Find the mean and variance for the following frequency distribution.

Classes

0-30

30-60

60-90

90-120

120-150

150-180

180-210

Frequencies

2

3

5

10

3

5

2

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Solution

Class

Frequency f_i

Mid-point x_i

y_i²

f_iy_i

f_iy_i²

0-30

2

15

–3

9

–6

18

30-60

3

45

–2

4

–6

12

60-90

5

75

–1

1

–5

5

90-120

10

105

0

0

0

0

120-150

3

135

1

1

3

3

150-180

5

165

2

4

10

20

180-210

2

195

3

9

6

18

30

2

76

Mean,

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Similar questions

Find the mean and variance for the following frequency distribution.

$\begin{matrix} Class & 0 - 30 & 30 - 60 & 60 - 90 & 90 - 120 & 120 - 150 & 150 - 180 & 180 - 210 Frequencies & 2 & 3 & 5 & 10 & 3 & 5 & 2 \end{matrix}$

Q. Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

Class	0-30	30-60	60-90	90-120	120-150	150-180
Frequency	12	21	34	52	20	11

Q. Construct a histogram for the following data:

Monthly school fee (in Rs):	30−60	60−90	90−120	120−150	150−180	180−210	210−240
Number of schools:	5	12	14	18	10	9	4

Q. Draw a less-than type cumulative frequency curve and find the median for the following data.

Daily self-study time in minutes	30-60	60-90	90-120	120-150	150-180	180-210
Number of students	5	16	38	96	48	17

Calculate mean, variance and standard deviation for the following frequency distribution:

$\begin{matrix} Class & 0 - 30 & 30 - 60 & 60 - 90 & 90 - 120 & 120 - 150 & 150 - 180 & 180 - 210 Frequency & 2 & 3 & 5 & 10 & 3 & 5 & 2 \end{matrix}$

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Classes	0-30	30-60	60-90	90-120	120-150	150-180	180-210
Frequencies	2	3	5	10	3	5	2

Class	Frequency f_i	Mid-point x_i		y_i²	f_iy_i	f_iy_i²
0-30	2	15	–3	9	–6	18
30-60	3	45	–2	4	–6	12
60-90	5	75	–1	1	–5	5
90-120	10	105	0	0	0	0
120-150	3	135	1	1	3	3
150-180	5	165	2	4	10	20
180-210	2	195	3	9	6	18
	30				2	76

Find the mean and variance for the following frequency distribution. Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210 Frequencies 2 3 5 10 3 5 2

Class Frequency fi Mid-point xi yi2 fiyi fiyi2 0-30 2 15 –3 9 –6 18 30-60 3 45 –2 4 –6 12 60-90 5 75 –1 1 –5 5 90-120 10 105 0 0 0 0 120-150 3 135 1 1 3 3 150-180 5 165 2 4 10 20 180-210 2 195 3 9 6 18 30 2 76 Mean,

Find the mean and variance for the following frequency distribution.

Classes

0-30

30-60

60-90

90-120

120-150

150-180

180-210

Frequencies

2

3

5

10

3

5

2

Class

Frequency f_i

Mid-point x_i

y_i²

f_iy_i

f_iy_i²

0-30

2

15

–3

9

–6

18

30-60

3

45

–2

4

–6

12

60-90

5

75

–1

1

–5

5

90-120

10

105

0

0

0

0

120-150

3

135

1

1

3

3

150-180

5

165

2

4

10

20

180-210

2

195

3

9

6

18

30

2

76

Mean,