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English Medium / Class 7 / Math / Operations on numbers - Average
Operations on numbers - Average
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Introduction

Average is a mathematical tool used to find a central value of a set of data. It helps us understand the general trend by combining all values and distributing them equally. It is widely used in sports for strike rates, in weather reporting, and for calculating grades in school.

The average line represents a balanced level where all data points contribute to a single central value.

Explanation Step by Step

To find the average, we follow two main steps: first, add all the given numbers together to find the "Sum." Second, divide this sum by the "Total Count" of numbers in that set.

Sub-topics

Operations on numbers - Average

Formula: Average = (Sum of all observations) / (Total number of observations)

Examples

Example 1: Pocket Money

Rahul received 20, 30, and 40 rupees on three consecutive days. What is his average pocket money?

Step 1: Find the sum: 20 + 30 + 40 = 90.
Step 2: Total days = 3.
Step 3: Average = 90 / 3 = 30.
Answer: The average pocket money is 30 rupees.
Tricky Example: The Power of Zero

A batsman scores 50, 0, and 100 runs in three matches. What is his average?

Step 1: Sum of runs = 50 + 0 + 100 = 150.
Step 2: Number of matches = 3 (Even though he scored zero, the match is counted).
Step 3: Average = 150 / 3 = 50.
Answer: The average is 50 runs. (If you forget to count the '0' match, you get the wrong answer!)

Tricks and Shortcuts

1. For consecutive numbers (e.g., 5, 6, 7, 8, 9), the middle number is always the average.

2. If you add a constant number to every value in a set, the average also increases by that same constant.

Common Mistakes

1. Excluding '0' from the total count: Students often forget that zero is a valid observation that must be counted in the denominator.

2. Adding incorrectly: A small error in the sum leads to a completely wrong average.

Practice Questions

Easy Questions

  1. Find the average of 5, 10, 15, 20.
  2. A student scores 70, 80, and 90 marks in three subjects. Find the average marks. (Real-life)
  3. The sum of 5 numbers is 100. What is their average? (Tricky - no addition needed!)

Medium Questions

  1. Find the average of the first 10 odd numbers.
  2. The average height of 4 plants is 12 cm. If one more plant of 17 cm is added, what is the new average? (Real-life)
  3. The average of 3 numbers is 20. If two of the numbers are 15 and 25, find the third number. (Tricky)

Hard Questions

  1. A family of 4 spends an average of 5000 rupees per month. If the father's income increases and the new average spending becomes 5500, how much extra did they spend? (Real-life)
  2. The average age of a group of 10 students is 15 years. When a new student joins, the average decreases by 1 year. Find the age of the new student. (Tricky)
  3. A car travels at 40 km/h for the first hour and 60 km/h for the next two hours. Calculate the average speed.

Revision Summary

Average provides a balanced view of data. Remember the formula: Sum / Count. Always include zeros in your count and look for patterns in consecutive numbers to save time.

The average temperature of the first four days of a week was 40.2 °C and the average temperature of the last four days was 41.3 °C. If the average temperature for a full week is 40.6°C, what is the temperature on the fourth day?

A
    
40.8 degrees
B
    
42.8 degrees
C
    
39.8 degrees
D
    
 41.8 degrees
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