Question

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Informatics about questions

1. Chapter = 16, Analyzing Data, (CG. BORD)

The data of high jump in international games ( Olympics) is given in the following table Find the mean, mode and Midian of the given observation



$\red{\begin{gathered}\boxed{\begin{array}{c|c|c}\bf \: S. No. \: \: \: &\bf \: year&\bf \: Height(in \: m) \\\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad}{}\\\sf1.&\sf1960&\sf1.85\\\sf2.&\sf1964&\sf1.90\\\sf3.&\sf1968&\sf1.82\ \\\sf4.&\sf1972&\sf1.92\\\sf5. &\sf1976&\sf1.93 \\ \sf6.& \sf1980& \sf1.97 \\ \sf7.& \sf1984 &\sf2.02 \\ \sf8.& \sf1988& \sf2.03 \\ \sf9. &\sf1992& \sf2.02 \\ \sf10.& \sf1996& \sf2.05 \\ \sf11.& \sf2000& \sf2.01 \\ \sf12.& \sf2004& \sf2.06 \\ \dfrac{\qquad}{}& \dfrac{\qquad\qquad}{ \sf }& \dfrac{\qquad\qquad}{} \end{array}}\end{gathered}}$



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$\sf \: Answer : \sf \\ \red{ \sf \: mean \implies1.965 \:metre.} \\ \green{ \sf \: median \implies1.99 \:metre.} \\ \orange{ \sf \:mode \implies2.02 \: metre.}$
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Answer 1

Given to find the mean , mode , median of the data :-

$\purple{\begin{gathered}\boxed{\begin{array}{c|c|c}\bf \: S. No. \: \: \: &\bf \: year&\bf \: Height(in \: m) \\\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad}{}\\\sf1.&\sf1960&\sf1.85\\\sf2.&\sf1964&\sf1.90\\\sf3.&\sf1968&\sf1.82\ \\\sf4.&\sf1972&\sf1.92\\\sf5. &\sf1976&\sf1.93 \\ \sf6.& \sf1980& \sf1.97 \\ \sf7.& \sf1984 &\sf2.02 \\ \sf8.& \sf1988& \sf2.03 \\ \sf9. &\sf1992& \sf2.02 \\ \sf10.& \sf1996& \sf2.05 \\ \sf11.& \sf2000& \sf2.01 \\ \sf12.& \sf2004& \sf2.06 \\ \dfrac{\qquad}{}& \dfrac{\qquad\qquad}{ \sf }& \dfrac{\qquad\qquad}{} \end{array}}\end{gathered}}$

SOLUTION:-

First we find the mean of the data

Mean is nothing but average That we have formula for finding mean

$\sf{Mean} = \dfrac{Sum\:of\:observations}{No.\:of\:observations}$

Sum of observations = 1.85 + 1.90 + 1.82 + 1.92 + 1.93 + 1.97 + 2.02 + 2.03 +2.02 + 2.05 + 2.01 + 2.06

Sum of observations = 23.58

No.of observations = 12

So,

$\sf{Mean} = \dfrac{Sum\:of\:observations}{No.\:of\:observations}$

$\sf{Mean} = \dfrac{23.58}{12}$

Mean = 1.965

___________________

Mode :-

The number which repeated frequently that means which repeated more times

• 1.85 repeated- 1 time
• 1.90 repeated- 1 time
• 1.82 repeated- 1 time
• 1.92 repeated  - 1 time
• 1.93 repeated- 1 time
• 1.97 repeated- 1 time

2.02 repeated- 2times

• 2.05 repeated- 1time
• 2.01 repeated- 1 time
• 2.06 repeated 1 time

Since , mode of the given data is 2.02

Mode = 2.02

____________________

Median - Middle most number is called median

First for finding median Arrange  the data in ascending/descending order  

Ascending order:

=  1.82 , 1.85 , 1.90 , 1.92 , 1.93 , 1.97 , 2.01 , 2.02, 2.02 , 2.03 , 2.05 , 2.06

No.of observations = 12 that means even observations  

Middle most numbers are 1.97 , 2.01

Since we have to find average of those two numbers

= 1.97 + 2.01/2

= 3.98/2

= 1.99

So, median of the data is 1.99

Median = 1.99

By using formula:-

Median for even observations =

n/2 + n/2 +1/2

n = 12(no.of observations)

Median = 12/2 +12/2+1/2

Median = 6th term + 7th term  /2

Median = 1.97+ 2.01/2

Median = 3.98/2

Median = 1.99__________________

If the no.of observations are even median will be the average of middle most numbers

If the no.of observations are odd median is the middle most number

Note:-

We can find the median by formula or without formula In this question I found through both methods

How to find middle most number ??

Refer attachment

Answer 2

$hope \: the \: follwing \: attachment \\ helps \: uh$