Compute arithmetic mean by using step-deviation method from the following data: 6 Marks (X) 0-10 10-20 20-30…

Question

Compute arithmetic mean by using step-deviation method from the following data: 6 Marks (X) 0-10 10-20 20-30 20 30-40 25 40-50 50-60 10 5 60-70 20 No. of Students 8

ScanSolve AI Tutor · Accepted Answer

To compute the arithmetic mean using the step-deviation method, we first need to organize the given data into a frequency distribution table and then apply the formula.

Assumed Data Interpretation:
Based on the provided text, the data is interpreted as follows:

Marks (X)	No. of Students (f)
0-10	6
10-20	8
20-30	20
30-40	25
40-50	5
50-60	10
60-70	20

Calculate Midpoints (m) for each class
The midpoint of a class is calculated as (Lower Limit + Upper Limit) / 2.
For 0-10: $m = (0+10)/2 = 5$
For 10-20: $m = (10+20)/2 = 15$
For 20-30: $m = (20+30)/2 = 25$
For 30-40: $m = (30+40)/2 = 35$
For 40-50: $m = (40+50)/2 = 45$
For 50-60: $m = (50+60)/2 = 55$
For 60-70: $m = (60+70)/2 = 65$
Choose an Assumed Mean (A) and determine Class Width (h)
Let's choose the midpoint of the class with the highest frequency (30-40, frequency 25) as the assumed mean. So, $A = 35$ .
The class width ( $h$ ) is the difference between the upper and lower limits of any class, or the difference between consecutive midpoints.
$h = 10 - 0 = 10$ (or $15 - 5 = 10$ ).

Calculate Step Deviations ( $d'$ )

The step deviation is calculated as $d' = (m - A) / h$ .

Class (X)	Frequency (f)	Midpoint (m)	$d = m - A$ ( $A=35$ )	$d' = d/h$ ( $h=10$ )	$f d'$
0-10	6	5	$5 - 35 = -30$	$-30/10 = -3$	-18
10-20	8	15	$15 - 35 = -20$	$-20/10 = -2$	-16
20-30	20	25	$25 - 35 = -10$	$-10/10 = -1$	-20
30-40	25	35	$35 - 35 = 0$	$0/10 = 0$	0
40-50	5	45	$45 - 35 = 10$	$10/10 = 1$	5
50-60	10	55	$55 - 35 = 20$	$20/10 = 2$	20
60-70	20	65	$65 - 35 = 30$	$30/10 = 3$	60

Sum Frequencies (N) and $f d'$
Sum of frequencies: $N = \sum f = 6 + 8 + 20 + 25 + 5 + 10 + 20 = 94$
Sum of $f d'$ : $\sum f d' = -18 - 16 - 20 + 0 + 5 + 20 + 60 = 31$
Apply the Step-Deviation Formula
The formula for the arithmetic mean using the step-deviation method is:
$\bar{X} = A + \left( \frac{\sum f d'}{N} \right) \times h$
Substitute the values:
$\bar{X} = 35 + \left( \frac{31}{94} \right) \times 10$ $\bar{X} = 35 + (0.329787...) \times 10$ $\bar{X} = 35 + 3.29787...$ $\bar{X} \approx 38.30$
The arithmetic mean is:
$38.30$

Compute arithmetic mean by using step-deviation method from the following data: 6 Marks (X) 0-10 10-20 20-30 20 30-40 25 40-50 50-60 10 5 60-70 20 No. of Students 8

Answer

Step-by-step solution

Calculate Midpoints (m) for each class

Choose an Assumed Mean (A) and determine Class Width (h)

Calculate Step Deviations ( $d'$ )

Sum Frequencies (N) and $f d'$

Apply the Step-Deviation Formula

Try one yourself

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More Statistics Questions

Compute arithmetic mean by using step-deviation method from the following data: 6 Marks (X) 0-10 10-20 20-30 20 30-40 25 40-50 50-60 10 5 60-70 20 No. of Students 8

Answer

Step-by-step solution

Calculate Midpoints (m) for each class

Choose an Assumed Mean (A) and determine Class Width (h)

Calculate Step Deviations (d′d'd′)

Sum Frequencies (N) and $f d'$

Apply the Step-Deviation Formula

Try one yourself

Still stuck on this one?

More Statistics Questions

Calculate Step Deviations ( $d'$ )