In a marriage hall 120 marriages were held in a particular year. The age distribution is as shown below Determine the maximum age among youngest 30% of brides.
Age | No. of Brides |
18-20 | 12 |
20-22 | 30 |
22-23 | 30 |
23-24 | 22 |
24-26 | 18 |
26-28 | 8 |
Concept/Principle
Original question: Determine the maximum age among youngest 30% of brides.
Let me rephrase the question.
- In hall, 120 brides are standing in ascending order of their age (20..23ā¦25 and so on)
- The first 30% brides =120 x 0.3=36 brides.
- The age of these 36 brides, is less than āmā years. Find āmā
The situation calls for a cumulative frequency (CF) graph.
Make a new column
Age | No. of Brides | c.f. (less than) |
18-20 | 12 | 0+12=12 |
20-22 | 30 | 12+30=42 |
22-23 | 30 | 42+30=72 |
23-24 | 22 | 72+22=94 |
24-26 | 18 | 94+18=112 |
26-28 | 8 | 112+8=120 |
This is cumulative frequency āless thanā graph.
Observive first cell of āCFā, it has number 12
It means 12 girls have age less than 20 years.
Similarly 42 girls have age less than 22 years and so on.
Now make a cumulative frequency graph, with Age in years on X-axis and C.F. on Y-axis
Basically weāve to plot these following numbers:
Age less than (X axis) | No of brides (Y axis) |
20 | 12 |
22 | 42 |
23 | 72 |
24 | 94 |
26 | 112 |
28 | 120 |
Now the biggest problem: (stupid) scales.
A typical graph paper has drawable area of 25 x 19 cm.
We want the graph to be evenly āspreadā across the paper, we donāt want a very small graph else we cannot find exact answer.
Scale on X-axis
- X axis= minimum observation is 20 and max is 28. So weāve to plot 28-20=8 years.
- If we take 1cm=1 year, then entire data can be plotted in 8 cm.
- but then graph will look too small and narrow.
- So letās increase the scale. Instead of 1 cm=1 year, letās take 2 cm=1 year.
- In that case, to plot 8 years, weād need 16 cm.
- Our graph paper can easily accommodate this, because we have 25x19cm paper.
- Therefore, scale on x axis: 2cm =1 year (or 1cm=0.5 year).
Scale on Y-axis
- Difference between maximum and minimum observation: 120-12=108 brides.
- How about 1 cm =5 brides?
- To plot approx 110 brides, weād need 110/5=22 cm. Again Our graph paper can easily accommodate this because weāve 25×19 cm paper.
- So we take scale on Y axis: 1 cm=5 Brides.
- Now plot those numbers. Itāll look something like this image:
Finding 30% brides
The question says āmaximum age among youngest 30% of bridesā
Total brides=120, and in the graph paper, weāve plotted them in ascending order (age is going on like 20ā¦.22ā¦23ā¦)
30% of total brides
=120 x 0.3
=36 brides
On the Y-axis, locate number 36 then draw a parpendicular line from that number to the cumulative frequency graph. (Pink colored line going towards right side.)
It will cut the cumulative frequency line somewhere.
From that point, draw anohter parpendicular line towards X-axis (blue line going downwards).
The point at which it cuts X-axis= our answer.
In above graph, it cuts at 21.75 years.
Therefore answer: maximum age among youngest 30% of brides is 21.75 years.
Practice questions
In a marriage hall 120 marriages were held in a particular year. The age distribution is as shown below:
Age | No. of Brides |
18-20 | 12 |
20-22 | 30 |
22-23 | 30 |
23-24 | 22 |
24-26 | 18 |
26-28 | 8 |
Find following
Question | Concept Explained in this youtube video |
Find Average age of brides | http://www.youtube.com/watch?v=FC8CQGY1CUE&feature=plcp |
Find median Age of brides using
|
http://www.youtube.com/watch?v=uaHBu2kz8pM&feature=plcp |
Find modal age of brides | http://www.youtube.com/watch?v=BUdd3-PBe6Q&feature=plcp |
Find Standard Deviation of the data. | http://www.youtube.com/watch?v=boHDPTX5YnU&feature=plcp |
Basically this is a āContinuous Data Seriesā. So, use this ready-reference Statistics formula table to solve above questions accordingly:
Thank you for such thankless job
LOLZ!!! What do you mean???
shouldn’t the answer be 21.6? (by formula…)
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The committee was constituted under the chairmanship of Prof Arun S Nigavekar, former chairman, University Grants Commission (UGC). “Till now, no decision has been taken by the government on these recommendations,” the Minister said.
i think this might help
nice sir .. I salute you … Helping people like me .. really you have saved our time, money etc etc .. which were going to waste by just attending coaching classes … Whatever you write in ur blog … it becomes landmark :) :) …
Hats off sir :) ..
Is it correct to solve this question like this
1st– 30%of120=36
2nd– age 18,19,20– no.=12+15=27
3rd– rest 36-27=9 in between 20 and 21 ie.9/15=0.6
hence answer is 20.6
i think the answer should be 21.6