SSC GD Average

• What is Average?
• Simple Average: The Basic Formula
• Solving Average Word Problems
• Understanding Weighted Average
• Practice More SSC GD Average Questions

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What is Average?

Imagine you have some things, and you want to share them equally among everyone. The Average is the number that everyone would get if everything was shared perfectly equally.

• It tells you the “middle value” or the “typical amount.”
• If you score 80, 90, and 100 in three tests, your average score is 90. This means 90 is your typical score.
• Learning how to calculate the average is very important for solving average ssc gd questions.

Why do we need the Average?

We use the average to compare groups or understand performance quickly.

• If Team A scores an average of 150 runs and Team B scores 120 runs, Team A is generally better.
• The average helps us summarize a lot of numbers into just one simple number.

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Simple Average: The Basic Formula

The simple average is the foundation for all ssc gd average questions. You only need two things to find it: the Sum and the Count.

Theory: How to Calculate Simple Average

1. Find the Sum: Add up all the numbers you have.
2. Find the Count: Count how many numbers you added together.
3. Divide: Divide the Sum by the Count.

The formula looks like this:

$$\text{Average}=\frac{\text{Sum of all numbers}}{\text{Total count of numbers}}$$

4 Solved Examples

Example 1: Finding the average of daily sales.

A shopkeeper sold 10, 20, 30, and 40 apples over four days. What is the average number of apples sold per day? This is a basic type of average ssc gd questions.

Solution:

1. First, let’s find the total number of apples sold (The Sum).

   • We add the sales from all four days: $10+20+30+40$
   • Sum $=100$

2. Now, let’s count how many days there were (The Count).

   • There are 4 days. Count $=4$

3. Write down the formula.

   • $$\text{Average}=\frac{\text{Sum}}{\text{Count}}$$

4. Put the numbers in and calculate it.

   • $$\text{Average}=\frac{100}{4}$$
   • $$\text{Average}=25$$

5. So, the answer is: The average number of apples sold is 25 per day.

Example 2: Finding the Sum when the Average is known.

The average weight of 5 friends is 45 kg. What is the total combined weight of all 5 friends?

Solution:

1. First, let’s understand what we need to find.

   • We know the Average (45 kg) and the Count (5 friends). We need the Sum (Total weight).

2. We change the formula around.

   • Since $\text{Average}=\frac{\text{Sum}}{\text{Count}}$, then $\text{Sum}=\text{Average}\times \text{Count}$.

3. Put the numbers in.

   • $$\text{Sum}=45\times 5$$

4. Calculate it.

   • $$\text{Sum}=225$$

5. So, the answer is: The total combined weight is 225 kg.

Example 3: Finding a missing number.

The average of four numbers is 15. Three of the numbers are 10, 12, and 18. What is the fourth number? These types of ssc gd average questions are very common.

Solution:

1. First, let’s find the total sum of all four numbers.

   • We use the formula: $\text{Sum}=\text{Average}\times \text{Count}$
   • $$\text{Sum}=15\times 4=60$$

2. Now, let’s find the sum of the three numbers we already know.

   • $$\text{Known Sum}=10+12+18=40$$

3. To find the missing number, we subtract the known sum from the total sum.

   • $$\text{Missing Number}=\text{Total Sum}-\text{Known Sum}$$
   • $$\text{Missing Number}=60-40$$

4. Calculate it.

   • $$\text{Missing Number}=20$$

5. So, the answer is: The fourth number is 20.

Example 4: Average of consecutive numbers.

Find the average of the first five odd numbers (1, 3, 5, 7, 9).

Solution:

1. First, let’s find the total sum of the numbers.

   • $$\text{Sum}=1+3+5+7+9$$
   • $$\text{Sum}=25$$

2. Now, let’s count how many numbers there are.

   • Count $=5$

3. Use the average formula.

   • $$\text{Average}=\frac{25}{5}$$

4. Calculate it.

   • $$\text{Average}=5$$

5. So, the answer is: The average of the first five odd numbers is 5. (A quick trick for consecutive odd/even numbers: the average is always the middle number!)

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Solving Average Word Problems

In the ssc gd average questions pdf in english, you will see problems that look like real stories. These problems often involve changes in a group (someone joins or leaves) or finding the average of a series of items (like runs or ages).

Theory: Handling Changes in Average

When a new person joins a group, the total sum changes.

• If the new person’s value is higher than the old average, the new average will go up.
• If the new person’s value is lower than the old average, the new average will go down.
• Always calculate the Total Sum before and after the change.

4 Solved Examples

Example 1: A person joins the group.

The average age of 10 students is 15 years. If a new teacher joins them, the average age increases by 1 year. What is the age of the teacher? This is a classic average ssc gd questions type.

Solution:

1. First, find the total age of the 10 students.

   • $$\text{Old Sum}=\text{Old Average}\times \text{Old Count}$$
   • $$\text{Old Sum}=15\times 10=150\text{ years}$$

2. Now, find the new average and the new count.

   • New Count $=10\text{ students}+1\text{ teacher}=11$
   • New Average $=15\text{ years}+1\text{ year increase}=16\text{ years}$

3. Find the new total age (students + teacher).

   • $$\text{New Sum}=16\times 11=176\text{ years}$$

4. To find the teacher’s age, subtract the old sum from the new sum.

   • $$\text{Teacher’s Age}=176-150$$
   • $$\text{Teacher’s Age}=26\text{ years}$$

5. So, the answer is: The teacher is 26 years old.

Example 2: Finding required score/value.

A batsman has an average of 40 runs in 15 innings. How many runs must he score in the 16th inning to increase his average to 42?

Solution:

1. First, find the total runs scored in 15 innings.

   • $$\text{Old Sum}=40\times 15=600\text{ runs}$$

2. Now, find the required total runs for 16 innings to reach the new average of 42.

   • $$\text{New Sum}=\text{New Average}\times \text{New Count}$$
   • $$\text{New Sum}=42\times 16=672\text{ runs}$$

3. The runs needed in the 16th inning is the difference between the new sum and the old sum.

   • $$\text{Runs Needed}=672-600$$

4. Calculate it.

   • $$\text{Runs Needed}=72\text{ runs}$$

5. So, the answer is: He must score 72 runs in the 16th inning.

Example 3: Average of a series of numbers.

What is the average of the first 5 multiples of 3? (Multiples are 3, 6, 9, 12, 15).

Solution:

1. First, list the numbers and find the sum.

   • Numbers: 3, 6, 9, 12, 15
   • $$\text{Sum}=3+6+9+12+15=45$$

2. Count how many numbers there are.

   • Count $=5$

3. Use the average formula.

   • $$\text{Average}=\frac{45}{5}$$

4. Calculate it.

   • $$\text{Average}=9$$

5. So, the answer is: The average is 9. (Note: For numbers in an arithmetic progression, the average is always the middle number, which is 9).

Example 4: Average of a series of squares.

Find the average of the squares of the first three natural numbers (1, 2, 3).

Solution:

1. First, find the squares of the numbers.

   • $1^2=1$
   • $2^2=4$
   • $3^2=9$

2. Find the sum of these squares.

   • $$\text{Sum}=1+4+9=14$$

3. Count how many numbers we used.

   • Count $=3$

4. Use the average formula.

   • $$\text{Average}=\frac{14}{3}$$

5. Calculate it.

   • $$\text{Average}=4.666...$$

6. So, the answer is: The average is $\frac{14}{3}$ or approximately 4.67.

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Understanding Weighted Average

Sometimes, not all numbers are equally important. When different groups have different sizes (or “weights”), we must use the Weighted Average. This concept is useful when solving complex average ssc gd problems.

Theory: Why “Weight” Matters

Imagine Class A has 10 students with an average score of 50. Class B has 2 students with an average score of 90.

• If you just average 50 and 90, you get 70. This is wrong!
• Class A (10 students) is much bigger, so its average (50) should “pull” the final average closer to 50.
• The formula requires us to find the total sum of all items first.

$$\text{Weighted Average}=\frac{(\text{Sum of Group 1})+(\text{Sum of Group 2})}{\text{Total Count of items in all groups}}$$

4 Solved Examples

Example 1: Merging two groups of students.

In a class, 20 boys have an average weight of 30 kg, and 10 girls have an average weight of 24 kg. What is the average weight of the whole class? This is a key type of average ssc gd questions.

Solution:

1. First, find the total weight of the boys (Sum 1).

   • $$\text{Boys’ Sum}=20\times 30=600\text{ kg}$$

2. Next, find the total weight of the girls (Sum 2).

   • $$\text{Girls’ Sum}=10\times 24=240\text{ kg}$$

3. Find the total weight of the whole class (Total Sum).

   • $$\text{Total Sum}=600+240=840\text{ kg}$$

4. Find the total number of students (Total Count).

   • $$\text{Total Count}=20\text{ boys}+10\text{ girls}=30$$

5. Calculate the Weighted Average.

   • $$\text{Weighted Average}=\frac{840}{30}$$
   • $$\text{Weighted Average}=28\text{ kg}$$

6. So, the answer is: The average weight of the whole class is 28 kg. (Notice 28 is closer to the boys’ average of 30 because there are more boys.)

Example 2: Mixing different prices.

A shopkeeper buys 5 kg of rice at ₹10 per kg and 10 kg of rice at ₹16 per kg. What is the average cost per kg of the mixed rice?

Solution:

1. First, find the total cost of the first type of rice.

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2. Next, find the total cost of the second type of rice.

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3. Find the total money spent (Total Sum).

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4. Find the total quantity of rice (Total Count).

   • $$\text{Total Count}=5\text{ kg}+10\text{ kg}=15\text{ kg}$$

5. Calculate the Weighted Average Price.

   • $$\text{Weighted Average}=\frac{210}{15}$$
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6. So, the answer is: The average cost of the mixed rice is ₹14 per kg.

Example 3: Finding the average of remaining items.

The average salary of 10 employees is ₹5000. If the manager’s salary (₹15000) is removed, what is the new average salary of the remaining 9 employees?

Solution:

1. First, find the total salary of all 10 people (employees + manager).

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2. Now, remove the manager’s salary to find the sum of the remaining 9 employees.

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3. The new count is 9 employees.

4. Calculate the new average.

   • $$\text{New Average}=\frac{35000}{9}$$
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5. So, the answer is: The new average salary is approximately ₹3888.89.

Example 4: Weighted average with percentages.

A student spends 60% of his time studying Science, where his average score is 80. He spends 40% of his time studying Math, where his average score is 90. What is his overall average score? (Think of percentages as weights). This helps prepare for complex average ssc gd problems.

Solution:

1. First, find the “weighted score” for Science (Score $\times$ Weight).

   • $$\text{Science Weight}=80\times 60=4800$$

2. Next, find the “weighted score” for Math.

   • $$\text{Math Weight}=90\times 40=3600$$

3. Find the total weighted score (Total Sum).

   • $$\text{Total Weighted Sum}=4800+3600=8400$$

4. The total weight (count) is $60$.

5. Calculate the Weighted Average Score.

   • $$\text{Weighted Average}=\frac{8400}{100}$$
   • $$\text{Weighted Average}=84$$

6. So, the answer is: His overall average score is 84.

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Practice More SSC GD Average Questions

To succeed in the SSC GD exam, you must practice many different types of ssc gd average questions. Look for an ssc gd average questions pdf in english to test your speed and accuracy.

Key Takeaways for SSC GD Average

• Always find the Sum first. Most mistakes happen when you forget to convert the average back into the total sum.
• Read the question carefully. Does the average increase or decrease? Is a person joining or leaving?
• Use the shortcut for consecutive numbers. If numbers are in a series (like 2, 4, 6, 8), the average is the middle number (6).

Keep practicing these average ssc gd questions regularly!