- Case Study-1 13. Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on 21st of June every year since 2015. To promote Yoga, Green park society in Pune organised a 7-day Yoga camp in their society. The number of people of different age groups who enrolled for this camp is given as follows:
Answers 1
Answer:
(i). Median Age= 58yrs
(ii). Value of x is 5.85 (approx. 6)
Step-by-step explanation:
Concept= Median and Mean of Grouped data
Given= Distribution Table and Mean
To find= Median and variable x
Explanation=
First we organize the data in our tabular form
Age Group No. of people([tex]f_{i}[/tex]) C.F Group Mark([tex]x_{i}[/tex]) [tex]f_{i} x_{i}[/tex]
15-25 8 8 20 160
25-35 10 18 30 180
35-45 15 33 40 600
45-55 25 58 50 1250
55-65 40 98 60 2400
65-75 24 122 70 1680
75-85 18 140 80 1440
∑[tex]f_{i}[/tex]=140 ∑[tex]f_{i} x_{i[/tex]=7710
(i). Median Age group of people enrolled in camps-
n=140(cf) , n/2= 70
Thus this observation lies between the age group 55-65(median class).
Lower Class limit(l)= 55, Class size(h)= 10, Frequency of median class(f)= 40
Cumulative frequency of class preceding the median class is(c) 58.
Formula to find median of grouped data is Median= [tex]l+{(n/2-c)/f} * h[/tex]
equating values we get, Median= 55+(70-58)/40 * 10= 55 +0.3*10= 55+3=58.
Median Age= 58yrs
(ii). Find x, when x people were added in group 65-75 and Mean was 58.
If x people were added in that group then number of people will become 24+x , Similarly the [tex]f_{i} x_{i}[/tex] value of 65-75 will become 1680+70x.
So now the new ∑[tex]f_{i} x_{i}[/tex]= 7710+70x .
Mean=∑[tex]f_{i} x_{i}[/tex]/∑[tex]f_{i}[/tex] , Equating the values we have ,
58= 7710+70x/140
=>8120=7710+70x
=>410=70x
=> x= 5.85 (approx. 6)
Therefor value of x is 5.85 (approx. 6)
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