Question

Find mean and medium of the first 10 prime numbers

Answer 1

Answer:

Mean = 12.9

Median = 12

Step-by-step explanation:

Prime Number : A prime number is a whole number greater than one which has only two factors mainly 1 or itself.

First 10 natural numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

We know that ;

Mean = $\sf \frac{Sum \: of \: observations}{No \: of \: observations}$

Sum of observations = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

= 129

No of observations = 10

Mean = $\frac{129}{10}$

Mean = 12.9

Hence, the mean of the first ten prime numbers is 12.9

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Median :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

No of observations, n = 10 (even)

Median = mean of $\mathsf{( \frac{n}{2} )\th}$ and $\mathsf{( \frac{n}{2} + 1 )\th}$ observations.

Median = $\frac{10}{2} \th$ and $\frac{10}{2} +1$

Median = 5 th and 6th term

Median = $\frac{1}{2}$ × (11 + 13)

Median = $\frac{24}{2}$

Median = 12

Hence, the median of the first ten prime numbers is 12.

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Extra information :

Mean : The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = $\sf \frac{Sum \: of \: observations }{Number \: of \: observations }$

Median : After arranging the given data in the ascending or descending order of magnitude, the value of the middle most observation, is called the median of the data.

Formula to find the median :)

Method : Arrange the data in increasing or decreasing order of magnitude. Let the total number of observation be n.

(i) If n is odd, then median

⇒ Value of $\mathsf{( \frac{n + 1}{2} )\th}$ observation.

(ii) If n is even, then median

⇒ mean of $\mathsf{( \frac{n}{2} )\th}$ and $\mathsf{( \frac{n}{2} + 1 )\th}$ observations.

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Answer 2

First 10 natural numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

We know that,

Mean = Sum of observations/No of observations

Sum of observations = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

= 129

No of observations = 10

Mean = 129/10

→ 12.9

➾ The mean of the first ten prime numbers is 12.9

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Median :



No of observations, n = 10


Median = 1/2 × (11 + 13)

= 24/2

= 12

➾ The median of the first ten prime numbers is 12.