in a single data. Next, the mean group data formula will be explained.
Group Data Mean Formula
Slightly different from the mean formula (average value) for single data, the mean formula for group data is formulated as follows.
Median Formula
How to determine the median on a single data is quite easy.
We can sort it from the smallest data to the largest data. If there is a lot of odd data, of course we can immediately determine the middle value.
What if the number of data is even?
On single data to determine the median, namely:
Suppose the number of data n, if n is odd then the median is determined by
Med = xn/2
If the number of data is even, then
The group data median will be explained.
Group Data Median Formula
The group data median can be determined if we already know the median class. Look for a data class that contains the middle value data. Group data median can be determined by
Med = tb + ((n/2) – Fkum)/fi) k
Information:
- Med: median
- tb: lower edge of the median class
- n: amount of data
- Fkum: cumulative frequency before median class
- fi: the median class frequency
- K: class length
Next will be discussed about the mode or data that often appears.
Mode Formula
To determine the mode, usually a single data frequency table is created to make it easier to determine the frequency of each data, then find the data with the greatest frequency.
Group Data Mode Formula
In grouped data, the mode can be determined by
Mo = tb + (d1 / (d1 + d2)) k
Information:
- Mo: group data mode
- tb: lower edge mode class
- d1: mode class frequency minus the previous class frequency
- d2: the frequency of the mode class is reduced by the class frequency afterwards
- k: class length
Examples of Mean, Median, and Mode Problems
Look at the following data to work on questions number 1 – 3.
| Mark | Frequency |
| 10 – 20 | 2 |
| 21 – 31 | 8 |
| 32 – 42 | 15 |
| 43 – 53 | 7 |
| 54 – 64 | 10 |
| 65 – 75 | 3 |
Based on these data, determine
- The mean of the data.
- The median of the data.
- the data mode
Discussion
Additional information is required by calculating the required information
| Mark | Frequency | Fkum | xi | fi x xi |
| 10 – 20 | 2 | 2 | 15 | 30 |
| 21 – 31 | 8 | 10 | 26 | 208 |
| 32 – 42 * | 15 | 25 | 37 | 555 |
| 43 – 53 | 7 | 32 | 48 | 336 |
| 54 – 64 | 10 | 42 | 59 | 590 |
| 65 – 75 | 3 | 45 | 70 | 210 |
*) is the median class and mode class
Means
Median
Med = tb + (((n/2) – Fkum)/fi) k
Med = 31.5 + (((45/2) – 10)/15) 11
Med = 31.5 + 9.17
Med = 40.67
mode
Mo = tb + (d1 / (d1 + d2)) k
Mo = 31.5 + (7/(7 + 8)) 11
Mo = 31.5 + 5.13
Mo = 36.63
Let's summarize the material above.
Conclusion
- The mean is the average value of a data. Group data mean can be calculated by
- The median is the middle value of the sorted data. The median can be determined by Med = tb + (((n/2) – Fkum)/fi) k
- The mode is a value that occurs frequently. The mode of a data can be determined by Mo = tb + (d1 / (d1 + d2)) k
Thus this article was written. Hopefully this article can be useful.
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