Long Questions

Here, Calculation of mean,

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1350}{50}$ = 27

Calculation of standard deviation, So, Standard deviation (σ) = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{6600}{50}}$ = 11.49
Finally, Coefficient of variation = $\frac{σ}{mean}$ × 100% = 42.55%

Here, Calculation of mean, Now, mean = $\frac{\sum fm}{N}$ = $\frac{1200}{20}$ = 60
Calculation of standard deviation, So, Standard deviation (σ) = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{14000}{20}}$ = 26.46
Finally, Coefficient of variation = $\frac{σ}{mean}$ × 100% = $\frac{26.46}{60}$ × 100% = 44.1%

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
10-20	15	4	60
20-30	25	10	150
30-40	35	12	420
40-50	45	8	360
50-60	55	6	330
	N = 40		∑fm = 1420

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1420}{40}$ = 35.5

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{5790}{40}}$ = 12.03

Here, Calculation of mean,
Sum of given data (∑X) = 35 + 30 + 15 + 5 + 30 + 10 + 25 = 140
Number of items (N) = 7

Now, mean = $\frac{\sum X}{N}$ = $\frac{140}{7}$ = 20

Finally, calculation of standard deviation,

x	|x - Mean| = X	X2
5	5-20 = -15	225
10	10-20 = -10	100
15	15-20 = -5	25
20	20-20 = 0	0
25	25-20 = 5	25
30	30-20 = 10	100
35	35-20 = 15	225
		∑X2 = 700

Hence, Standard deviation (σ) = $\sqrt{\frac{\sum X^2}{N}}$ = $\sqrt{\frac{700}{7}}$ = 10
Also, Its coefficient = $\frac{σ}{\text{Mean}}$ = $\frac{10}{20}$ = 0.5

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
0-10	5	2	10
10-20	15	6	90
20-30	25	5	125
30-40	35	4	140
40-50	45	3	135
	N = 20		∑fm = 500

Now, mean = $\frac{\sum fm}{N}$ = $\frac{500}{20}$ = 25

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{3000}{20}}$ = 12.427

Here, Calculation of mean,
Sum of given data (∑X) = 30 + 33 + 37 + 40 + 44 + 50 = 234
Number of items (N) = 6

Now, mean = $\frac{\sum X}{N}$ = $\frac{234}{6}$ = 39

Finally, calculation of standard deviation,

x	|m - Mean| = X	X2
30	30-39 = -9	81
33	33-39 = -6	36
37	37-39 = -2	4
40	40-39 = 1	1
44	44-39 = 5	25
50	50-39 = 11	121
		∑X2 = 267

Hence, Standard deviation (σ) = $\sqrt{\frac{\sum X^2}{N}}$ = $\sqrt{\frac{267}{7}}$ = 6.67
Also, Its coefficient = $\frac{σ}{\text{Mean}}$ = $\frac{6.67}{39}$ = 0.17

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
30-40	35	2	70
40-50	45	3	135
50-60	55	6	330
60-70	65	5	325
70-80	75	4	300
	N = 20		∑fm = 1160

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1160}{20}$ = 58

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{3020}{20}}$ = 12.288

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
25-35	30	5	150
35-45	40	4	160
45-55	50	6	300
55-65	60	7	420
65-75	70	3	210
	N = 25		∑fm = 1240

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1240}{25}$ = 49.6

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{4296}{25}}$ = 13.1087

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
5-15	10	7	70
15-25	20	3	60
25-35	30	6	180
35-45	40	4	160
45-55	50	5	250
	N = 25		∑fm = 720

Now, mean = $\frac{\sum fm}{N}$ = $\frac{720}{25}$ = 28.8

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{5464}{25}}$ = 14.78

Here, Calculation of mean,

Now, mean = $\frac{\sum fm}{N}$ = $\frac{3100}{100}$ = 31

Finally, calculation of standard deviation, Hence, Standard deviation (σ) = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{16800}{100}}$ = 12.96
And, its coefficient = $\frac{σ}{\text{Mean}}$ = $\frac{12.96}{31}$ = 0.42

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
0-4	2	7	14
4-8	6	7	42
8-12	10	10	100
12-16	14	15	210
16-20	18	7	126
20-24	22	6	132
	N = 52		∑fm = 624

Now, mean = $\frac{\sum fm}{N}$ = $\frac{624}{52}$ = 12

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{1904}{52}}$ = 6.05

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
0-4	2	15	30
4-8	6	12	72
8-12	10	10	100
12-16	14	8	112
16-20	18	5	90
	N = 50		∑fm = 404

Now, mean = $\frac{\sum fm}{N}$ = $\frac{404}{50}$ = 8.08

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{1415.68}{50}}$ = 5.32

Here, Calculation of mean,
Sum of given data (∑X) = 5 + 10 + 20 + 15 + 25 = 75
Number of items (N) = 5

Now, mean = $\frac{\sum X}{N}$ = $\frac{75}{5}$ = 15

Finally, calculation of standard deviation,

x	|m - Mean| = X	X2
5	5-15 = -10	100
10	10-15 = -5	25
15	15-15 = 0	0
20	20-15 = 5	25
25	25-15 = 10	100
		∑X2 = 250

Hence, Standard deviation (σ) = $\sqrt{\frac{\sum X^2}{N}}$ = $\sqrt{\frac{250}{7}}$ = 7.07
Also, Its coefficient = $\frac{σ}{\text{Mean}}$ = $\frac{7.07}{15}$ = 0.47

Here, Calculation of mean,

Class interval (C.I.)	Mid value (m)	Frequency (f)	f × m
10-20	15	4	60
20-30	25	10	250
30-40	35	12	420
40-50	45	8	360
50-60	55	6	330
	N = 40		∑fm = 1420

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1420}{40}$ = 35.5

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{5790}{40}}$ = 12.03

Here, Calculation of mean,

x	Frequency (f)	f × x
6	1	6
8	14	112
10	25	250
12	27	324
14	18	252
16	9	144
18	4	72
20	2	40
	N = 100	∑fx = 1200

Now, mean = $\frac{\sum fm}{N}$ = $\frac{1200}{100}$ = 12

Finally, calculation of standard deviation, Hence, Standard deviation = $\sqrt{\frac{\sum fx^2}{N}}$ = $\sqrt{\frac{848}{100}}$ = 2.912