1. What is Statistics?
Ans: Statistics is a process of scientific method that deals with description of data in the form of numerical value which helps for collection, tabulation, classification, analysis and interpretation of data related top p[re determined purpose is called Statistics.
2. Explain the meaning of the term ‘Statistics’.
Ans: The term ‘Statistics’ have been derived from ‘Latin’ word ‘Status’, Greek word ‘Statistique’, Italian word ‘Statista’, and German word ‘Statistic’. So that meaning of these word is ‘Political state’ or ‘a government’.
3. Discuss the needs and importance of statistics in education and psychology.
Ans: Statistics is very important in education and psychology which are discussed in the following bellows:
i. For Construction of Psycholigical Test:
Statistical methods helps in the construction of various psychological test like- achievement test, intelligence test, aptitude test, interest inventories, attitudes etc.
ii. For presentation score:
It helps us in proper and systematic presentation of the scores obtained from various educational and psychological cal tests and measure.
iii. To make prediction:
It helps the teacher to render guidance to the students to make prediction regarding their future progress.
iv. To know individual difference:
Statistics also helps to know individual difference of the students in terms of their academic performance.
v. To keep various types of Record:
It provides the teachers to keep various records of his students as well as of the school record.
vi. To make selection, classification and promotion:
Statistics also helps the teachers to make selection, classification and promotion of the students.
4. What are the different methods of Statistics?
Ans: There are some methods of statistics to study and evaluate data collected from various sources:
(a) Frequency distribution.
(b) Measures of central tendency.
(c) Measures of variability.
(d) Graphical representation.
5. What do you mean by Frequency distribution? What steps you will follow do construct a frequency distribution table?
Ans: The scores of data which are tabulated in a frequency table is known as frequency distribution or frequency distribution table. For constructing a frequency distribution table the following steps are essentials:
i. Determination of Range:
Firstly, We should find out the range of raw scores. Range refers to the difference between the highest and the lowest scores.
ii. Class-Interval:
After finding the range, Secondly we should determined the class-interval. The class-interval depends upon the range and the number of interval required according to the range of the scores.
iii. Midpoint of the class-interval:
The midpoint of interval is the logical choice that the scores are represented with in a given class-interval by some single value.
iv. Tallies:
After determining the class-interval, we should make tallies. A tally represent a scores that lies in anyone particular class-interval.
v. Frequencies:
After making the tallies, In final steps, we should given the number of frequencies. The total number of frequencies is the same as the total number of scores. We represent by ‘N’ the total number of frequencies.
N.B- Without mid point of the class-interval, frequency distribution table we can put. But giving mid point of the class-interval is better for other purpose.
6. Tabulate the following 50 scores into frequency distribution using an interval of 5.
75, 62, 37, 48, 63, 62, 87, 62, 65, 81
71, 67, 46, 61, 38, 55, 68, 52, 55, 62
41, 60, 58, 83, 48, 57, 65, 60, 74, 51
51, 61, 77, 70, 77, 78, 32, 63, 35, 63
56, 73, 71, 69, 60, 74, 46, 68, 43, 64.
Solution:
Highest Score= 87
Lowest score= 32
Range= 87-32=55
Class-
Interval –Midpoint- Tallies–frequency
85 – 89 87 I 1
80 – 84 82 II 2
75 – 79 77 IIII 4
70 – 74 72 IIII I 6
65 – 69 67 IIII I 6
60 – 64 62 IIII IIII III 13
55 – 59 57 IIII 5
50 – 54 52 III 3
45 – 49 47 IIII 4
40 – 44 42 II 2
35 – 39 37 III 3
30 – 34 32 I 1
N= 50
7. What is Measures of central tendency? Write two uses of measures of central tendency.
Ans: Measure of Central Tendency is the central value of a set of data which is defined as “the statistical measure that identifies a single as representative of an entire distribution.”
The two uses of measure of central tendency are mention below:
(a) It is an average which represents all of the scores made by the group as a whole.
(b) It enables to compare two or more groups in terms of typical performance.
8. What are the types of measures of central tendency?
Ans: There are commonly three types of measures of central tendency. These are:
(a) Arithmetic Mean.
(b) Median
(c) Mode
9. What is Mean or Arithmetic Mean? Write three uses or merits of Mean as a measure of central tendency.
Ans: The scores are added and their sum is then divided by the number of the item is called Mean. It is defined as ‘the average of a set of number which reflects the central tendency of the position of the numbers.’
The two uses of Mean as a measure of central tendency are:
(a) The mean can be used to know average idea or picture of a set of data.
(b) It is used to comparing two or more groups or frequency distribution in terms of typical or characteristics performance.
(c) It is used because it is the simplest but most useful measure of central tendency.
10. What is Median?
Ans: The median is the value in the middle of a data set that lie 50% of the case when the data are arranged in ascending or descending order which is called Median.
11. Mention three advantages or merits of Median as a measure of central tendency.
Ans: The three advantages or merits of Median as a measure of central tendency are mentioned below:
(a) Median is very easy to calculate and also simple to understand as a measure of central tendency.
(b) It is not affected by the extreme values between the largest and the smallest values because it is a positional average which is not dependent on magnitude.
(c) It’s value can be represented graphically with the help of ogive curves. But it is not possible in case of an arithmetic mean.
12. Write two disadvantages or demerits of Median as a measure of central tendency.
Ans: The two disadvantages or demerits of Median as a measure of central tendency.
(a) In ungrouped data, the arranging scores of the data in ascending or descending order of magnitude is time consuming in case of a large number of observations.
(b) It is a positional average which does not consider the magnitude of all the items.
13. What is Mode ?
Ans: The number of scores that occurs in the list several times which is known as Mode.
The formula of Mode is –
Mode= 3 Median – 2 Mean
14. Write two uses of Mode.
Ans: The two uses of mode are mentioned below:
(i) Mode is used where quick and appropriately measure of central tendency is desired.
(ii) Mode is used when we need to know the most often recurring score or value of the item in a series.
(iii) We complete mode when we have a graphical representation of the distribution.
15. What do you mean by Measure of Variability?
Ans: The extended data which cases tend to gather round the central tendency and to which they disperse themselves in a data set or statistical distribution is called Measures of Variability or Variation.
16. What are the different methods of Measures of Variability?
Ans: There are mainly four methods of measures of variability which are mentioned below:
(i) Range
(ii) Quartile Deviation
(iii) Mean Deviation or Average deviation
(iv) Standard Deviation
17. What is Range?
Ans: The difference between the highest and the lowest scores in a series is called Range.
18. Write two uses of Range.
Ans: The two uses of Range are:
(a) When rough and quick comparison is needed then we can use range as a measure of variability.
(b) When knowledge of extreme scores is all that is wanted then we can use range as a measure of variability.
19. Write the formula of Range in ungrouped data.
Ans: (Highest score – lowest score).
20. Write two difference between polygon and histogram.
Ans: The two difference between polygon and histogram are:
(i) The frequency polygon is a line graph of the given frequency distribution whereas, Histogram is essentially the bar graph of this distribution.
(ii) In the frequency polygon, all of the scores within given interval are represented by the midpoint of the interval. But in a histogram the scores are spread uniformly over the entire interval.
(iii) Frequency polygon gives a much better conception to know the trend of the distribution, But a Histogram is unable to tell such a thing.
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