Step Deviation Method

Q.

Class	5−15	15−25	25−35	35−45	45−55	55−65	65−75
Frequency	6	10	16	15	24	8	7

Q. ​The following table shows the marks scored by 80 students in an examination:

Marks	Less than 5	Less than 10	Less than 15	Less than 20	Less than 25	Less than 30	Less than 35	Less than 40
Number of students	3	10	25	49	65	73	78	80

Calculate the mean marks correct to 2 decimal places.

Q.

Class	20−30	30−40	40−50	50−60	60−70
Frequency	25	40	42	33	10

Q.

Find the mean age of 100 residents of a town from the following data.
$\begin{array}{ccccccccc}Ageequalandabove\left(inyears\right)& 0& 10& 20& 30& 40& 50& 60& 70\\ Numberofpersons& 100& 90& 75& 50& 25& 15& 5& 0\end{array}$

Q.

Calculate Mean and standard deviation for the following distribution

X	$5$	$15$	$25$	$35$	$45$
f	$5$	$8$	$15$	$16$	$6$

Q.

Calculation (i) Arithmetic Mean (ii) Standard Deviation and (iii) Co-efficient of variation for the following frequency distribution.

Class Interval	Frequency
30 – 35 35 – 40 40 – 45 45 – 50 50 – 55	5 10 16 15 4
Total	50

Q.

What is standard deviation of the following series

Measurement	Frequency
$0-10$	$1$
$10-20$	$3$
$20-30$	$4$
$30-40$	$2$

1. $81$

2. $76$

3. $9$

4. $2.26$

Q.

Class	0−10	10−20	20−30	30−40	40−50
Frequency	7	10	15	8	10

Q. Calculate $\frac{\sum f_i{u}_i}{\sum f_i}$ for the given data using step-deviation method.
$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

1. $\frac{1}{188}$
2. $0$
3. $250$

Q.

Find the mean of the following frequency distribution using step-deviation method:

Class	84−90	90−96	96−102	102−108	108−114	114−120
Frequency	15	22	20	18	20	25

Q.

The marks scored by 60 students in a mathematics test are given below.

Marks (X)	10	20	30	40	50	60
No. of students (f)	8	12	20	10	7	3

Find the Variance and Standard Deviation of the marks.

Q.

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution.

Class Interval	Frequency
20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50	8 3 15 12 8 4
	N = 50

Q.

For the given distinct values x₁, x₂, x₃ .....x_n occurring with frequencies f₁, f₂, f₃, ... f_n respectively. The mean deviation about mean would be

1. 

2. 

3. 

4. 

Q. The histogram below represents the scores obtained by 25 students in a Mathematics mental test. Use the data to: [4 MARKS]
i) frame a frequency distribution table.
ii) to calculate mean
iii) to determine the modal class

Q.

Construct a histogram from the following distribution of total marks obtained by 65 students of X class in the final examination

$\begin{array}{ccccccc}Marks(mid-points):& 150& 160& 170& 180& 190& 200\\ No.ofstudents& 8& 10& 25& 12& 7& 3\end{array}$

1. 

2. 

3. 

4. None of these

Q.

Find mean by step deviation method.

1. 41.25

2. 25.70

3. 46.06

4. 39.23

Q.

Find the mean of the following using step deviation method.

1. 60

2. 68

3. 69

4. 70

5. 65

Q. Calculate the mean of the following distribution using step - deviation method.

$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 30-40& 10\\ 40-50& 6\\ 50-60& 8\\ 60-70& 12\\ 70-80& 5\\ 80-90& 9\end{array}$

1. 54
2. 60
3. 58.6
4. 59.6

Q. Find the mean of the following frequency distribution, using step-deviation method:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	12	13	10	8

Q.

How do you calculate the expected frequency in Hardy Weinberg equilibrium?

Q.

The daily wages of 40 workers of a factory are given in the following table.

Wages in Rs.	30 – 34	34 – 38	38 – 42	42 – 46	46 – 50	50 – 54
No. of workers	4	7	9	11	6	3

Calculate (i) Mean (ii) Variance and (iii) Standard Deviation of wages and also interpret the findings.

Q. Calculate the mean using step deviation method.

1. $62$
2. $63$
3. $65.3$
4. $64$

Q. In the ____ method of calculating mean, we divide the deviations by the same number to simplify calculations.

1. direct
2. step deviation
3. direct deviation
4. assumed mean

Q.

Find the mean of the step deviations:
$\begin{array}{ccccc}Classinterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

1. $250.52$

2. $0$

3. $\frac{1}{188}$

4. $250$

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

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	12	18	15	25	26	15	9

Q. _________, Mean method and Assumed Mean method, these are the three methods to find the standard deviation of grouped data.

1. Indirect method
2. Deviation method
3. Long method
4. Direct method

Q.

Find the mean of the following distribution, by step deviation method.

1. 29.6

2. 40.5

3. 30.9

4. 24.8

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

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of students	12	18	27	20	17	6

Q. Find the mean of the following frequency distribution:

Q. Calculate $\frac{\sum f_i{u}_i}{\sum f_i}$ for the given data using step-deviation method.
$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

1. $0$
2. $250$
3. $\frac{1}{188}$
4. 100