Question

The weight of 12 students are:
40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46, and 34.
find the median weight.
If the weight of 62kg is replaced by 35kg, find the new median weight.
​

Answer 1

Answer:

This is the answer

Hope it helps

Answer 2

$\bold{Required \: answer:-}$

$\bold{Question: }$

• The weight of 12 students are:

40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46, and 34.

find the median weight.

If the weight of 62kg is replaced by 35kg, find the new median weight.

$\bold{Solution: }$

Given,

• weight of 12 students -

40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46, and 34.

To find:

• New median weight

• New median weight after being replaced by 35kg

Steps of finding median:

Step 1. Arrange the given data in ascending order or descending order of their magnitude (value).

Step 2. Count the total number (n) of observations in the given data.

Step 3.

If n is odd, median

$→( \frac{n + 1}{2}) {}^{th} \: term$

If n is even, median

$→ \frac{1}{2} (value \: of \: ( \frac{n}{2} {}^{}) {}^{th} \: term \: + \: value \: of \: ( \frac{n}{2} + 1) {}^{th} \: term)$

$\bold{Step \: by \: step \: explaination:}$

First we have to arrange the given heights in ascending order.

That is,

34, 37, 40, 41, 46, 48, 50, 51, 54, 59, 61, 62

As we know n is number of terms.

thus n = 12.

n is even so median weight

$= \: [( \frac{12}{2}{}^{}) {}^{th} \: term \: + \: ( \frac{12}{2} + 1) {}^{th} term$

$= \: \frac{1}{2} [6 {}^{th} term + 7 {}^{th} term]$]

As we know 6th term is 48 and 7th term is 50.

So,

$= \frac{1}{2} [48kg \: + \: 50kg]$

$= \: \cancel\frac{1}{2} \times \: \cancel98$

= 49 kg

According to the question replacing 62kg by 35kg

So,

$median \: = \: \dfrac{1}{2} [( \dfrac{12}{2}) {}^{th} term \: + \: ( \dfrac{12}{2} + 1) {}^{th} term]$

= 1/2 [6th term + 7th term]

= 1/2 [46 + 48] kg

= 47kg