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RD Chapter 7 Statistics Ex 7.4 Solutions

Question - 1 : -
Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median :
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Answer - 1 : -

Arranging in ascending order, we get
694, 696, 699, 705, 710, 712, 715, 716, 719, 724, 725, 728, 729, 734, 745 Here N = 15 which is odd

Question - 2 : -
The following is the distribution of height of students of a certain class in a certain city :
 
Find the median height.

Answer - 2 : - Arranging the classes in exclusive form and then forming its cumulative frequency table as given

Question - 3 : - Following is the distribution of I.Q. of 100 students. Find the median I.Q.

Answer - 3 : -

Arranging the classes in exclusive form and then forming it in cumulative frequency table as shown below :
 
Here N = 100
∴ N/2 = 100/2 = 50
∴ Corresponding median class is = 94.5-104.5
l = 94.5, f= 33, F = 34 and h = 10

Question - 4 : - Calculate the median from the following data :

Answer - 4 : - Writing the given data in cumulative frequency table as shown

Question - 5 : - Calculate the median from the following data :

Answer - 5 : -


Question - 6 : - Calculate the missing frequency from the following distribution, it being given that the median of the distribution

Answer - 6 : - Median = 24, let p be the missing frequency.

Question - 7 : -
The following table gives the frequency distribution of married women by age at marriage:
 
Calculate the median and interpret the results.

Answer - 7 : - Writing classes in exclusive form,

Question - 8 : -
The following table gives the distribution of the life time of 400 neon lamps :
 
Find the median life.

Answer - 8 : -


Question - 9 : - The distribution below gives the weight of 30 students in a class. Find the median weight of students 

Answer - 9 : - Here  N =30 ,N/2 = 30/2 which  lies in the class 55 – 60 ( ∵ 13 < 15 < 19)

Question - 10 : - Find the missing frequencies and the median for the following distribution if the mean is 1.46.

Answer - 10 : -

Mean = 1.46, N= 200
Let p1 and p2 be the missing frequencies

⇒ p1+ 2p2= 292 – 140 =152
114-p2 + 2p2= 152
⇒ p2 =152- 114 = 38
∴ p1=114-p2= 114-38 = 76
Hence missing frequencies are 76 and 38
Median = Here N/2 = 200/2 =100
∴ cf of2nd class is 46 + 76 = 122
∴ Median= 1

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