Chapter 32: Statistics – Exercise 32.5

Statistics – Exercise – 32.5 – Q.1

x	f	fx	x-mean	(x-mean)2	f(x – mean)2
4.5	1	4.5	-33.14	1098.45	1098.45
14.5	5	72.5	-23.14	535.59	267.96
24.5	12	294	-13.14	172.73	2072.82
34.5	22	759	-3.14	9.88	217.31
44.5	17	756.5	6.86	47.02	799.35
54.5	9	490.5	16.86	284.16	2557.47
64.5	4	258	26.86	721.31	2885.22
	N = 70	2635			12308.57

 

Statistics – Exercise – 32.5 – Q.2

X	F	Fx	x-mean	F(x-mean)	(x-mean)2	F(x-mean)2
0	51	0	-6	-306	36	1836
1	203	203	-5	-1015	25	5075
2	383	766	-4	-1532	16	6128
3	525	1575	-3	-1575	9	4725
4	532	2128	-2	-1064	4	2128
5	408	2040	-1	-408	1	408
6	273	1638	0	0	0	0
7	139	973	1	139	1	139
8	43	344	2	86	4	172
9	27	243	3	81	9	243
10	10	100	4	40	16	160
11	4	44	5	20	25	100
12	2	24	6	12	36	72
	2600	10078		-5522		21186

Here, N = 2600,       Σf_ix_i = 10078

σ² = 8.14846 – 4.51072

σ² = 3.64

 

Statistics – Exercise – 32.5 – Q.3

(i)

xi	Cum. Freq	fi	fixi	f1x12
10	15	15	150	1500
20	32	17	340	6800
30	51	19	570	17100
40	78	27	1080	43200
50	97	19	950	47500
60	109	12	720	43200
		N = 109	Total = 3810	Total = 159300

(ii)

xi	fi	fixi	f1x12
2	1	2	4
3	6	18	54
4	6	24	96
5	8	40	200
6	8	48	288
7	2	14	98
8	2	16	128
9	3	27	243
10	0	0	0
11	2	22	242
12	1	12	144
13	0	0	0
14	0	0	0
15	0	0	0
16	1	16	256
	N = 40	Total = 239	Total = 1753

 

Statistics – Exercise – 32.5 – Q.4

(i)

x	f	fx	x-mean	(x- mean)2	f(x – mean)2
3	7	21	-9.79	95.88	671.13
8	10	80	-4.79	22.96	229.6
13	15	195	0.21	0.04	0.65
18	10	180	5.21	27.13	271.26
23	6	138	10.21	104.21	625.26
	48	614			1797.02

Here, N = 48, and Σf_ix_i = 614

(ii)

xi	fi	f1x12
2	4	16
3	9	81
4	16	256
5	14	350
6	11	396
7	6	294
	N = 60	Total = 1393