Question

find the median of three consecutive integers whose mean is 25 ​

Answer 1

Answer:

Step-by-step explanation:

Given :

• The mean of 3 consecutive integers is 25.

To Find :

• The median of those 3 consecutive numbers.

Solution :

Let the 3 consecutive numbers be :

• x
• x + 1
• x + 2

Now, we know that :

$:\implies \sf Mean = \dfrac{Sum \ of \ all \ the \ observations }{Total \ no. \ of \ observations}$

$:\implies \sf 25 = \dfrac{x + (x + 1) + (x + 2) }{3}$

$:\implies \sf 25 = \dfrac{3x + 3}{3}$

$:\implies \sf 25 \times 3 = 3x + 3$

$:\implies \sf 75 = 3x + 3$

$:\implies \sf 75 - 3 = 3x$

$:\implies \sf 72 = 3x$

$:\implies \sf \dfrac{72}{3} = x$

$:\implies \bf \boxed{\bf 24 = x}$

Now, the numbers are :

• x = 24
• x + 1 = 24 + 1 = 25
• x + 2 = 24 + 2 = 26

Now, finding median :

>> Median means the middle term. Firstly arrange in ascending order.

24, 25, 26

Here, the middle value is 25.

⊕ Hence, the median of three consecutive numbers is 25...!!

Answer 2

Answer:

three consecutive integers 24,25,26 whose mean is 25 and median 25.

Step-by-step explanation:

Given,

Mean of three consecutive number is 25

Let,

1 number is n , 2 number will be n + 1 , 3 number will be n + 2

Mean of these numbers,

$\frac{n + n+ 1+n+2}{3} = 25$

$\frac{3n + 3}{3} = 25$

n + 1 = 25

n = 24

First number = 24 = n

Second number = n + 1 = 24 + 1 = 25

Third number = 26

Median

If odd number terms exists then median  = $\frac{n +1}{2}$

where n is number of term

We have 3 terms so,

Median term = $\frac{3 + 1}{2}$ = 2

our terms are 24,25,26

Final answer

median = 25