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Mathematics 8 - Statistics

Welcome to Math 8 - Statistics! In this course, you will learn how to get the measures of central tendency of ungrouped data (Mean, Median, Mode).

STATISTICS - Mean, Median, and Mode

In this course, you will learn how to get the measures of central tendency of ungrouped data (Mean, Median, Mode).

Measures of Central Tendency

Measure means method and central tendency means average value of any statistical series. Thus, we can say that central tendency means the methods of finding out the central value or average value of statistical series of quantitative information. In a simpler term, it is where most values fall. It aims to provide an accurate description of the entire data in the distribution. The central tendency of the data can be found using the three important measures namely mean, median and mode.


 Mean represents the average value of the data. It is the sum of the measurements divided by the number of cases in a set of data. It is found by adding the measurements of observation and dividing the sum by the number of observations.         

Example: Find the mean score of the results of 10 students in a 10-item quiz.
          10          9          5          9          8          10          6          7          9          7

        Formula: M=  (∑▒x)/N
                        
        Solution: M=  (10+9+5+9+8+10+6+7+9+7)/10
                            =  80/10
                        M= 8

Answer: The mean score is 8.

Median is the middle value of the data when it is arranged in ascending or descending order.

Example 1: The Santos family has 5 children, aged 9, 12, 7, 16 and 13. What is the age of the middle child?

Solution: Arrange the data in ascending or descending order and find the middle number.
           Ascending order: 7, 9, 12, 13, 16
           Descending order: 16, 13, 12, 9, 7

Answer: The age of the middle child is 12.


Example 2: Six teenagers receive the allowances listed below. Find the median allowance.
                            ₱200, ₱150, ₱300, ₱250, ₱400, ₱350

Solution: Arrange the data in ascending or descending order and find the middle number.
                           ₱150, ₱200, ₱250, ₱300, ₱350, ₱400

      If there are two middle values, get their average.
                           Md=(250+300)/2=  550/2=275

Answer: The median allowance is ₱275.


Mode represents the frequently occurring value in the data. 

Example: Listed below are the marks obtained by 10 students in mathematics out of 50. Identify the mode.
                      38, 42, 49, 48, 30, 48, 50, 38, 48, 47
Solution: Identify the most frequent number. Since the 48 is the most frequent number, then we can say that the mode is 48.

Answer: The mode is 48.