The Modes Are: Values, Formulas, Example Problems and Their Solutions
The Modes Are: Values, Formulas, Example Problems and Their Solutions – What is meant by mode in mathematics? On this occasion About the knowledge.co.id will discuss it, including understanding, formulas and of course other things that also cover it. Let's look at the discussion together in the article below to better understand it.
The Modes Are: Values, Formulas, Example Problems and Their Solutions
In a mathematics subject, simply the definition of the mode is the value that appears most often. In the group data that has been presented with the frequency, the mode is a value that has the greatest frequency.
Modis is divided into two forms, namely, single data mode and group data mode. When you want to find the value of the mode contained in single data, it can be said that it is quite easy for data in general, but if you are looking for a value in group data mode can be said to be not as easy as when searching for data in single data mode, therefore we need to use a certain formula to found it.
In material mode generally has a value of more than 1. If you have found that the value with the greatest frequency has 2 values, then the mode is the two values. Likewise if 3, 4, and so on. However, usually the mode value is only 1.
The mode symbol in the equation is Mo.
Single Data Mode
Single data is raw data that is still random. In general, this data can be used immediately if it only shows a maximum of 30 pieces of data.
This single data at an advanced level will be processed in tabular form and in the form of statistical diagrams to make it easier to read.
The mode of a single data set can be seen by examining which value appears most frequently.
How to Determine the Mode Value in Single Data
Problems example
Look at the two sample questions below so you can understand the value of the mode from the basic stages.
a. calculate the mode of height for grade 11 students, namely: 142 145 143 148 144 142 146 148 147 146 145
Answer:
The data above states that the value 142 appears 2 times, 143 = 1, 144 = 1, 145 = 2, 146 = 2, 147 = 1, and 148 = 2
The modes of the data above are 142, 14, 146, and 148.
b. Determine the mode value of the math value data from grade 9 students is: 10, 9, 8, 7, 8, 9, 8, 6, 6, 7, 9, 8, 7, 9, 10, 9, 8, 7, 7, 6, 7, 8, 9, 10, 9, 8, 6, 7, 9, 10
For data that is more than 10 it will be easier to sort first. This way you will be able to determine the median value as well as the mode value. Even so, you only need to calculate the mode first this time.
The data is sorted into:
6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10
From the sorted data we can see that the value that appears frequently is number = 9. This means, based on the existing scores, that grade VI students with a score of 9 are the most frequently found.
Group Data Mode
In group data mode here it's still easy for you to find out. Group data is still in simple group data.
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: the mode class frequency is reduced by the previous class frequency
- d2: class mode frequency minus the frequency that class thereafter
- k: class length
Problems example
1. Draw the group data below in tabular form and also determine the mode value!
6, 9, 10, 8, 8, 9, 8, 6, 6, 7, 9, 8, 7, 9, 8, 9, 8, 7, 7, 10, 7, 8, 9, 10, 9, 7, 6, 7, 9, 10
Answer:
Data after sorting:
6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10
Enter the data in tabular form by calculating the frequency of the number of students who get a certain value.
| Math Test Scores | Number of students (frequency) |
| 6 | 4 |
| 7 | 7 |
| 8 | 7 |
| 9 | 8 |
| 10 | 4 |
| Total | 30 |
The group data mode in the table is 9 because it gets the frequency with the largest value.
2. Determine the mode of the data below!
Student Weight Table
| Weight (kg) | Number of Students (frequency) |
| 35 | 8 |
| 36 | 9 |
| 37 | 8 |
| 38 | 7 |
| 39 | 7 |
| 40 | 6 |
| Total | 45 |
Answer:
The mode value of the data above is the body weight of 36 kg because the body weight of 36 has the greatest frequency value.
Mode of Group data with Frequency Distribution Table
The frequency distribution table is also included in the group data. It's just that, in this table, the data values are written in the form of a certain range, which is called an interval or class.
Nonetheless, the mode value for the group data is formulated:
Information :
MP = mode
• Xi = the lower edge of the mode class
• fi = mode class frequency
• f1 = difference between the frequency of the mode class and the previous class
• f2 = the difference between the frequencies of the mode class and the class after that
Problems example
Let's calculate the mode value from the table data below!
| Mark | Frequency |
| 11 – 20 | 3 |
| 21 – 30 | 5 |
| 31 – 40 | 10 |
| 41 – 50 | 11 |
| 51 – 60 | 8 |
Answer:
The frequency of the largest value is 11 in class 41-50, so 41-50 is called the mode class and is obtained:
- Xi = the lower edge of the mode class, namely = 41- 0.5 = 40.5
- fi = mode class = 11
- f1 = the difference between the mode class and the previous class, namely = 11 – 10 = 1
- f2 = the value of the difference between the mode class and the following class, namely = 11 – 8 = 3
- p = class length = upper edge of class – lower edge of class = 50.5 – 40.5 = 10
the mode is = 40.5 + (11/(1+3))10 = 40.5 + 27.5 = 68
Problems example
Observe the following table and find the group mode.
Answer:
The frequency of the mode in the data above is 18, while in the mode class above it is 65-69, while the lower edge of the mode frequency (b) = 64.5.
d1= 18 – 6 = 2
d2= 18 – 9 = 9
l = 69.5 – 64.5 = 5
Mo= b0 + (d1/d1+d2) x l = 64.5 + (12/12+9) x 5 = 64.5 + 12/21 x 5 = 64.5 + 2.86 = 67.36.
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