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Properties of a good measure of disperison.

1. It should be based on all the observation.

2. It should be readily comprechensible.

3. It should be fairly & easily understood.

4. It should be medable to further algebric treatment.

5. It should be affected as little as possible by fluctuation in sampling.

Students are supposed of collect the price of any five vegetables from the market over a week. Then they should calculate their correlation of co – efficients.

Dispersion is a measure of the Variation of the items. According to Prof. C.R. Conn, Dispersion is a measure of the extent to which the individual item vary. The measures of dispersion are required to measure the amount of variation of values about the central values.

Example:

Suppose the monthly incomes in rupees of five households are as Rs. 4500, 6000, 5500, 3750 and 4700 The arithmatic mean of income is Rs. 4700. The amount of Variation in income is shown by deviation from the central values. In this case the deviation from the arithmean. are Rs. 390, 110,610,1140 & 190. Deviation being considered as the total Variation in the mean.

Average of the series refers to the central tendency of the series. It represents behaviour of all the items in the series. But different item tends to different from each other and from and from the averages. Dispersion measures the extent to which different items tend to disperse away from the central tendency.

Here, largest value 

(L) = 21, smallest value (S) = 10 

∴ Range = L – S = 21 – 10 = 11

We should measure dispersion about some particular value because in that case.

1. We can assess how precise is the central tendency observations in the series. Greater value of dispersion implies lesser represent activeness of the central tendency and vice versa.

2. We can precisely assess how scattered are the actual observation from their representative value.

Open ended distributions are those distribution in which either the lower limit of the lower class or the upper limit of the highest class or both are not specified.

Here, upper limit of the highest class 

(L) = 72 lower limit of the lowest class (S) = 62 

∴ Range = L – S = 72 – 62 = 10

Range and Quantile deviation based on the speread of values.

Standard deviation is independent of origin as it is not affected by the Value of constant from which deviations are calculated. The value of the constant does not figure in the standard deviation formula.

Range is unduely uneffected by extreme range.

Absoluite value ofdispersioa (Quartile value of devition = \(\frac{Q_3-Q_1}{2}\)

= \(\frac{45000-18000}{2}\)

= 13500

Correct option is (c) 0

Correct option is (c) Quartile Deviation

Range is unduly affected based on the spread of values.

Mean deviation and standard deviation are the measure of dispersion from average.

Range = 100 – 20 = 80

Comparison of alternative measure of the dispersion has been discussed below.
1. Rigidly defined:
All the four measures the range, quartile deviation, mean deviation & standard deviation are rigidy defined. There is no Vagueness in their definitions.

2. Ease of calculation:
The range is the easiest one to calculate. Quartile deviation requires calculation of the upper & lower quartiles but that is also easy enough. However, the mean deviation & standard deviation require a little more systematic calculation they, too are easy.

3. Simple interpretaion:
All measures of dispersion are easy to interpret. While the range and quartile deviation measure disperrsion in a general way the mean deviation and standard deviation measure dispersion in terms of deviation from a central value. Thus the mean deviation and standard deviation give a better idea about the dispersion of values within the range.

4. Based on all values:
The range and Quantile deviation do not depend on all values where as the mean deviation and standard deviation use all values of the variable the range is affected the most by extreme values.

5. Amendable to algebraic treatment:
The standard deviation is perhaps the earliest for analytical work. Other measure can be also dealt with analytically but derivation are harder.

Correct option is:(A) 5 patients

The desirable characteristics of dispersion are as follows:

• The definition of a measure of dispersion should be clear and precise.
• It should be simple to understand and easy to compute.
• It should be based on all observations of the data.
• It should be least affected by sampling i.e., it should be stable measure.
• It should be suitable for further algebric and statistical calculation.
• It should be least affected by extreme observations of the data.

Range = L – S = 70 – 20 = 50

The relative measures of dispersion are used for comparing two or more groups in terms of the variability.

The measure obtained by dividing the difference between the third quartile Q₃ and Q₁ the first quartile of the data by 2 is called quartile deviation and it is denoted by Q_d, i.e.,

Q_d = \(\frac{Q_3−Q_1}{2}\)

Here, x_H = Upper limit of the last class 30 – 34 = ₹ 34

x_L = Lower limit of the initial class 5-9 = ₹ 5

Absolute measure of range of age:

R = x_H – x_L

= 34 – 5 = ₹ 29 thousand

Relative measure of range of age:

Coefficient of range = \(\frac{x_H−x_L}{x_H+x_L}=\frac{R}{x_H+x_L}\)

= \(\frac{29}{34+5}\)

= \(\frac{29}{39}\)

= 0.74

The difference between the highest and lowest observation of the data is called the range and it is denoted by the symbol R., i.e., R = x_H – x_L

We will determine the stability of factory in context to daily production by comparing the coefficient of variation of daily production of Factory A and Factory B.

Factory A:
x̄ = Average daily production = 50
s = Standard deviation =10
Coefficient of variation = \(\frac{s}{x¯}\) × 100
= 10 / 50 × 100 = 20 %

Factory B:
x̄ = Average daily production = 48
s = Standard deviation = 12
Coefficient of variation = \(\frac{s}{x¯}\) × 100
= 12 / 48 × 100 = 25 %
The coefficient.of variation of daily production of factory A is less than that of factory B. Hence, the- daily production of factory A is more stable.

Correct option is (a) 10 %

Here, n = 5
x: 1, 2, 3, 4, 5

(x – x̄): – 2, -1, 0,1, 2 ∴Σ(x – x̄) = 0
(x – x̄)²: 4, 1, 0, 1, 4 ∴Σ (x – x̄)2 = 10
Standard deviation:
s = \(\sqrt\frac{Σ(x−x¯)^2}{n}=\sqrt\frac{10}{5}=\sqrt{2}\)= 1.41

Correct option is (a) 19 and 6

Correct option is (c) (i) 5 (ii) 15

The mighty empire refers to the British Empire who ruled us earlier.

Missions are always bigger than organizations and these organizations are always bigger than the individuals who run them.

If we have low aim the spirit of enterprise will diminish and can’t achieve anything.

By working together we can provide facilities at reasonable prices.

According to Dr. Kalam creative process or power or the power of imagination is important in life to become a winner.

We are witnessing good progress in the software sdctor but all of the hardware is imported. Our exports consist raw materials but we cannot convert these into a wide range of products. We don’t have international markets. We have hundreds of defense production industries but we don’t manufacture missiles, battle tanks and other defense equipment.

People expect proper diagnostic facilities in clinics and affordable drugs reaching our masses. People also expect the facilities at reasonable prices.

All these institutions are full of discussion and debate. There are endless debates, arguments, theories and there is little progress. The theme of developed India is lacking so they should take the full responsibility and lead the country.

We notice it in Assam.

In the software sector, we have good progress. Butalmostall of the hardware is imported. We can’t rise on the value scale. India cannot design an operating System that will become a household name in the world of computers.

We should manufacture cars dotting the roads in Seoul. We should build power stations for the USA, Japan and China. India should design an operating system that will become a household name in the world of computers. India should manufacture and market battle tank, missiles, aircrafts, guns and other equipment. Students should get ready to transform India into a developed nation.

Tata brought steel industry to India during the British rule. Acharya P.C ray developed the chemical and pharmaceutical industries. Madan Mohan Malaviya started Banaras Hindu University and Syed Khan started Aligarh University. Their main intention was to see India come up in the world.

Karnataka, Tamil Nadu, Maharastra, Andra Pradesh are the states faring better than others in the country.

He tells students to develop creative power and to think in the right direction. He tells them to use their energy and to get ready to transform India into a developed nation. He asks of the teachers to ignite the minds of the students and to equip them with all the necessary knowledge so that they can come up in life.

The phrase ‘old and young alike’ means both the old and the young people in Paragraph 1 .

Maharshi Rabindranath Tagore named the school Shantiniketan.

Shantiniketan is termed as the darling of our hearts by Gurudev.

The boys in Shantiniketan practice Carpentry, spinning, weaving, drafting, painting music etc in the afternoon. They learn these types of handwork.

A Good School: The teachers are pillars for school. They must be educated, kind, learned, disciplined and have lot of patience. They must love their profession and children. Magnificent building, spacious class rooms and big fields are not as much important. The way of teaching should encourage the students creative thinking.

Give importance to boost the children’s talent. The students should have free ness to ask questions. Handiwork’s and games and sports should include in their curriculum. The students should also be obedient, disciplined and love to learn.

The afternoon classes start at 2 ‘O’Clock in Shantiniketan. The class chiefly consists of handiwork. The boys could learn their own choice of interest. The different handiwork’s to be taught were Carpentry, Spinning, Weaving, drafting, painting, music etc.