Question

The median of the following observations is 93,32,47,55,78,65,95,100,86,70 O A) 43 O B) 59 O C) 44 O D) 74​

Answer 1

Answer:

Step-by-step explanation:

According to the information provided in the question it is given as

93,32,47,55,78,65,95,100,86,70

We need to find the median of following

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.

Median represents the middle value for any group. It is the point at which half the data is more and half the data is less.

Arranging the data in ascending order

32,47,55,65,70,78,86,93,95,100

Here observed that no of observation is 10

Hence median is =

             

Answer 2

Answer:

Given Data :-

$\leadsto$ 93, 32, 47, 55, 78, 65, 95, 100, 86, 70.

To Find :-

• What is the median is the following observations.

Formula Used :-

$\clubsuit$ Median Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Median =\: \dfrac{\bigg(\dfrac{n}{2}\bigg)^{th}\: Observation + \bigg(\dfrac{n}{2} + 1\bigg)^{th}\: Observation}{2}}}}\: \: \: \bigstar$

where,

• n = Number of Observations

Solution :-

First, we have to arrange all the observations in an ascending order :

$\mapsto \sf 93, 32, 47, 55, 78, 65, 95, 100, 86, 70$

$\mapsto \bf 32, 47, 55, 65, 70, 78, 86, 93, 95, 100$

Now, we have to find the number of observations :

$\mapsto \sf 32, 47, 55, 65, 70, 78, 86, 93, 95, 100$

So,

$\longrightarrow \sf\bold{\purple{Number\: Of\: Observations =\: 10}}$

As we can observe there are 10 number of observations and 10 is an even number.

So, according to the question by using the formula we get,

$\footnotesize \implies \bf Median =\: \dfrac{\bigg(\dfrac{n}{2}\bigg)^{th}\: Observation + \bigg(\dfrac{n}{2} + 1\bigg)^{th}\: Observation}{2}$

$\footnotesize \implies \sf Median =\: \dfrac{\bigg(\dfrac{10}{2}\bigg)^{th}\: Observation + \bigg(\dfrac{10}{2} + 1\bigg)^{th}\: Observation}{2}$

$\footnotesize \implies \sf Median =\: \dfrac{5^{th}\: Observation + (5 + 1)^{th}\: Observation}{2}$

$\footnotesize \implies \sf Median =\: \dfrac{5^{th}\: Observation + 6^{th}\: Observation}{2}$

Now,

➳ 32 = 1st Observation

➳ 47 = 2nd Observation

➳ 55 = 3rd Observation

➳ 65 = 4th Observation

➳ 70 = 5th Observation

➳ 78 = 6th Observation

➳ 86 = 7th Observation

➳ 93 = 8th Observation

➳ 95 = 9th Observation

➳ 100 = 10th Observation

So, according to this term we get,

$\small \implies \sf Median =\: \dfrac{70 + 78}{2}$

$\small \implies \sf Median =\: \dfrac{\cancel{148}}{\cancel{2}}$

$\implies \sf Median =\: \dfrac{74}{1}$

$\small \implies \sf\bold{\red{Median =\: 74}}$

$\therefore$ The median is 74 .

Hence, the correct options is option no (D) 74 .

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