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Class 12 Education Chapter 7 Statistics in Education
Selected Questions-Answers
A. Fill in the blanks: (Marks for each – 1)
1. The difference between the highest and the lowest value is called—.
Ans: Range.
2. Range is a measure of —.
Ans: Variability.
3. Histogram is a — line diagram.
Ans: Simple.
4. In a polygon, the frequencies are plotted on the — axis.
Ans: OY.
5. The mode of a distribution is the value having the highest —.
Ans: Frequency.
6. In a histogram, the area of each rectangle is proportional to the—.
Ans: Frequency within the class interval.
7. In a histogram, each rectangle of a class is formed on the basis of—.
Ans: Frequency.
8. — diagram is a bar diagram without gaps.
Ans: Histogram.
9. — is appropriately a simple line diagram.
Ans: Frequency polygon.
10. In the assumed mean method, the assumed mean is the — of any class interval.
Ans: Mid-point.
11. The three commonly used measures of central tendency are mean, — and mode.
Ans: Median.
12. The measure used to know how far the values are scattered from the measure of central tendency is called —.
Ans: Variability or deviation.
13. The value below which we obtain half of the total items is called—.
Ans: Median.
14. In a frequency distribution table, the value which occurs most frequently is called —. H. S. ’15
Ans: Mode.
15. While determining the measure of central tendency as —, all values are taken into consideration. H. S. ’18
Ans: Mean.
B. State whether True or False: (Marks for each – 1)
1. The median is affected by the highest value.
Ans: False.
2. Mode is not affected by the range.
Ans: True.
3. The median is the middle value of a class interval.
Ans: True.
4. A polygon is a line diagram.
Ans: True.
5. Central tendency is the representative value of a set of data.
Ans: True.
6. Even if the exact values of extreme items are not given, the median can be determined.
Ans: True.
7. In a frequency polygon, frequencies are plotted on the OX axis.
Ans: False.
8. Mean is a reliable measure of central tendency.
Ans: True.
9. We can determine statistics from statistics and by statistics.
Ans: True.
10. Pie chart is a circle broken up to represent data.
Ans: True.
11. The difference between the highest and lowest value is called range.
Ans: True.
12. Median is sensitive to extreme values.
Ans: False.
13. The first quartile is the value below which 75 percent of the items lie.
Ans: False.
C. Answer the following questions:
1. Why is histogram called a continuous bar diagram?
Ans: In a histogram, frequencies are represented by rectangles drawn according to their heights. These rectangles are adjacent to each other without any gaps; therefore, it is called a continuous bar diagram.
2. What is a pie chart?
Ans: A pie chart is an important circular diagram. In a pie chart, a circle is divided into sectors according to requirement, and each sector represents a specific part of the data.
3. What is frequency?
Ans: In statistics, frequency refers to how often a particular value, category, or outcome appears in a dataset. Arranging unorganized numbers in an orderly manner is called frequency distribution. For a particular frequency distribution, all class intervals should be of equal width.
4. What do you mean by class interval?
Ans: In statistics, collected data are divided into classes as required. Each class is called a class interval. All class intervals are generally of equal width.
5. What is a frequency distribution table?
Ans: Arranging disorganized numbers systematically in tabular form is called a frequency distribution table. Tabulation gives a new form to the data and makes them easier to understand.
6. What is meant by range?
Ans: Range is the simplest measure of dispersion of a set of numbers. It is obtained by subtracting the smallest value from the largest value. For example, suppose a test is administered to 50 boys and 50 girls. If the boys’ marks range from 16 to 62 and the girls’ marks range from 18 to 44, then the range of boys’ marks is 62 – 16 = 46, and the range of girls’ marks is 44 – 18 = 26. Though simple, it can provide meaningful information about variability. It helps in making comparative studies between two or more groups. However, if the number of observations is very small, the reliability of range decreases.
7. What is a bar diagram? What are its types? H. S. ’15, ’20
Ans: A bar diagram represents frequencies by vertical or horizontal bars drawn on a common base according to their specific values. Bar diagrams are of two types: discrete bar diagrams and continuous bar diagrams. When the class intervals are separate from one another, a discrete bar diagram is used. When the data are continuous, a continuous bar diagram or histogram is used.
8. What is meant by pie chart? Describe the rules for constructing a pie chart.
Ans: A pie chart is a type of circular diagram. In a pie chart, data are represented within a circle. The total value of the data is taken as 360°. Then the 360° angle is divided into proportional sectors according to the data values, and each sector represents the numerical value of individual data.
9. Write the differences between histogram and a frequency polygon.
Ans: The differences between histogram and frequency polygon are as follows— Frequency Polygon: To draw a frequency polygon, graph paper is used. First, a horizontal line named OX is drawn. Second, a vertical line named OYis drawn. Third, class intervals are plotted on the OX axis and frequencies onthe OY axis. Fourth, the plotted frequency points are joined by straight linesto obtain the polygon. Histogram: To draw a histogram, a horizontal line OX and a vertical line OY are drawn as in the frequency polygon. Class intervals are plotted on the OX axis and frequencies on the OY axis. Rectangles are drawn over each class interval with heights proportional to frequencies; these adjacent rectangles form the histogram.
10. What is frequency distribution? Discuss its use in education and statistics.
Ans: Frequency distribution is a convenient technique for arranging collected data systematically and in an organized form. It is a type of tabulation in which collected values are divided into several groups, and the number of observations falling into each group is written against it. Thus a frequency distribution table is prepared. In statistics, its necessity is noteworthy. For example, if the marks obtained by students of a class in a subject need to be known quickly, by preparing a frequency distribution table we can find the highest and lowest marks.
Moreover, mean, median and mode can easily be calculated from such a table.
11. What is quartile deviation? Discuss its use as a measure of variability. H. S. ’20
Ans: Quartile deviation is a suitable measure of dispersion. It is defined as half of the difference between the third quartile (75 percent point) and the first quartile (25 percent point).
Its uses as a measure of variability are—
(a) It is used when the median is the measure of central tendency.
(b) It is useful when the upper or lower parts of a distribution are incomplete.
(c) It helps to understand the spread of the middle 50 percent of the data.
12. Describe the merits of range and quartile deviation as measures of variability.
Ans: The merits of range are—
(a) It is very easy to calculate and understand.
(b) It is useful as a rough measure.
(c) It helps in giving a brief description of data.
(d) It is the simplest measure of dispersion. The merits of quartile deviation are—
(a) Since it is not dependent on extreme values, it is more reliable than range.
(b) It is easy to calculate and interpret.
(c) It is a useful measure of dispersion, especially for skewed distributions.
13. What is meant by the deviation or variability of data? What are its measures? Write about the uses of range.
Ans: The study of how far the collected values lie close to or away from the mean is called measurement of variability or deviation. The measures of variability are—
(a) Range,
(b) Quartile deviation,
(c) Mean deviation,
(d) Standard deviation.
The uses of range are—
(a) It is useful as a rough measure.
(b) It indicates the difference between the highest and lowest values.
(c) It provides an idea about the dispersion of data.
14. What is a circular diagram? Describe the method of constructing a circular diagram.
Ans: In statistics, a circular diagram or pie diagram is used to represent data. In such a diagram, the whole data are assumed to be represented by a circle. The values of different characteristics are shown by sectors of the circle. The total value of the data is taken as 360°. Then the 360° angle is divided into proportional parts according to the data, and each part represents thenumerical value of the corresponding data.
15. Write the formula for calculating the mean by the assumed mean method. H.S. ’19
Ans: The formula for calculating the mean by the assumed mean method is:
Mean (X¯) = A + (?fd / ?f) × i
where,
A = Assumed Mean,
f = Frequency,
d = Deviation of class mark from the assumed mean,
i = Class interval width.
17. Mention two characteristics of population education.
Ans: The two characteristics of population education are—
(a) Population education is a governmental educational programme.
(b) It is an awareness-oriented programme.
