AHSEC| CLASS 12| EDUCATION| CHAPTER - 7| EDUCATIONAL STATISTICS| SOLVED QUESTIONS FOR 5 MARK EACH| H.S. 2ND YEAR
EDUCATIONAL STATISTICS
Solved questions for 5 mark each:
1. Define
statistics? Explain the utility of the science in the field of education and
Psychology. Exam paper - 2018
Ans:
According to Seligman, Statistics is the science which deals with the methods
of collecting, classifying, presenting, comparing and interpreting the
numerical data collected by means of some light on any field of investigation.
The utility
of statistics in education and psychology can be described below:
(i) To
measure intelligence, memory etc.: Statistics helps to measure and record
the intelligence, memory, thinking, taste etc. of the students and on analyzing
such data generally very useful conclusions are drawn.
(ii)
Construction of Intelligence Tests: It also helps in construction of
intelligence tests which are based on the analysis of past records of
intelligence of the students. The importance of intelligence tests in the field
of education and psychology can hardly be overstated.
(iii)
Fixation of Criterion: For effective measurement of achievement and other
mental abilities of the student fixation of the criterion as a standard of
comparison is necessary. Comparative study of mental abilities in terms of
individual scores is not possible without a standard criterion. Only statistics
can help us determine a reliable parameter for such a study.
(iv)
Maintenance of records: In almost all educational institutions records are
kept regarding income-expenditure, number of students, examination results etc.
Statistical methods are used to keep such records.
2. What is a
frequency distribution? State its importance in statistical investigation.
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 a given number.
(b) Choose the
magnitude of the class interval. Correct the gap position.
(c) Giving
tally marks of scores in the column matching the respective class intervals.
(d) Placing
tally marks of the respective intervals on the figure to show clearly the
number of frequencies.
Significance:
(i) It can
reduce the size of scores to make them easily understandable.
(ii) The table
can show us whether the scores are more inclined towards the upper or lower
limit of the distribution than whether they are normally distributed.
(iii) The
table can show in which class interval the highest or lowest frequencies are
found.
(iv) In
addition, aggregate is helpful for making graphic representation of data by
drawing polygons or histograms.
3. Calculate
the mean by long method from the following table Exam paper – 2015
|
Class
Interval |
Frequencies |
|
78-79 76-77 74-75 72-73 71-70 68-69 66-67 64-65 62-63 60-61 |
3 5 6 8 7 14 11 2 5 4 |
4. Calculate the mean marks of
30 students given in the following distribution by 'assumed mean' method and
also find the median of the distribution. (8 points)
|
Class Interval |
33-36 |
29-32 |
25-28 |
21-24 |
17-20 |
13-16 |
9-12 |
5-8 |
1-4 |
|
F |
1 |
1 |
4 |
10 |
5 |
3 |
3 |
2 |
1 |
5. What is variability of
scores and what are its measures? Discuss the uses of range.
6. What is quartile deviation?
Discuss the uses of quartile deviation as a measure of variability.
Ans: Quartiles are those 3
values of distribution which divide the entire distribution into 4 equal parts.
The quartile
deviation (Q) is half the scale distance between the 75th and 25th percentiles
in a frequency distribution. The 25th percentile or Q1, also called
the first quartile, is the bottom point those accounts for 25% of the score.
The 75th percentile or Q3, also called the third quartile, is the
bottom point those accounts for 75 percent of the score.
Formula to
find – Q3 = 3/1 (Q3 – Q1)
To find Q, we
must calculate the Q1 or 25th (P25) and Q3 or
75th (P75) percentiles. These values obtained by the same method
employed in the calculation of mean formula are -
Uses:
(i) It helps
to find out the degree of variability or deviation or dispersion of the data.
(ii) It makes
possible comparisons between different groups.
(iii) It is
very important in comparing the solutions to various social problems in
different regions.
(iv) It serves
as a useful check on central tendency in drawing conclusions from averages or
comparisons of measures.
(v) They are
of great importance in statistical analysis of data.
7. Explain the properties of
range and quartile deviation as measures of variability.
Ans: Properties of Category:
(i) When the
data are too few or too scattered to justify the computation of a more precise
measure of the variability range.
(ii) Range is
used when the knowledge of the peak score of the total spread is sufficient.
(iii) It is
used for coarse and quick comparison.
8. Discuss their relative
importance of range and quartile deviation as measures of variability.
Ans: Properties of
Quartile Deviation: Quartile Deviation can be defined as half of the distance
of the scale between 75th and 25th percentile in a frequency distribution. The
25th percentile of the distribution of scores is in the first quartile, or Q1,
and the 75th percentile is in the third quarter, or Q3. The 50th
percentile of a distribution is popularly known as the mean or median. The
difference between the third and first quartile is the inter-quartile
difference. Dividing this difference by 2 gives us the quartile deviation.
The formula
representing the concept is:
Q = Q3
- Q1 / 2
(i) When
median is a measure of center frequency.
(ii) When
there are scattered or extreme scores that affect the standard deviation (SD)
dissimilarity.
(iii) When the
concentration is around the mean, 50% of the cases in the middle are of primary
interest.
(iv) When
delivery is incomplete at either end.
9. Calculate the Quartile
deviation for the following distribution of scores. Exam paper - 2016, 2019
|
Class Interval |
50-54 |
45-49 |
40-44 |
35-39 |
30-34 |
25-29 |
20-24 |
15-19 |
10-14 |
5-9 |
|
F |
1 |
7 |
3 |
4 |
6 |
7 |
12 |
6 |
8 |
2 |
10. Calculate the mean by long
method from the following table:
|
Class Interval |
78-79 |
76-77 |
74-75 |
73-72 |
71-70 |
68-69 |
66-67 |
64-65 |
62-63 |
60-61 |
|
F |
3 |
5 |
6 |
8 |
7 |
14 |
11 |
2 |
5 |
4 |
11. Represent the following
data of student’s enrolment in a primary school by pie diagram. Exam paper - 2014, 2018
|
Class |
No. of Students |
|
I II III IV |
40 56 50 45 |
12. Represent of following data of student’s enrolment in
a primary school by bar diagram. (Use graph paper). Exam paper - 2014
|
Class |
Boys |
Girls |
|
I II III IV |
55 35 46 44 |
42 48 40 36 |
13. Make a comparative study of the properties of mean,
median and mode as measures of central tendency.
Ans: A comparative study of the properties of mean,
median and mode as measures of central tendency is as follows:
(i) Mean is used
to know the representative value of the scores.
The median is
used when the exact midpoint of a distribution is required.
Mode is used
when a quick and accurate measure of central tendency is required.
(ii) When the
distribution of scores is normal, the natural and justified mean is used.
The median is
used when the scores are clearly skewed or abnormally distributed.
The mode is
used when the highest recurring score is sought.
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