Consider the set of numbers {1,2,2,3,3,3,…,10,10,10,10,10,10,10,10,10,10}, where the numbernappearsntimes forn=1to 10 What is the (absolute value) of the - Maths -

Question

Consider the set of
numbers

{
1 , 2 , 2 , 3 , 3 , 3 , … , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 } ,
where the number n
appears n
times for n
= 1
to 10 What is the (absolute value) of the difference between the
mode and the median of this set?

Ayush Jha · Accepted Answer

The mode is the most frequently occurring observation.

So in this case Mode is 10.

Median is the value of the middle-most observation (s).

Now the total number of terms are

= 1+2+3+......+10

$= \frac{n (n + 1)}{2} = \frac{10 (11)}{2} = 55$

Since total number of terms is odd. So the term which is median

$= \frac{55 + 1}{2} = 28 t e r m$

So the 28th term is 7. So,

Therefore,

Median - Mode=|7 - 10|

=3

Consider the set of numbers { 1 , 2 , 2 , 3 , 3 , 3 , … , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 } , where the number n appears n times for n = 1 to 10. What is the (absolute value) of the difference between the mode and the median of this set?

Consider the set of numbers

${1, 2, 2, 3, 3, 3, \dots, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10},$

where the number n appears n times for n = 1 to 10. What is the (absolute value) of the difference between the mode and the median of this set?