Types of Averages

By

 

Types of Averages

Averages are used to represent a central value of a dataset. The three main types of averages are:

  1. Arithmetic Mean (Mean)

  2. Median

  3. Mode

1. Arithmetic Mean (Mean)

The arithmetic mean is the most common type of average, calculated by dividing the sum of all values by the number of values.

Formula:

Mean=Sum of all valuesTotal number of values

Example:
Find the mean of 10, 20, and 30.

Solution:

Mean=10+20+303=603=20

So, the mean is 20.

2. Median

The median is the middle value when numbers are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers.

Example 1 (Odd set of numbers):
Find the median of 3, 5, 7, 9, 11.

Solution:
Sorted order: 3, 5, 7, 9, 11
The middle number is 7, so the median is 7.

Example 2 (Even set of numbers):
Find the median of 4, 8, 12, 16.

Solution:
Sorted order: 4, 8, 12, 16
The middle numbers are 8 and 12, so the median is:

8+122=202=10

So, the median is 10.

3. Mode

The mode is the number that appears most frequently in a dataset. A dataset may have one mode, multiple modes, or no mode.

Example 1 (Single Mode):
Find the mode of 3, 5, 7, 5, 9, 5, 11.

Solution:
Since 5 appears most frequently, the mode is 5.

Example 2 (Multiple Modes):
Find the mode of 2, 4, 6, 4, 6, 8.

Solution:
Both 4 and 6 appear twice, so the dataset has two modes: 4 and 6 (bimodal).

Example 3 (No Mode):
Find the mode of 1, 2, 3, 4, 5.

Solution:
Since no number repeats, there is no mode.

Multiple Choice Questions (MCQs)

  1. What is the mean of 15, 25, and 35?
    a) 20
    b) 25
    c) 30
    d) 35

    Answer: b) 25

  2. What is the median of 10, 20, 30, 40, and 50?
    a) 20
    b) 30
    c) 40
    d) 50

    Answer: b) 30

  3. What is the mode of 2, 3, 3, 5, 7, 8, 8, 9?
    a) 2
    b) 3 and 8
    c) 5
    d) 9

    Answer: b) 3 and 8

  4. If a dataset has no repeating values, what is the mode?
    a) 0
    b) The smallest number
    c) The highest number
    d) No mode

    Answer: d) No mode

  5. If the numbers are 12, 18, 24, and 30, what is the median?
    a) 18
    b) 21
    c) 24
    d) 22

    Answer: d) 21

Comments

Post a Comment

Popular posts from this blog

Problems on Averages

By
  1. Basic Problems: Finding the Average of Given Numbers The average (arithmetic mean) of a set of numbers is calculated using the formula: Average = Sum of all values Total number of values Average = Total number of values Sum of all values ​ Example: Find the average of  12, 18, 24, and 30 . Solution: Sum of numbers =  12 + 18 + 24 + 30 = 84 Total numbers =  4 Average = 84 4 = 21 Average = 4 84 ​ = 21 So, the  average is 21 . 2. Missing Number Problems: Finding the Missing Value When Average is Given When the average of a group is known, and one number is missing, we use the formula: Total Sum = Average × Total numbers Total Sum = Average × Total numbers Example: The average of  4 numbers  is  20 . Three of the numbers are  18, 22, and 19 . Find the missing number. Solution: Total sum =  Average × Total numbers Total Sum = 20 × 4 = 80 Total Sum =...
Read more

Special Numbers and Their Properties

By
  1. Perfect Numbers Definition A  perfect number  is a  positive integer  that is equal to the sum of its  proper divisors  (excluding itself). Examples of Perfect Numbers 6  → Proper divisors:  1, 2, 3 1 + 2 + 3 = 6  ✅ (Perfect Number) 28  → Proper divisors:  1, 2, 4, 7, 14 1 + 2 + 4 + 7 + 14 = 28  ✅ (Perfect Number) 496  → Proper divisors:  1, 2, 4, 8, 16, 31, 62, 124, 248 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496  ✅ (Perfect Number) MCQs on Perfect Numbers 1. Which of the following is a perfect number? a) 10 b) 15 c) 28 d) 30 ✅  Answer: c) 28 2. The smallest perfect number is: a) 5 b) 6 c) 7 d) 9 ✅  Answer: b) 6 2. Armstrong Numbers Definition An  Armstrong number  (also called a  narcissistic number ) is a number that is equal to the sum of its  digits raised to the power of the number of digits . Examples of Armstrong Numbers 153  → 3-digit number 1³ + 5³ + 3³ = ...
Read more

Shortcut Tricks for Average

By
  1. Quick Mental Math Techniques A. Choosing a Base Value for Faster Calculation Instead of summing all numbers directly, choose a base value close to the average and find deviations from it. Example:  Find the average of  48, 52, 46, 54, and 50 . Shortcut Trick:  Choose  50  as a base value because it is near most numbers. Now, calculate the deviations: 48 → -2 ,  52 → +2 ,  46 → -4 ,  54 → +4 ,  50 → 0 Total deviation =  (-2 + 2 - 4 + 4 + 0) = 0 New sum =  50 × 5 + 0 = 250 Average = 250 ÷ 5 = 50 ✅ Answer:  50  (calculated quickly without full addition). 2. Using the Difference Method for Faster Calculations This method is useful when numbers are close to a particular reference point. Example:  Find the average of  98, 102, 104, 96, and 100 . Shortcut Trick:  Choose  100  as the reference point. 98 → -2 ,  102 → +2 ,  104 → +4 ,  96 → -4 ,  100 → 0 Total deviation = ...
Read more