Mean, Mode and Median and How to Calculate Them

Statistics and Probability

In the chapters on data analysis, statistics and probability, O-level students are introduced to elementary statistics such as central tendency, range, graphs and plots,set notations, and conditional probability. Probability is a fundamental concept in mathematics and serves as a building block for more advanced topics such as statistics, calculus, and mathematical modeling. It introduces students to concepts like uncertainty, randomness, and the analysis of events.

Further into the chapter, A-level students will learn binomial distribution, normal distribution and other forms of statistics such as sampling and hypothesis testing. Statistics in the JC level or level h2 math takes up a significant proportion of Paper 2, it is estimated to fill up to 30% of your total A Level Grade in Probability and Statistics!

To clarify the various terms and how to use them, this article will only explain the fundamental terms which are mean, mode and median. These are three different statistics commonly used to measure central tendency. 

What is mean in math

Mean is the average of the numbers. The mean is calculated by adding all the terms or numbers and dividing them by the total number of terms. For example, the following are the grades of a class of students from a math tuition centre.

 

60, 60 ,70, 70, 80 ,80 ,50, 50, 50. 

The mean of the above set of data will be (60 + 60 + 70 + 70 + 80 +  80 + 50 + 50) / 8 

= 63.333… 

What is mode in math 

Mode is the number that occurs the most.

The mode of the above data set is 50.

What is median in math

Median is the middle number when a data is ordered. 

The median of the above data set is the 5th number in the data set, which is 80. 

Range and Standard Deviation

Following the mean, mode and median, range and standard deviation are often added as questions in part (b). 


The range is simply the difference between the largest value and the smallest value. 

In the above data set, 80 – 50 = 30. The range would be 30.  

This is used to represent a simple measure of data dispersion. 

The interquartile range measures the difference between the upper and lower quartile value. 

The lower quartile is the median to the left of the median.  

The upper quartile is the median to the right of the median. 

Similarly, a standard deviation is another measure of data dispersion.

The formula is: √Sum of the squares  of the deviations from the mean/ number of terms in the data set.

 

For example in the data set 8, 11, 11 ,13, 14 and 15.
 

The standard deviation can be calculated as follows:

Mean =  (8 + 11 + 11 + 13 + 14 +15) / 6 = 12

 

Determine how much each score differs from the mean and add the square. 

(8-12)2 + (11-12)2 + (11-12)2 + (13-12)2 + (14-12)2 + (15-12)2

 

Insert this into the formula 

(-4)2 + (-1)2 + (-1)2 +12 + 22 + 32 = √5.33

= 2.3 

Linear Regression

The line of best fit is usually called the linear regression line, which follows the equation, y= ax +b. It is a line that best represents the relationship between the data sets in a scatter plot. (usually a straight line). 

Other Definitions

Random experiments: A process whereby the result depends on chance and therefore cannot be predicted 

Outcome: The result of an experiment 

Sample space: Set of all possible outcomes of an experiment. 

Event: Subset of the sample space, which constitutes multiple outcomes. 

Population Standard Deviation:  The population standard deviation is a measure of how much variation there is among individual data points in a population. It’s a way of quantifying how spread out the data is from its mean

Formula for Population Standard Deviation:

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