Important Questions for CBSE Class 10 Maths Chapter 14 - Statistics 4 Mark Question

CBSE Class 10 Maths Chapter-14 Statistics – Free PDF Download

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CBSE Class 10 Maths Chapter-14 Statistics Important Questions

CBSE Class 10 Maths Important Questions Chapter 14 – Statistics

4 Mark Questions

1. In the following distribution, locate the median mean and mode.
   

   Monthly consumption of electricity	65-85	85-105	105-125	125-145	145-165	165-185	185-205
   No. of consumers	4	5	13	20	14	7	4

   Ans.

   Monthly consumption of electricity	No. of consumers	C.F	Class Mark (X)	FX
   65-85	4	4	75	300
   85-105	5	9	95	475
   105-125	13	22	115	1495
   125-145	20	42	135	2700
   145-165	14	56	155	2670
   165-185	8	64	175	1400
   185-205	4	68	195	780
   				∑ƒx=9320

   Now and this is in 125-145 class
   Median class = 125-145
   Here,
   We know that 
   
   Hence, Median = 137
   Again Mean 
   For mode, since the maximum frequency is 20 and this corresponds to the class 125-145
   Here,
   
   Thus, Median = 137, Mean = 137.05 and Mode = 135.76
   The three measures are approximately the same in the class.

2. Find the mean, mode and median for the following data:
   

   Classes	0-10	10-20	20-30	30-40	40-50	50-60	60-70
   Frequency	5	8	15	20	14	8	5

   Ans. We have

   Classes	Mid-value	Frequency			C.f
   0-10	5	5	-3	-15	5
   10-20	15	8	-2	-16	13
   20-30	25	15	-1	-15	28
   30-40	35	20	0	0	48
   40-50	45	14	1	14	62
   50-60	55	8	2	16	70
   60-70	65	5	3	15	75

   Let assumed mean a = 35, h = length of class interval= 10
   Mean 
   
   Since, Maximum frequency = 20
   Modal class = 30-40
   
   Mode = 
   
   Hence, mode = 34.55
   Since,, which lies in the class 30-40
   i.e., Median class = 30-40
   
   Median = 
   
   Hence, Median = 34.75

3. Find the mean, mode and median for the following data:
   

   Classes	10-20	20-30	30-40	40-50	50-60	60-70	70-80
   Frequency	4	8	10	12	10	4	2

   Ans. We have

   Classes	Mid value				c.f
   10-20	15	4	-3	-12	4
   20-30	25	8	-2	-16	12
   30-40	35	10	-1	-10	22
   40-50	45	12	0	0	34
   50-60	55	10	1	10	44
   60-70	65	4	2	8	48
   70-80	75	2	3	6	50

   Let assumed mean a = 45, Here h = 10
   We know that mean 
   
   Mean 
   Since maximum frequency = 12
   Modal class = 40-50
   Here,
   Now Mode 
   
   Mode = 45
   Now 
   Median class is 40-50
   Now median 
   Here 
   Median = 
   
   Thus, Median = 42.5