AHSEC| CLASS 12| EDUCATION| CHAPTER - 7| EDUCATIONAL STATISTICS| SOLVED QUESTIONS FOR 4 MARK EACH| H.S. 2ND YEAR

EDUCATIONAL STATISTICS

Solved questions for 4 mark each:

1. Difference between rectangle and polygon.

Ans: Histogram: The totality of all the rectangles drawn on a horizontal line with areas proportional to the frequencies of the respective class intervals is called a histogram.

Frequency Polygon: The data collected and tabulated can be represented graphically with the help of frequency polygons. To draw a frequency polygon, a baseline has to be drawn first. Let the base line be 'X'. Then a vertical line named 'Y' should be drawn on the left side. Then we plot the mind-points of the class-interval along the line Y. By joining the points, we will get the frequency polygon.

2. What are the different parts of a frequency distribution table? Exam paper - 2017

Ans: The different parts of a frequency distribution table are:

(i) Determination of Range: Range is the difference between the highest and the lowest marks. It is not a satisfactory indicator of variability as it only takes into account the extremes of the series. It is unreliable when N is small or when the frequency distribution has many gaps (zero f).

Consider the following series:

(a) 100, 40, 40, 20 (b) 80, 30, 50, 40

Central tendency

Variability

Series (a) Mean = 50

Series (b) Mean = 50

Range = 100-20=80

Range = 80-30=50

(ii) Size: In order to make a classification, the size of the grouping has to be determined. The class interval can be sized based on the range using 3, 4, 5, 10 units in length. The number of class intervals can be determined by dividing the range by a tentatively selected grouping interval.

(iii) Tally: Tally displays the score which lies in a particular class interval. A tally is given for each score opposite the corresponding class interval. The fifth match is made by a slash (llll) on the last four heights.

(iv) Frequencies: Frequencies are represented in the third column of the frequency distribution. When all the frequencies are added, the total number of cases of N is obtained.

(v) Mid-point of an interval in a frequency distribution: If all the scores within a given class-interval are represented by a single one, then the mid-point of the interval is logical.

3. What do you understand by frequency distribution of statistical data? Exam paper - 2013, 2014

Ans: Frequency Distribution Table: The table where the raw scores are systematically arranged may be known as 'Frequency Distribution Table'. In a frequency distribution table, there are three columns which are class interval, tally mark and frequency. The range of the variable in a particular sub-category is called the class-interval and the number of items in a class-interval is known as the class frequency. The distribution in the form of class frequencies on class intervals is called frequency distribution of variables.

In order to prepare the frequency distribution table, the following methodological steps should be followed:

(a) To identify the lowest and highest score of as given number.

(b) Choose the magnitude of the class interval. Correct the gap position.

(d) Placing tally marks of the respective intervals on the figure to show clearly the number of frequencies.

The different parts of the frequency distribution table are:

(i) Size: In order to classify, the size of the grouping has to be determined. The class interval can be sized based on the range using 3, 4, 5, 10 units in length. The number of class intervals can be determined by dividing the range by a tentatively selected grouping interval.

(ii) Tally: Tally displays the score which lies in a particular class interval. A tally is given for each score opposite the corresponding class interval. The fifth match is made by a slash (llll) on the last four heights.

(iii) Frequencies: Frequencies are represented in the third column of the frequency distribution. When all the frequencies are added, the total number of cases of N is obtained.

(iv) Mid-point of an interval in a frequency distribution: If all the scores within a given class-interval are represented by a single one, then the mid-point of the interval is logical.

4. Explain how a frequency table is prepared indicating the number of classes and the width of the class intervals.

Ans: Frequency refers to the number of times a particular value appears in a distribution. For example, in the distribution of values, 4, 5, 5, 6, 5, 4, 5 has a frequency of 3, 4 has a frequency of 2, and 6 has a frequency of 1.

5. Discuss the various methods of graphical representation of educational data. Exam paper - 2020

Ans: Graphical representation of frequency distribution can be done mainly with the help of four types of groups.

They are:

(i) Frequency polygon: A frequency polygon is a figure representing data on a graph paper. Score value is measured along the x-axis and frequency along the y-axis. The exact limits of the intervals are shown at regular distances from the origin along the baseline and the frequencies against each interval are measured on the y-axis.

(ii) Histogram: This is another tool where the class interval is represented by a separate rectangle. The area of each rectangle of the histogram is directly proportional to the measures within the interval.

(iii) Bar Diagram: When statistical data is represented by rectangular bars, the diagram thus drawn is called a bar diagram. They consist of a set of equidistant rectangles, one for each group or range of data, with values represented by the height of the rectangles.

(iv) Pie-diagram: When a circle is sub-divided into different sectors to represent different data, it is called Pie-diagram. To represent the data by pie-diagram we first draw a circle with any radius. The angle at the center of the circle is 360 degrees which represents the set. It can be divided into several smaller angles whose degrees will be proportional to the values of the components. The angle representing each item or sector can be calculated with the help of the following formula

6. Represent the following data of student’s enrolment in a primary school by bar diagram.

Class

Boys

Girls

III

Ans:-

Class

Boys

Girls

III

7. What is Quartile Deviation? If 1st quartile is 34.56 and Quartile Deviation is 8.97, find the 3rd Quartile. Exam paper - 2015, 2017,20

Ans: The quartile deviation is the half-distance between the first and third quartiles or the 25th and 75th percentiles in a frequency distribution. The first quartile in a distribution refers to the point below which 25% of the scores fall, i.e., one fourth of the total number of scores, denoted by the symbol Q₁. The third quartile in a distribution refers to the point below which 75% of the scores fall, i.e., three fourth of the total number of scores denoted by Q₃.

The quartile deviation is also called the semi-interquartile or interquartile range.

The quartile deviation or Q is calculated by the formula.

8. Explain how to prepare a frequency table indicating the choice of number of classes and width of class intervals.

Ans: The organization of data and grouping of scores into classes or ranges is known as frequency distribution. Frequency stands for the number of scores in a test or experiment.

Frequency distribution classifying scores by following essential steps – (i) determination of range (ii) class interval (iii) tally mark (iv) frequencies (v) midpoint of an interval with the help of frequency distribution table we classify the collected Can organize data in a systematic way.

9. Mention the advantages of central tendency.

Ans: The advantages of central tendency are as follows -

(i) It is an average or typical value, which represents all the marks scored by the group as a whole.

(ii) It helps in comparing two or more groups in terms of specific performance.

(iii) The measure of central tendency can form the representational value of any phenomenon or facts to a great extent.

(iv) Through the measures of central tendency, we can have a different view about the collected data or facts.

10. Result of a primary school is present below. Draw a pie diagram.

Class

No. of Students passed

III