Case Study 3:- India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.
It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Based on the above information, answer the following questions:
(i) Write the modal class. 1
(ii) Find the median of the given data. 2
OR
Find the mean rainfall in this season.
(iii) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-division had good rainfall ? 1
Solution:-
(i) The modal class is the class with the highest frequency
Model class is 600-800.
(ii)
|
Rainfall (mm) |
Number of Sub-division | Cummulative frequency |
|
200 – 400 |
2 |
2 |
|
400 – 600 |
4 |
6 |
|
600 – 800 |
7 |
13 |
|
800 – 1000 |
4 |
17 |
|
1000 – 1200 |
2 |
19 |
|
1200 – 1400 |
3 |
22 |
|
1400 – 1600 |
1 |
23 |
| 1600 – 1800 | 1 |
24 |
N/2 = 24/2 = 12
Median class = 600 – 800
To find the median, we use the formula:
Median = 
where:
L = Lower boundary of the median class (600)
n = Total number of sub-divisions (24)
F = Cumulative frequency of the class before the median class (2 + 4 = 6)
f = Frequency of the median class (7)
h = Class width (800 – 600 = 200)
Median = 
Median = 
Median = 600 + 171.43
Meidan = 771.43 approx
So, the median rainfall is approximately 771.43 mm.
OR
Mean
| Rainfall (mm) | Number of Sub-division | x | fx |
| 200 – 400 | 2 | 300 | 600 |
| 400 – 600 | 4 | 500 | 2000 |
| 600 – 800 | 7 | 700 | 4900 |
| 800 – 1000 | 4 | 900 | 3600 |
| 1000 – 1200 | 2 | 1100 | 2200 |
| 1200 – 1400 | 3 | 1300 | 3900 |
| 1400 – 1600 | 1 | 1500 | 1500 |
| 1600 – 1800 | 1 | 1700 | 1700 |
| 24 | 20400 |
Mean of the rainfall = 
Mean rainfall = 850
(iii) Sub-divisions with Good Rainfall:
Sub-divisions with at least 1000 mm rainfall are considered to have good rainfall.
Good rainfall sub-divisions = 2 + 3 + 1 + 1 = 7
Therefore, 7 sub-divisions had good rainfall during the monsoon season.
Case Study 1:- the discus throw is an event in which an athlete attempts to throw a discus. The sthlete spins anti-clockwise around one and half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre and ∠ABO = 30°. PQ is parallel to OA.
Based on above information :
(a) Find the length of AB. 1
(b) Find the length of OB. 1
(c) Find the length of AP. 2
OR
Find the length of PQ. 2
Solution:- See full solution
Case Study 2:- While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide.
Based on the above information, answer the following questions:
(i) Write an algebraic equation depicting the above information. 1
(ii) Write the corresponding quadratic equation in standard form. 1
(iii) What should be the new dimensions of the enlarged photo ? 2
OR
Can any rational value of x make the new area equal to 220 cm² ?
Solution:- See full solution