Find out the arithmetic mean using the step deviation method. Ite… - Vidyadip

Question

Find out the arithmetic mean using the step deviation method.

Item	Frequency
More than 0	28
More than 10	24
More than 20	14
More than 30	4

Hint: In the above problem, cumulative frequencies are given. Firstly, it will be changed into exclusive class interval and thereafter we will calculate arithmetic mean using the step deviation method.

✓

Answer

Calculation of Arithmetic Mean by Step Deviation Method
Items	Mid-Value (m)	Frequency (f)	dm(m - A) (A = 15)	$\text{d}'\text{m}\Big(\frac{\text{dm}}{\text{c}}\Big)$ (c = 10)	fd'm
0-10	5	28 - 24 = 4	-10	-1	-4
10-20	15	24 - 14 = 10	0	0	0
20-30	25	14 - 4 = 10	+10	+1	+10
30-40	35	4	+20	+2	+8
		$\Sigma\text{f}=28$			$\Sigma\text{f}\text{d}'\text{m}=+14$

$\therefore\ \overline{\text{X}}=\text{A}+\frac{\Sigma\text{fd}'\text{m}}{\Sigma\text{f}}\times\text{c}$
$=15+\frac{14}{28}\times10=15+5$
$\Rightarrow\ \overline{\text{X}}=20$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "6 Marks Question" from Measures of Central Tendency→Measures of Central Tendency — all question types→Economics STD 11 Commerce question papers→CBSE Board STD 11 Commerce question papers→CBSE Board question paper generator→

Similar questions

Explain any six factors determining price elasticity of demand.

Read the following hypothetical information carefully and answer the questions 1-6 on the basis of the same:

Units Consumed	Total Utility	Marginal Utility
1	10	10
2	18	-
3	25	7
4	-	6
5	34	3
6	-	0

1. At 2nd unit consumed, marginal utility is _________ .
(a) 6 (b) 7 (c) 8 (d) 28
2. At 4th unit consumed, total utility is __________ .
(a) 24 (b) 31 (c) 32 (d) 13
3. Which of the following statements is correct?
(a) Total utility increases when marginal utility is positive
(b) Total utility is maximum when marginal utility is also maximum
(c) Total utility diminishes only when marginal utility is negative
(d) Both (a) and (c)
4. Identify the correct formula to calculate Marginal Utility.
(a) $M U=\Sigma T U$ (b) $M U=T U_n-T U_{n-1}$ (c) $M U=T U_n-T U_{n+1}$ (d) None of these
5. Read the following statements carefully and choose the correct alternative among those given below:
Statement 1: Total utility is the summation of marginal utilities.
Statement 2: Marginal utility curve slopes upward from left to right.
Alternatives:
(a) Both the statements are true
(b) Both the statements are false
(c) Statement 1 is true and Statement 2 is false
(d) Statement 2 is true and Statement 1 is false
6. At 6th unit consumed, total utility is __________ .
(a) 0 (b) 11.1 (c) 31 (d) 34.

The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.

Production yield (kg. per hectare)
50-53	53-56	56-59	59-62	62-65	65-68	68-71	71-74	74-77
Number of farms
3	8	14	30	36	28	16	10	5

Statistics is indispensible in every field. Explain.

Why is standard deviation considered to be the best measure of dispersion?

The two important functions of classification are:

Scrutiny and editing of data.
Presentation and interpretation of data.
Reducing bulk data and facilitating comparison.
forming trend and tendencies.

Explain the chain of effects of an increase in demand for a commodity on its equilibrium price and quantity.

State any four uses of different types of Index Numbers.

Following table represents the demand schedule of households, A, B and C. Derive market demand schedule.

Price (₹)	Household A (Units)	Household B (Units)	Household C (Units)
8	6	12	22
7	7	13	23
6	8	14	24
5	9	15	25
4	10	16	26

Represent the following data of annual profits of a firm through a time series graph:

Years	2013	2014	2015	2016	2017	2018
Profits (in '000 ₹)	60	72	75	65	80	95