Question

find the mean and median of first 10 prime numbers

Answer 1

The first 10 prime numbers are 2,3,5,7,11,13,17,19,23,29
n=10 (even)
median=(n/2 th observation+(n+1)/2 th observation)/2
            =(10/2 th observation+11/2 th observation)/2
             =(5 th observation+6 th observation)/2
              =(11+13)/2
                 =24/2
=12

Answer 2

Given:

We have prime numbers.

To Find:

We have to find the mean and median of the first prime numbers?

Step-by-step explanation:

• First 10 prime number are 2,3,5,7,11,13,17,19,23,29.
• Now mean of a set of data is given by the sum of observations divided by the total number of observations.
• Sum of first 10 prime number will be

         $2+3+5+7+11+13+17+19+23+29=129$

• Now mean of the above observation will be

       $Mean=\frac{sum}{\textrm{no. of terms}} =\frac{129}{10} =12.9$

• Hence,  mean of first 10 prime numbers will be  12.9
• Now For median we have data2,3,5,7,11,13,17,19,23,29.

• As the above data is already in ascending form and number of terms is 10.
• For even number of terms median of data it given by the formula.

        $Median=\frac{(\frac{n}{2} +1)th+\frac{n}{2}th }{2} th$

• Now put the value of n is 10 in the above equation.

       $Median=\frac{(\frac{10}{2} +1)th+\frac{10}{2}th }{2} th\\Median=\frac{6th+5th}{2}$

• Now we have the 5th term in the above data is 11 and 6th term is 13 put in above equation.

      $Median=\frac{11+13}{2} =\frac{24}{2} =12$

• Hence, the median of data is 12.

Thus mean is 12.9 and median is 12.