Download App

Measures of Central Tendency — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Central Tendency6 Marks
Question
Calculate the upper and lower quartiles for the following frequency distribution.
Class Interval
Frequency (f)
13-25
6
25-37
11
37-49
23
49-61
7
61-73
3
Total
50
✓

Answer

Calculation of Upper and Lower Quartiles
Class Interval
Frequency (f)
Cumulative Frequency (cf)
13-25
6
6
25-37
11
17
37-49
23
40
49-61
7
47
61-73
3
50
 
$\text{n}=\Sigma\text{f}=50$
 
Here, $n = 50$
$\therefore$ Lower Quartile number $(q_1) =\text{Size of }\Big(\frac{\text{n}}{4}\Big)\text{th item}$
$=\Big(\frac{50}{4}\Big)\text{th item}=12.5\text{th item}$
cf just greater than 12.5 is 17 and the corresponding class is 25-37.
So, $l_1 = 25$
$cf = 6, f = 11$ and, $c = 12$
$\therefore\ \text{Q}_1=\text{l}_1+\frac{\frac{\text{n}}{4}-\text{cf}}{\text{f}}\times\text{c}$
$=25+\frac{12.5-6}{11}\times12$
$=25+\frac{6.5}{11}\times12=25+7.09$
$\Rightarrow\ \text{Q}_1=32.09$
Now,
Upper Quartile number $(q_3) =\text{Size of }3\Big(\frac{\text{n}}{4}\Big)\text{th item}$
$= 37$.5th item
cf just greater than 37.5 is 40 and corresponding class is $37-49.$
So, $l_1 = 37, cf = 17$
$f = 23$
$c = 12$
$\therefore\ \text{Q}_3=\text{l}_1+\frac{\frac{3\text{n}}{4}-\text{cf}}{\text{f}}\times\text{c}$
$=37+\frac{37.5-17}{23}\times12$
$=37+\frac{20.5}{23}\times12$
$=37+10.70\Rightarrow\ \text{Q}_3=47.70$

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

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.
→
The yield of wheat and rice per acre for 10 districts of a state is as under:
District
1
2
3
4
5
6
7
8
9
10
Wheat
12
10
15
19
21
16
18
9
25
10
Rice
22
29
12
23
18
15
12
34
18
12
Calculate for crop.
Mean deviation about Mean.
→
Construct the following indices by taking 2015 as the base:
  1. Simple Aggregative Price Index.
  2. Index of Average of Price Relatives.
Items
A
B
C
D
E
Prices ₹ (2015)
6
2
4
10
8
Prices ₹ (2016)
10
2
6
12
12
Prices ₹ (2017)
15
3
8
14
16
→
Discuss merits and demerits of quartile $NESE$ deviation.
→
Calculate Quartile deviation from the following data:
Marks: 0-10 10-20 20-30 30-40 40-50
No. of Students: 4 15 28 16 7
→
Units of OutputMarginal Revenue (₹)Marginal Cost (₹)
12020
22010
3206
4204
52020
62030
 1. On the basis of the data given above, the producer's equilibrium is struck when output level is
     (a) 1 unit  (b) 2 units (c) 5 units (d) 6 units
2. On the basis of your answer of the above question, the profit at the equilibrium output is
    (a) 0 (b) 10 (c) 24  (d) 40
3. Which of the following is correct?
    (a) Producer's equilibrium is struck at that level of output where profit is maximised
    (b) Net profit refers to the difference between TR and TC
    (c) Normal profits are a part of TC
    (d) All of these
4. Identify the correct formula to calculate Gross Profits.
   (a) Gross Profits = TR-TFC
   (b) Gross Profits = TR-TVC
   (c) Gross Profits = TR - TC
   (d) Gross Profits TR-TFC-TVC
5. Read the following statements carefully and choose the correct alternative among those given below:
Statement 1: In case MR > MC, we can increase profit by increasing output.
Statement 2: A firm will always finds its equilibrium output under falling MC.
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. In which stage of production, a producer attains his equilibrium?
   (a) In the first stage of production
   (b) In the second stage of production
   (c) In the third stage of production
   (d) In all the above stages of production
→
→
Explain market equilibrium when the number of firms happens to increase or decrease in the market and only normal profits are earned.
→
How is the equilibrium price and equilibrium quantity of a normal commodity affected by an increase in the income of its buyers? Explain with the help of a diagram.
→
There are four consumers of a fruit called smile. They are: Isla, Ifraah, Ila and Ibema. Their demand curves for smile are given below. Derive the market demand curve.
Price (₹)Quantity Demanded by Isla (Units)Quantity Demanded by Ifraah(Units)Quantity Demanded by Ila (Units)Quantity Demanded by Ibema (Units)
1167158
2116126
37594
44462
52330
61200



→