Mean, Median & Mode
In this course, students will learn how to calculate and understand the three main measures of central tendency: mean, median, and mode.
The mean is the average of a set of numbers, found by adding all the values and dividing by the total number of values.
The median is the middle value when the numbers are arranged in order.
The mode is the number that appears most frequently.
Through this course, students will practice finding the mean, median and mode for discrete and continuous data.
Related Lessons:
Mean
The mean of a set of data represents the average value. For discrete data, it is calculated by adding all values and dividing by the number of values. For continuous data, the mean is found using the midpoint of each class, multiplied by its frequency, then dividing the total by the sum of frequencies. Mathematically,
\(mean=\frac{\sum f x}{\sum f}\)
Median
The median is the middle value of a data set when the numbers are arranged in order. For a data set with an odd number of values, the median is the middle number. For a data set with an even number of values, the median is the average of the two middle numbers. Finding the median is a two steps process:
- Find the middle position using the formula: \(Position=\frac{No\ of\ data\ set\ +\ 1}{2}\)
- The second step is to manually count the position to find the median
Mode
The mode is the value that appears most frequently in a data set. For discrete data, it is simply the number that occurs most number of times. If the data set has two modes, we must remember to use the word “and” instead of “or”, e.g. 2 and 5 are the mode, else no marks will be awarded.
Stem & Leaf
A stem-and-leaf diagram is a way of organizing and displaying data to make it easier to read and interpret. Each value is split into a stem (the leading digit or digits) and a leaf (the final digit), allowing the data to be arranged in order while keeping the original values visible.
- If the data set has two digits, the first digit is the stem, and the second digit is the leaf
- If the data set has three digits, the first two digits are the stem, and the last digit is the leaf
Dot Diagram
A dot diagram is a way of displaying data using dots above a number line. Each dot represents one value, and repeated values are shown by stacking dots vertically.
Example 1
A class of 35 students took a Science Test. The results are displayed in the dot diagram.
- For the whole class, write down the
(i) modal score
(ii) median score - Using the dot diagram data, complete the single ordered stem-and-leaf diagram to represent the scores of all 35 students.
Example 2
A die was thrown 40 times and the frequency of each score was recorded in the table above.
- Write down the modal score.
- Find the median score.
- Calculate the mean of these scores.
- The die was then thrown another 20 times. The mean of these 20 throws was 3.4. Calculate the overall mean for all 60 throws.