
Find the mean of squares of the first 10 natural numbers.
Answer
501.3k+ views
Hint: We will use the formula of sum of the squares of first n natural numbers with n = 10 and then the formula of mean given as: sum of the observations / total number of observations to calculate the value of the mean of the squares of the first 10 natural numbers.
Complete step-by-step answer:
We are required to calculate the value of the mean of the squares of the first 10 natural numbers.
We know the formula of the mean of n numbers is given by: sum of all the n observations / n
So, the sum of the squares of the first n natural numbers is given by:
We need to find the sum of squares of the first 10 natural numbers i.e., we need to find the value when n = 10.
sum of the squares of the first 10 natural numbers =
Now, the mean of the squares of the first 10 natural numbers = sum of the squares of the first 10 natural numbers / 10
Mean =
Therefore, the mean of the squares of the first 10 natural numbers is 38.5.
Note: In this question, you may get confused while starting the solution with the formula of sum of first n natural numbers. You can also solve this question by directly calculating the mean of the square of the first 10 natural numbers namely 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Their squares will be 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. Using the formula of mean, we get . Hence, the answer is verified as well.
Complete step-by-step answer:
We are required to calculate the value of the mean of the squares of the first 10 natural numbers.
We know the formula of the mean of n numbers is given by: sum of all the n observations / n
So, the sum of the squares of the first n natural numbers is given by:
We need to find the sum of squares of the first 10 natural numbers i.e., we need to find the value when n = 10.
Now, the mean of the squares of the first 10 natural numbers = sum of the squares of the first 10 natural numbers / 10
Therefore, the mean of the squares of the first 10 natural numbers is 38.5.
Note: In this question, you may get confused while starting the solution with the formula of sum of first n natural numbers. You can also solve this question by directly calculating the mean of the square of the first 10 natural numbers namely 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Their squares will be 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. Using the formula of mean, we get
Recently Updated Pages
Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE
