Question

what is the mean of all two digit numbers?

Answer 1

Answer:

54.5

Step-by-step explanation:

let the two digit numbers be 10, 11, 12, ..............., 99

total no.of observations(N) = 99 - 10 + 1 = 90

first term(a)  = 10

last term(l) = 99

sum of all the numbers = (n/2)*(a + l)

                                       = 45 * (99 + 10)

                                        = 4905

mean = (sum of all observations) / no.of observations

          = 4905 / 90

          = 54.5

Answer 2

Mean of all two digit numbers is 54.5.

Given:

• All two digit numbers.

To find:

• Mean

Solution:

Formula to be used:

1. Sum of n terms of AP: $\bf S_n = \frac{n}{2} (a + l)$
2. nth term of AP: $\bf a_n = a + (n - 1)d$
3. Mean: $\bf \overline x = \frac{ \Sigma \: x_i}{n}$

Step 1:

Find total 2 digit numbers.

As

10,11,12,...99

Here AP is formed;

a= 10

d=1

l(an)=99

Find total number:

$99 = 10 + (n - 1)1$

or

$n - 1 = 89$

or

$\bf n = 90$

Step 2:

Find sum of all 2 digit numbers.

$S_{90} = \frac{90}{2} (10 + 99)$

or

$S_{90} = 45 \times 109$

or

$\bf S_{90} = 4905$

Step 3:

Find mean.

According to the formula of mean.

$Mean = \frac{4905}{90}$

or

$\bf Mean = 54.5$

Thus,

Mean of all two digit numbers is 54.5.

Learn more:

1) Mean of 20 observations is 15.5. Later it was found that 24 was misread as 42. Find the correct mean.

https://brainly.in/question/13575596

2) The mean of x-2a,x-a,x,x+a,x+2a is

https://brainly.in/question/48463680