37
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:
Rainfall (mm)
Number of Sub-divisions
200-400
2
400-600
4
600-800
7
800-1000
4
1000-1200
2
1200-1400
3
1400-1600
1
1600-1800
1
Based on the above information, answer the following questions:
(I) Write the modal class.
(II) Find the median of the given data.
It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018:
Rainfall (mm)
Number of Sub-divisions
200-400
2
400-600
4
600-800
7
800-1000
4
1000-1200
2
1200-1400
3
1400-1600
1
1600-1800
1
Based on the above information, answer the following questions:
(I) Write the modal class.
(II) Find the median of the given data.
Show SolutionHide Solution↓
(i) Modal Class is 600-800
(ii) $\frac{N}{2} = 12$, median class is 600 – 800
Rainfall
$x_i$
$f_i$
cf.
200-400
300
2
2
400-600
500
4
6
600-800
700
7
13
800-1000
900
4
17
1000 - 1200
1100
2
19
1200-1400
1300
3
22
1400-1600
1500
1
23
1600-1800
1700
1
24
24
Median = $600 + \frac{200}{7} (12-6)$ or $771-4$
OR
(ii)
Rainfall
$X_i$
$f_i$
$f_i x_i$
200-400
300
2
600
400-600
500
4
2000
600-800
700
7
4900
800-1000
900
4
3600
1000 - 1200
1100
2
2200
1200-1400
1300
3
3900
1400-1600
1500
1
1500
1600-1800
1700
1
1700
24
20400
Mean = $\frac{20400}{24} = 850$
(iii) Sub-divisions having good rainfall = $2 + 3 + 1 + 1 = 7$.
(ii) $\frac{N}{2} = 12$, median class is 600 – 800
Rainfall
$x_i$
$f_i$
cf.
200-400
300
2
2
400-600
500
4
6
600-800
700
7
13
800-1000
900
4
17
1000 - 1200
1100
2
19
1200-1400
1300
3
22
1400-1600
1500
1
23
1600-1800
1700
1
24
24
Median = $600 + \frac{200}{7} (12-6)$ or $771-4$
OR
(ii)
Rainfall
$X_i$
$f_i$
$f_i x_i$
200-400
300
2
600
400-600
500
4
2000
600-800
700
7
4900
800-1000
900
4
3600
1000 - 1200
1100
2
2200
1200-1400
1300
3
3900
1400-1600
1500
1
1500
1600-1800
1700
1
1700
24
20400
Mean = $\frac{20400}{24} = 850$
(iii) Sub-divisions having good rainfall = $2 + 3 + 1 + 1 = 7$.