RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B

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TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 9
Chapter NameMean, Median, Mode of Grouped Data
Exercise9 B
CategoryRS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B

Question 1:

ClassFrequency fiC.F.
0 – 1033
10 – 2069
20 – 30817
30 – 401532
40 – 501042
50 – 60850
N=∑ fi=50

Now, N=50⟹N2=25
The cumulative frequency just greater than 25 is 32 and corresponding class is 30 – 40.
Thus, the median class is 30 – 40
l = 30, h = 10, f = 15, c = C.F. preceding class 30 – 40 is 17 and N2= 25
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 1.1
Hence the median is 35.33

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Question 2:
We prepare the frequency table, given below

ClassFrequency fiC.F.
0 – 733
7 – 1447
14 – 21714
21 – 281125
28 – 35025
35 – 421641
42 – 49950
N=∑ fi=50

Now,N=50⟹N2=25
The cumulative frequency is 25 and corresponding class is 21 – 28.
Thus, the median class is 21 – 28
l = 21, h = 7, f = 11, c = C.F. preceding class 21 – 28 is 14 and N2= 25
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 2.1
Hence the median is 28.

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Question 3:
We prepare the frequency table given below:

Daily wagesFrequency fiC.F.
0 – 1004040
100 – 2003272
200 – 30048120
300 – 40022142
400 – 5008150
N=∑ fi=150

Now, N=150⟹N2=75
The cumulative frequency just greater than 75 is 120 and corresponding class is 200 – 300.
Thus, the median class is 200 – 300
l = 200, h = 100, f = 48
c = C.F. preceding median class = 72 and N2= 75
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 3.1
Hence the median of daily wages is Rs. 206.25.
Question 4:
We prepare the frequency table, given below:

ClassFrequency fiC.F.
5 – 1055
10 – 15611
15 – 201526
20 – 251036
25 – 30541
30 – 35445
35 – 40247
40 – 45249
N=∑ fi=49

Now, N=49⟹N2=24.5
The cumulative frequency just greater than 24.5 is 26 and corresponding class is 15 – 20.
Thus, the median class is 15 – 20
l = 15, h = 5, f = 15
c = CF preceding median class = 11 and N2=24.5
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 4.1
Median of frequency distribution is 19.5
Question 5:
We prepare the cumulative frequency table as given below:

ConsumptionFrequency fiC.F.
65 – 8544
85 – 10559
105 – 1251322
125 – 1452042
145 – 1651456
165 – 185763
185 – 205467
N=∑ fi=67

Now, N=67⟹N2=33.5
The cumulative frequency just greater than 33.5 is 42 and the corresponding class 125 – 145.
Thus, the median class is 125 – 145
l = 125, h = 20, and c = CF preceding the median class = 22, N2= 33.5
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 5.1
Hence median of electricity consumed is 136.5
Question 6:
Frequency table is given below:

HieghtFrequency fiC.F.
135 – 14066
140 – 1451016
145 – 1501834
150 – 1552256
155 – 1602076
160 – 1651591
165 – 170697
170 – 1753100
N=∑ fi=100

N=100⟹N2=50
The cumulative frequency just greater than 50 is 56 and the corresponding class is 150 – 155
Thus, the median class is 150 – 155
l = 150, h = 5, f = 22, c = C.F.preceding median class = 34
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 6.1
Hence, Median = 153.64
Question 7:
The frequency table is given below. Let the missing frequency be x.

ClassFrequency fiC.F.
0 – 1055
10 – 202530
20 – 30x30+x
30 – 401848+x
40 – 50755+x

Median = 24
Median class is 20 – 30
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 7.1
l = 20, h = 10, f = x, c = C.F. preceding median class = 30
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 7.2
Hence, the missing frequency is 25.
Question 8:
Let f1 and f2 be the frequencies of classes 20 – 30 and 40 – 50 respectively, then
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 100
Median is 35, which lies in 30 – 40, so the median class is 30 – 40.
l = 30, h = 10, f = 40, N = 170 and c = 10 + 20 +f1 = (30 + f1)
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 8.1
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 8.2
Question 9:
Let f1 and fbe the frequencies of class intervals 0 – 10 and 40 – 50
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 9.1
Median is 32.5 which lies in 30 – 40, so the median class is 30 – 40
l = 30, h = 10, f = 12, N = 40 and c = f1 +5+9= (14 + f1)
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 9.2
Question 10:
The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

ClassFrequency fiC.F.
18.5 – 25.53535
25.5 – 32.596131
32.5 – 39.568199
39.5 – 46.5102301
46.5 – 53.535336
53.5 – 60.54340
N=∑ fi=340

N=340⟹N2=170
The cumulative frequency just greater than 170 is 199 and the corresponding class is 32.5 – 39.5.
Median class is 32.5 – 39.5
l = 32.5, h = 7, f = 68, c = C.F. of preceding median class = 131
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 10.1
Hence median is 36.5 years
Question 11:
Given series is in inclusive form converting it into exclusive form and preparing the cumulative frequency table, we get

Wages per day(in Rs.)Frequency fiC.F.
60.5 – 70.555
70.5 – 80.51520
80.5 – 90.52040
90.5 – 100.53070
100.5 – 110.52090
110.5 – 120.5898
N=∑ fi=98

N=98⟹N2=49
The cumulative frequency just greater than 49 is 70 and corresponding class is 90.5 – 100.5.
median class is 90.5 – 100.5
l = 90.5, h = 10, f = 30, c = CF preceding median class = 40
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 11.1
Hence, Median = Rs 93.50
Question 12:
The given series is converted from inclusive to exclusive form and preparing the cumulative frequency table, we get

MarksFrequency fiC.F.
10.5 – 15.522
15.5 – 20.535
20.5 – 25.5611
25.5 – 30.5718
30.5 – 35.51432
35.5 -40.51244
40.5 -45.5448
45.5 -50.5250
N=∑ fi=50

N=50⟹N2=25
The cumulative frequency just greater than 25 is 32.
The corresponding class is 30.5 – 35.5.
Thus, the median class is 30.5 – 35.5
l = 30.5, h = 5, f = 14, c = C.F preceding median class = 18
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 12.1
Hence, Median = 33
Question 13:
The given series is converted from inclusive to exclusive form and preparing the cumulative frequency table, we get

MarksFrequency fiC.F.
0.5 – 5.577
5.5 – 10.51017
10.5 – 15.51633
15.5 – 20.53265
20.5 – 25.52489
25.5 – 30.516105
30.5 – 35.511116
35.5 – 40.55121
40.5 – 45.52123
N=∑ fi=123

N=123⟹N2=61.5
The cumulative frequency just greater than 61.5 is 65.
The corresponding median class is 15.5 – 20.5.
Then the median class is 15.5 – 20.5
l = 15.5, h = 5, f = 32, c = C.F. preceding median class = 33
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 13.1
Hence, Median = 19.95
Question 14:

MarksFrequency fiC.F.
0 – 101212
10 – 202032
20 – 302557
30 – 402380
40 – 501292
50 – 6024116
60 – 7024116
70 – 8036200
N=∑ fi=200

N=200⟹N2=100
The cumulative frequency just greater than 100 is 116 and the corresponding class is 50 – 60.
Thus the median class is 50 – 60
l = 50, h = 10, f = 24, c = C.F. preceding median class = 92, N2= 100
RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9B 14.1
Hence, Median = 53.33

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