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Chapter 32: Statistics – Exercise 32.1

Statistics – Exercise – 32.1 – Q.1(i)

First arrange the given numbers in ascending order writer these numbers in ascending order

3011, 2780, 3020, 2354, 3541, 4150, 5000

we get 2354, 2780, 3011, 3020, 3541, 4150, 5000

Clearly, the middle number is median, 3020

Calculation of mean Deviations


	
		
		
	
	

		

			
xi
			
|di| = |xi - 3020|
		
		

			
3011
			
9
		
		

			
2780
			
240
		
		

			
3020
			
0
		
		

			
2354
			
666
		
		

			
3541
			
521
		
		

			
4150
			
1130
		
		

			
5000
			
1980
		
		

			
Total
			
di = Σ|xi - 30200|=4546
		
	


 



 

Statistics – Exercise – 32.1 – Q.1(ii)

Clearly, the middle observations are 46 and 48. So, median = 47


	
		
	
	

		

			
35
		
		

			
38
		
		

			
42
		
		

			
44
		
		

			
46
		
		

			
48
		
		

			
54
		
		

			
55
		
		

			
63
		
		

			
70
		
	


We have,

Σ|xi - 47| = Σdi = 86



 

Statistics – Exercise – 32.1 – Q.1(iii)

Arranging the observations in ascending order of magnitude, we have


	
		
	
	

		

			
30
		
		

			
34
		
		

			
38
		
		

			
40
		
		

			
42
		
		

			
44
		
		

			
50
		
		

			
51
		
		

			
60
		
		

			
66
		
	


Clearly, the middle observations are 42 and 44. So, median = 43

Σ|xi - 43| = Σdi = 87



 

Statistics – Exercise – 32.1 – Q.1(iv)

Arranging the observations in ascending order of magnitude, we have


	
		
	
	

		

			
22
		
		

			
24
		
		

			
25
		
		

			
27
		
		

			
28
		
		

			
29
		
		

			
30
		
		

			
31
		
		

			
41
		
		

			
42
		
	


Clearly, the middle observation are 28 and 29. So median = 28.5

Calculation of mean Deviation


	
		
		
	
	

		

			
X-values
			
Deviation from Median
		
		

			
22
			
6.5
		
		

			
24
			
4.5
		
		

			
30
			
1.5
		
		

			
27
			
1.5
		
		

			
29
			
0.5
		
		

			
31
			
2.5
		
		

			
25
			
3.5
		
		

			
28
			
0.5
		
		

			
41
			
12.5
		
		

			
42
			
13.5
		
		

			
Total
			
47
		
	


We have,

Σ|xi - 28.5| = Σdi = 47



 

Statistics – Exercise – 32.1 – Q.1(v)

Arranging the observations in ascending order of magnitude, we have


	
		
	
	

		

			
34
		
		

			
38
		
		

			
42
		
		

			
44
		
		

			
47
		
		

			
48
		
		

			
53
		
		

			
55
		
		

			
63
		
		

			
70
		
	


Clearly, the middle observation is, So, median = 47.5

Calculation of Mean Deviation


	
		
		
	
	

		

			
X-values
			
Deviation from Median
		
		

			
38
			
9.5
		
		

			
70
			
22.5
		
		

			
48
			
0.5
		
		

			
34
			
13.5
		
		

			
63
			
15.5
		
		

			
42
			
5.5
		
		

			
55
			
7.5
		
		

			
44
			
3.5
		
		

			
53
			
5.5
		
		

			
48
			
0.5
		
		

			
Total
			
84
		
	


We have,

Σ|xi - 47.5| = Σdi = 84 



 

Statistics – Exercise – 32.1 – Q.2(i)



Calculation of Mean Deviation


	
		
		
	
	

		

			
X - values
			
Deviation from mean
		
		

			
4
			
6
		
		

			
7
			
3
		
		

			
8
			
2
		
		

			
9
			
1
		
		

			
10
			
0
		
		

			
12
			
2
		
		

			
13
			
3
		
		

			
17
			
7
		
		

			
Total
			
24
		
	


We have,

Σ|xi - 10| = Σi = 24 



 

Statistics – Exercise – 32.1 – Q.2(ii)



Calculation of Mean Deviation


	
		
		
	
	

		

			
X-values
			
Devlation From Mean
		
		

			
13
			
1
		
		

			
17
			
3
		
		

			
16
			
2
		
		

			
14
			
0
		
		

			
11
			
3
		
		

			
13
			
1
		
		

			
10
			
4
		
		

			
16
			
2
		
		

			
11
			
3
		
		

			
18
			
4
		
		

			
12
			
2
		
		

			
17
			
3
		
		

			
Total
			
28
		
	


We have,

Σ|xi - 14| = Σdi = 28 

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