Explore topic-wise InterviewSolutions in .

Correct Answer is: (a) Yes

Data are presented in three ways:

1. Subjective or descriptive presentation 

2. Tabulation 

3. Graphical presentation

When the rahge of data and class length are given, number of classes is determined by the following formula:

Number of classes =  \(\frac{range} {class\, length}\)

Data is usually presented in three ways.

Correct Answer is: (b) Mode

The grouped frequency distribution is presented in the form of frequency rectangular diagram, frequency polygon, frequency curve, cumulative frequency curve, etc.

Correct Answer is: (c) Median

(a) Simple Bar Diagram

(b) Multiple-bar diagram

When the data are classified on the basis of time is known as chronological classification.

Eg : hour, day, week, months, years etc.

A numeric value showing the repetition of value of observation is called frequency of that observation. It is denoted by symbol.

Correct option is (d) Number of children per family

In the given data, there are two attributes:

1. Sex of employees and
2. Marital status.

According to these two attributes data is classified and table is prepared as follows :
Table showing the number of employees working in an office according to their sex and marital status

Explanation:

Suppose, the number of males = x.
∴ No. of females = 1600-x
No. of males = No. of females + 1600 x 15100
∴ x = 1600 – x + 240
∴ 2x = 1840
∴ x = 920
∴ No. of females = 1600 – 920 = 680

Suppose the number of married employees = x
∴ No. of unmarried employees = 1600 – x
Now, No. of unmarried employees = No. of married employees – 800.
∴ 1600 – x = x – 800
∴ 2x = 1600 + 800 = 2400
∴ x = 1200
∴ No. of unmarried employees = 1600 – 1200
= 400]
[Note: The figures shown in bold are obtained by simple calculation.

Classes can be formed in two ways:

1. Exclusive type

2. Inclusive type

1. Exclusive type:

When the class intervals are so fixed that the upper limit of one class is the lower limit of the new class, it is known as the exclusive method of classification.

Example:

2. Inclusive Type:
Under this method the upper class limit of the frequency class will not become the lower limit of next class. This type of classification is called as Inclusive type.

(a) Long-term tendency

When the data is classified on the basis of weight, height, Kgs etc can be called as Quantitative classification.

Classification is of two types:

1. Quantitative classification and
2. Qualitative classification.

A frequency curve is a curve which is plotted by joining the midpoints of all tops of a histogram by free hand smoothed curves.

The formation of discrete frequency distribution is quite simple. The number of items a particular value is repeated is noted down and mentioned against that values instead of writing that value repeatedly.

Eg : In the distribution 3,4,6, 6, 8, 8, 8, 8,1, 1, 1, we can write :

Graphs showing arithmetic values of variables are called as time series graphs.

The different types of classification are:

1. Quantitative classification

2. qualitative classification

3. Spatial classification

4. Temporal classification

The major two limitations of graphic presentation of time series data:

1. Very limited use

2. Easily can be misused.

For constructing continuous frequency distribution the following points are to be considered :

• When the variable of the data is continuous or the range of variable is large, continuous frequency distribution should be constructed.
• Generally, the number of classes should be any number from 6 to 15. Under special circumstances, the number of classes may be less than 6 or more than 15.
• Considering the number of classes k and the range of data R. class length is decided using the following formula: c = RK
• The value of c is selected such that ck ≥ R and c is positive integer.
• Generally, the class length of each class is kept equal. But under the circumstances that range of the data is large, keeping in view the number of classes, classes of different lengths can be constructed.
• Usually, the initial class should begin with the observation multiple of class length and a number smaller than and close to the lowest observation of the data.
• Classes can be chosen either inclusive type such as 10-14, 15-19, 20-24, … or exclusive type such as 10- 15, 15-20, 20-25
• For data on continuous variable exclusive type of classes should be preferred and when the range of discrete data is large one, then inclusive type of classes should be preferred.

The guru tries to confuse the king by expressing his desire to be killed first. Then to further confuse the king he tells the story of becoming the king in the next incarnation. Apparently, it may sound like a case of pure lie to save your dear one’s life. But if we go deeper consciously or unconsciously the guru is trying to save everybody’s life in the kingdom. Ultimately he is able to pull everybody out of the misery of living in the kingdom of fools.

The limitations of diagrams are as follows :

• Lack of accuracy in drawing diagrams leads to wrong interpretation.
• Illusionary effect of diagrams misleads the public opinion.
• There is a loss of accuracy in presenting the data by diagrams.

Sum of the frequencies up to the value of an observation or class is called cumulative frequency (cf) and its distribution is called cumulative frequency distribution.

Two types of cumulative frequency distribution are :

1. ‘Less than’ type cumulative frequency distribution: The sum of the frequencies upto the specified value of the observation or specified upper boundary point of a class is called ‘less than’ type cumulative frequency of that specified value or class and the distribution is called ‘less than’ type cumulative frequency distribution. Here, cumulative frequencies are in ascending order.

2. ‘More than’ type cumulative frequency distribution: The sum of all the frequencies of the specified value of the observation or the lower boundary point of the specified class and the values or classes succeeding to it, is called ‘more than’ type cumulative frequency and its distribution is called ‘more than’ type cumulative frequency distribution. Here, cumulative frequencies are in descending order.

The circular representation of data is called as pie diagram.

Following are the steps involved in the preparation of pie – diagram.

1.  Convert each component as a percentage of the total.

2.  Multiply the percentage by \(\frac{360°}{100}\) = 3.6 + 0 convert into degrees.

3.  Starting with the twelve ‘O’ clock position on the circle (clockwise) draw the large component circle. 

4.  Draw other components in clockwise succession in descending order of magnitude except for each -all components like all others and miscellaneous which are shown last.

5.  Use different columns or shades to distinguish between different components.

6.  Explain briefly the different components either within the components in the figure or outside by arrows.

Example of qualitative classification:

Literacy in Bihar (in percentage)

The types of diagrams are three :

1. One dimensional diagram,
2. Two-dimensional diagram and
3. Pictogram.

The guru’s words of wisdom were that it was the city of fools. He advised the disciple to leave the city because he would not know what they would do next. The disciple remembers this when he was going to be executed.

Given data is ‘more than’ type cumulative frequency distribution.
∴ Class length = Difference between the adjoining lower boundary points = 54.5 – 49.5 = 5
Now, upper boundary point of the class = lower boundary point + class length
For initial class lower boundary point = 44.5
∴ initial class is 44.5 – 49.5.

For inclusive continuous frequency distribution lower limit of initial class = 44.5 + 0.5 = 45 and upper limit of initial class = 49.5 – 0.5 = 49.
Thus, for given data the initial class in inclusive form, we get 45-49.
In this manner, we will obtain the class for each lower boundary point.
We will find the frequency of each class from the given ‘more than’ cumulative frequency as follows :

Frequency of a class = (‘more than’ cumulative frequency of a class) – (‘more than cumulative frequency of immediate following class)

Frequency of class for 44.5 = (‘more than’ cumulative frequency of a class for 44.5) – (‘more than cumulative frequency of immediate following class for 49.5)
= (500 – 470) = 30

In this manner we will obtain the frequency for the rest of classes.
For the given data, we get the inclusive continuous frequency distribution as follows :

A table showing ‘more than’ cumulative frequency corresponding to the lower boundary point of various classes is called ‘more than’ type cumulative frequency distribution for continuous data.

Correct option is (a) 28

When the data about different places; things or times are given on more than one mutually related characteristics, multiple bar diagram is drawn.

The characteristic of the best table to represent qualitative data is ‘the table satisfies the objective of classification’.

(1) A Grand Figure : ‘Old Shylock’ is a grand figure in The Merchant of Venice. He is imagined to be on the wrong side of forty with unkempt hair and dressed in a long Jewish garberdine. 

(2) His Miserliness : His miserliness is peculiarly Jewish. He loves only riches. So he grudges even his servant, Launcelot’s food, sleeping by day and the cost of his clothes. His concentrated love on riches makes him a bad father, and causes Jessica to feel that his house is ‘hell for her. 

(3) His Usury : His usury is no less Jewish. It is based on the authority of his holy scriptures : the interest on money is a well won thrift, as it is based on a bargain. So for him bargain was a way to thrive. 

(4) His Cruelty : Shylock’s cruelty in business dealings is also Jewish through and through. Once a bargain is made with the Jew, the Jew must get his due. Due to his cruelty he did not care for the feelings of his customers and even of his daughter. He is very sensitive to injustice. When his sensitiveness strikes his miserliness, he goes almost mad. 

So to conclude we can say that if not the hero of the play, Shylock, undoubtedly is the most dominant and strong character in the play ‘The Merchant of Venice’.

Generally speaking a hero is the principal main figure of noble qualities especially one whose career is the thread of the story. He should have a number of virtues of head and heart. He should be a person of high rank, respected and valued in society. There are only two main characters in the play ‘The Merchant of Venice’ who may be claimant of the hero-Shylock and Antonio.

Now let us compare the characters of both of them. Shylock is the forceful and dynamic personality. In the trial scene he has shown his single minded devotion, will and energy with which he stands out for the rights of his people evoke our admiration. On the other hand Antonio is a weak and passive character. He is indifferent to life and to this world. He is a weak character. It was fair Portia who saved his life.

But morally Antonio is far superior to Shylock. He is self sacrificing, generous and noble hearted. He is a sincere and affectionate friend, and risks even his life to help his friend in the hour of need dramatically also Antonio is much more important than Shylock. All the other characters of the play are grouped round him. The play begins and ends with him. Lastly Antonio is the merchant in reality having a vast field of business on sea while Shylock is only a money lender. So whichever angle we consider Shylock cannot be regarded as the hero of the play. This honour goes only to Antonio. 

Given data is ‘less than’ type cumulative frequency distribution.
Class length = Difference between two adjoining upper boundary points
= 35 – 30 = 5
Now, lower boundary point of a class = upper boundary point – class length
∴ for initial class, lower boundary point = 30 – 5 = 25 and we get initial class 25 – 30.

In this manner we will obtain class for each upper boundary point.
We find the frequency of a class as follows :
Frequency of a class = (‘less than ‘ cumulative frequency of a class) – (‘less than’ cumulative frequency of preceeding class)
Class frequency for upper boundary point 35 = 17 – 0 = 17
In this manner, we will obtain the class frequency for each upper boundary point.

For the given data exclusive continuous frequency distribution is obtained as follows:

The main objective of percentage divided bar diagram is to compare effectively the mutually related sub-data.

A complex table refers to a table which reveals more than one quality of the data.

When the data about different places, things or times consist of several mutually related sub-data on different components are given, divided bar diagram is drawn.

Correct option is (d) 1.975

Some such images used in the poem are ‘mouth like a fireplace’, ‘chimney for a nose’, ‘brave as a barrel full of bears’, ‘brave as a tiger in a rage’, ‘went at the pirate like a robin at a worm’, etc.

(1) A Grand Figure : ‘Old Shylock’ is a grand figure in The Merchant of Venice. He is imagined to be on the wrong side of forty with unkempt hair and dressed in a long Jewish garberdine. 

(2) His Miserliness : His miserliness is peculiarly Jewish. He loves only riches. So he grudges even his servant, Launcelot’s food, sleeping by day and the cost of his clothes. His concentrated love on riches makes him a bad father, and causes Jessica to feel that his house is ‘hell for her. 

(3) His Usury : His usury is no less Jewish. It is based on the authority of his holy scriptures : the interest on money is a well won thrift, as it is based on a bargain. So for him bargain was a way to thrive. 

(4) His Cruelty : Shylock’s cruelty in business dealings is also Jewish through and through. Once a bargain is made with the Jew, the Jew must get his due. Due to his cruelty he did not care for the feelings of his customers and even of his daughter. He is very sensitive to injustice. When his sensitiveness strikes his miserliness, he goes almost mad. 

So to conclude we can say that if not the hero of the play, Shylock, undoubtedly is the most dominant and strong character in the play ‘The Merchant of Venice’.

(1) A Grand Figure : ‘Old Shylock’ is a grand figure in The Merchant of Venice. He is imagined to be on the wrong side of forty with unkempt hair and dressed in a long Jewish garberdine. 

(2) His Miserliness : His miserliness is peculiarly Jewish. He loves only riches. So he grudges even his servant, Launcelot’s food, sleeping by day and the cost of his clothes. His concentrated love on riches makes him a bad father, and causes Jessica to feel that his house is ‘hell for her. 

(3) His Usury : His usury is no less Jewish. It is based on the authority of his holy scriptures : the interest on money is a well won thrift, as it is based on a bargain. So for him bargain was a way to thrive. 

(4) His Cruelty : Shylock’s cruelty in business dealings is also Jewish through and through. Once a bargain is made with the Jew, the Jew must get his due. Due to his cruelty he did not care for the feelings of his customers and even of his daughter. He is very sensitive to injustice. When his sensitiveness strikes his miserliness, he goes almost mad. 

So to conclude we can say that if not the hero of the play, Shylock, undoubtedly is the most dominant and strong character in the play ‘The Merchant of Venice’.

Correct option is C. Simile

When the volume of the data is large then considering both length and breadth, a diagram drawn is called two dimensional diagram.

• In two dimensional diagrams the total value is shown as an area.
• Square, rectangle, circle, pie diagram are two dimensional diagrams.

Circle diagram: When the volume of the data regarding two or more places, things or times is large, then circle diagrams are drawn for such data.

• In circle diagram, square roots of the volume of different data are taken as the radius of circle. Arranging the radius in ascending or descending order, circles are drawns with centers on the same line at equal distance from each other. When the data on time are given then circles are drawn in order of time only.
• If the square root of the volume is too large, then divide by a constant and if it is too small then multiply by a constant. In this manner determine the radius.

Pie diagram: If the data on different places, things or times consist of several mutually related sub-data are numerically large, pie diagram is drawn.

• In this diagram, the total volume of the data is represented by a circle of suitable radius and this circle is divided into sectors in accordance with sub-data.
• Here, total volume of the data is taken as 360° and the volume of sub-data are expressed in terms of measures of angle and are presented on circle with respective circular sectors.

A diagram drawn by considering only one characteristic of the data is called one-dimensional diagram.

The types of one dimensional diagrams are four :

1. Bar diagram: It is used to represent the data on different places, things or times. To draw bar diagram, the different places, things or times are taken on X-axis and the measure of respective places, things or time on Y-axis with appropriate scale. Bars with equal width at equal distance are drawn with the height proportional to the measure. The diagram formed in such manner is called bar diagram.

In bar diagram the logical order of bars should be maintained. To make comparative study easy, the bars showing places or things should be arranged in proper order on the graph but the bars showing times are presented as it is on graph paper.

2. Multiple or adjacent bar diagram: When the data about different places, things or times are collected on more than one mutually related characteristics, then multiple bar diagram is drawn by placing the related bars close to each other. If the data given are related to time, then bars are drawn in order of, time but when the data are not related to time then they are arranged in ascending or descending order of any one of the characteristics of the data.

3. Simple divided bar diagram: If the data on different places, things or times consist of several mutually related sub-data on different components are given then simple divided bar diagram is drawn.
In this diagram first of all a bar of proper width and height proportional to the total value of the data is drawn. Then it is divided in accordance with the sub-data into different segments by various signs.

4. Percentage divided bar diagram: In simple divided bar diagram the mutually related sub-data cannot be effectively compared. To overcome this difficulty, percentage divided bar diagram is drawn.

In this diagram taking the total value of data as 100%, the percentages of sub-data are calculated. A bar of appropriate width and height proportional to 100% is drawn and is divided in accordance with the percentage of sub-data. By such diagram the mutually related sub-data can be effectively compared but the total value cannot be compared.