\(\overline { x } 12=\frac { { N }_{ 1 }\overline { x } 1+{ N }_{ 2 }\overline { x } 2 }{ { N }_{ 1 }+{ N }_{ 2 } } \)
65 = \(\frac { (62+50)+(Y\times 30) }{ 80 } \)
30Y = 2494
Y = 2490/30 = 83

In case of equal class interval simply we draw the frequencies of equal width but when class intervals are unequal these frequencies need to be adjusted. It will be clear from the example given below:

Median=size of \(\frac{N}{2}\) Item
Median=size of \(\frac{50}{2}=50\) item 25th item lies in 20-30
We can find median by using the formula equal to
\(Median=l_1+\frac{(\frac{N}{2}-C)}{f}(i)\)

I₁ = 20; f = 10; \(\frac{N}{2}=25\)
C=10;i=10
\(Median=20+\frac{25-15}{8}(10)=28.625\)

Median = size of \(\frac{N+1}{2}\)
size of \(\frac{41+1}{2}=Item\)
Item 19 to 28 have a value equal to 35. Therefore, median = 35.

In this case the law of diminishing marginal utility will not apply because every effort to get education/ knowledge increases the utility.
Value: Analytic

(l) The price line shows the relationship between the market price and a competitive firm's output level.
(il) The vertical height of the price line is equal to the market price as shown in the given figure.

(i) A unit tax is a tax that the government imposes per unit sale of output.
(ii) For example, suppose that the unit tax imposed by the government is Rs.3. Then, if the firm produces and sells 20 units of the goods, the total tax that the firm must pay to the government is
20 x 3 = 60.
(iii) So, if the unit tax increases, the firm's cost of production increases which will shift the supply curve leftward.

Cleanliness reduces chances of people falling ill and, thus ensure better health. This, in turn, will reduce forced absenteeism from work, raise efficiency level and thus raise country's production potential. Rise in potential shifts PP curve to the right.

Q = \({ 5L }^{ \frac { 1 }{ 2 } }{ K }^{ \frac { 1 }{ 2 } }\) (given)
Q = 5 x \({ 100 }^{ \frac { 1 }{ 2 } }{ 100 }^{ \frac { 1 }{ 2 } }\)
Q = 5 x 10 x 10 = 500 units
So, the maximum possible output(Q) = 500 units.

(i) It happens because when AVC falls, SMC is less than AVC.
(ii) When AVC starts rising, SMC is more than AVC.
(iii) So, it is only when AVC is constant and at its minimum point, that SMC is equal to AVC. Therefore, SMC curve cuts AVC curve at its minimum point.

The central problems of an economy are:
(i) What to produce and in what quantity?
(ii) How to produce?
(iii) For whom to produce?

Given Q = 10 - 3P.
When P = \({5\over3},Q=10-3\times{5\over3}=5\)
Differentiating Q with respect to P,
we get,
We know,\({\triangle Q\over \triangle P}=-3\)
\(ED={\triangle Q\over \triangle P}\times {P\over Q}=-3\times{5/3\over 5}\)
\(=-3\times{5\over3}\times{1\over5}=[-]1\)
Negative Sign of ED indicates that inverse relationship between price and quantity demanded.
PED = 1 [Unitary elastic demand].

(i) Complementary goods are those which are useless in the absence of other goods and which are demanded jointly.

(ii) There would always exist an inverse relationship between price of complementary goods and demand for given commodity.
(iii) It means, with a rise in price of complementary goods, the demand for given commodity falls and vice-versa.
(iv) For example pen and refill, tea and sugar are complements to each other.

(i) The subject matter of economics includes microeconomics and macroeconomics.
(ii) Microeconomics, studies the behaviour of individual economic units of an economy like households, firms, individual consumers and producers etc. It does not study the economy as a whole.
(iii) Macroeconomics is the part of economic theory that studies the economy as a whole, such as national income,  aggregate employment, general price level, aggregate consumption, aggregate investment, etc.