Chapter 32: Statistics – Exercise 32.2

Statistics – Exercise – 32.2 – Q.1

xi	fi	Cum.Freq	|di| = |xi - 61|	fi|di|
58	15	15	3	45
59	20	35	2	40
60	32	67	1	32
61	35	102	0	0
62	35	137	1	35
63	22	159	2	44
64	20	179	3	60
65	10	189	4	40
66	8	197	5	40
	N = 197			Total = 336

Corresponding value for median is 61

 

Statistics – Exercise – 32.2 – Q.2

We have to calculate mean deviation from the median. So, first we calculate the median.

x	f	cf	d = (x – med)	fd
0	14	14	4	56
1	21	35	3	63
2	25	60	2	50
3	43	103	1	43
4	51	154	0	0
5	40	194	1	40
6	39	233	2	78
7	12	245	3	36
	245			366

we have N = 245 ⟹ N/2 = 122.5

The cumulative frequency just greater than N/2 is 154 and the corresponding value of x is 4.

Hence, Median = 4

 

Statistics – Exercise – 32.2 – Q.3

xi	fi	Cum fre	|di| = |xi - 13|	fi|di|
5	2	2	8	16
7	4	6	6	24
9	6	12	4	24
11	8	20	2	16
13	10	30	0	0
15	12	42	2	24
17	8	50	4	32
	N = 50			Total = 136

Value corresponding to 25 is median = 13

 

Statistics – Exercise – 32.2 – Q.4(i)

xi	fi	fixi	|di| = |xi - 9|	fi|di|
5	8	40	4	32
7	6	42	2	12
9	2	18	0	0
10	2	20	1	2
12	2	24	3	6
15	6	90	6	36
	26	Total = 234		Total = 88

Mean = 9

 

Statistics – Exercise – 32.2 – Q.4(ii)

x	f	xf	d = (x - mean)	fd
5	7	35	9	63
10	4	40	4	16
15	6	90	1	6
20	3	60	6	18
25	5	125	11	55
	25	350		158

 

Statistics – Exercise – 32.2 – Q.4(iii)

x	f	xf	d = (x – mean)	fd
10	4	40	40	160
30	24	720	20	480
50	28	1400	0	0
70	16	1120	20	320
90	8	720	40	320
	80	4000		180

 

Statistics – Exercise – 32.2 – Q.4(iv)

xi	fi	fixi	|di| = |xi - 21.65|	fi|di|
20	6	120	1.65	9.9
21	4	84	0.65	2.6
22	5	110	0.35	1.75
23	1	23	1.35	1.35
24	4	96	2.35	9.4
	20	Total = 433		Total = 25

Mean = 21.65

 

Statistics – Exercise – 32.2 – Q.5

xi	fi	Cum. Freq	|di| = |xi - 30|	fi|di|
15	3	3	15	45
21	5	8	9	45
27	6	14	3	18
30	7	21	0	0
35	8	29	5	40
	29			Total = 148

Median = 30

We have to calculate mean deviation from the median, So, first we calculate the median,

x	f	cf	d = (x-med)	fd
35	4	4	39	456
42	2	6	32	64
54	4	10	20	80
74	20	30	0	0
89	12	42	15	180
91	5	47	17	85
94	3	50	20	60
	50			625

We have N = 50 ⟹ N/2 = 25

The cumulative frequency just greater than N/2 is 30 and the corresponding value of x is 74.

Hence, median = 74

xi	fi	Cum. Freq	|di| = |xi - 12|	fi|di|
10	2	2	2	4
11	3	5	1	3
12	8	13	0	0
14	3	16	2	6
15	4	20	3	12
	20			Total = 25

Median = 12