EMPOWERMENT....
STATISTICS (ENGLISH)
A special programme for plus one improvement exam 2023
Essay (Statistics)
Q1: Calculate Mean, Median and Mode for the following Data
class frequency
0-20 2
20-40 6
40-60 16
60-80 10
80-100 6
Ans:
X fX Cf
10 20 2
30 180 8
50 800 24
70 700 34
90 540 40
ΣfX=2240
Arithmatic Mean=∑fx/N
=2240/40=56
Median=N/2th item (N=∑f)
= 20 th item
Median Class=40-60
Median=L+(N/2-cf)÷f×C
=40+(20-8)÷16×20
=40+15=55
Mode
Model class=40-60(Class with highest frequency
Mode=L+(f1-f0)C/2f1-f0-f2
=40+(16-6)20/2×16-6-10
= 40+200/16
= 40+12.5=52.5
Q2: Draw ogive and find median.
Class 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
f 5 15 20 10 15 5 15 10
Less than classes Less than cumulative frequency
Less than 5 5
Less than 10 15 + 5=20
Less than 15 20+15+5= 40
Less than 20 10+20+15+5=50
Less than 25 15+10+20+15+5=65
Less than 30 5+15+10+20+15+5=70
Less than 35 15+5+15+10+20+15+5=85
Less than 40 10+15+5+15+10+20+15+5=95
More than classes More than cumulative frequency
More than 0 5+15+20+10+15+5+15+10=95
More than 5 15+20+10+15+5+15+10=90
More than 10 20+10+15+5+15+10=75
More than 15 10+15+5+15+10=55
More than 20 15+5+15+10=45
More than 25 5+15+10=30
More than 30 15+10=25
More than 35 10
Q3:Draw histogram and find mode.
Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
Number 5 10 20 25 20 10 5
of
students
Ans:
Short essay – Statistics (score 5, score 4)
Q1.Describe various methods of data collection.
1. Personal interview 2. Mailing Questionnaire 3. Telephone interview
1. Personal interview:-The investigator conducts face to face interviews with the respondents.
Merits :-* High response* All types of questions can be used
Demerits :-* More money expensive method* More time taking method
2. Mailing questionnaire method:-Questionnaire is sent to each individual by post or mail with a
request to complete and return it by a given date.
Merits :-* Less expensive* Suitable to remote area*
Demerits :-* Can not be used by illiterates* Reactions can not be watched
3. Telephone interview:-The data are collected from the respondents with the help of telephone.
Merits :-* High response rate * Less time
Demerits :-* Limited use* Reactions can not be watched
Q2: Prepare a frequency distribution table by taking class interval of 10 for the following
data. (exclusive method) 29, 8, 10,11, 36, 49,40,35,24,30,32,29,26,46,6,25
Ans:
Class Tally marks frequency
0-10 // 2
10-20 // 2
20-30 //// 5
30-40 //// 4
40-50 /// 3
N=16
Q3. List out the parts of a statistical table.
Ans: a) Table number b) Title c) Unit of measurement. d) Stubs – Row headings. e) Captions –
Column headings. f) Body of the table – Part of numerical data. g) Sources note h) Foot note
Q4. List out the qualities of a good questionnaire.
Ans: * questions should not be too long* questions should move from general to specific * questions should
be precise and clear * questions should be enable to answer quickly * questions should not use double
negatives * questions should not indicate alternatives to the answer
Q5. Draw scatter diagrams representing;
a) perfect negative correlation b) perfect positive correlation c) positive correlation d) negative
correlation
Ans:
positive correlation
Y * *
* *
* *
Xnegative correlation
Y * *
* *
* *
X
Q6: Point out any four issues in the construction of index numbers.
Ans: * Problem based upon the purpose of index.
* Problem based upon selection of appropriate formula.
* Problem of selection of base year.
* Problem based upon data sources.
Statistics (score 3 & 2)
Q1. List out the uses of statistics.
1. Statistics helps to simplify the complexity of data 2. Statistics helps to study the relationship between
different economic variables. 3. Statistics helps to compare data. 4. Statistics helps the government to
formulate plans and policies.
Q2. Explain any three types of classification.
1. Chronological classification 2. Geographical or spatial classification 3. Qualitative classification
4. Quantitative classification
Q3. Explain Pilot survey and it’s advantages.
* survey conducted before actual survey * Try-out survey
Merits :-
* Helps to know the drawbacks of the questionnaire
* Helps to assess the cost and time involved in the actual survey
Q4. Differentiate population and sample.
Population means universe or the totality of items under study. Sample is the subset or part of
population.
Q5. Differentiate between primary data and secondary data.
Primary data - # First hand or original sources of data. # Primary data are in the form of raw
materials.
Secondary data - # Second hand sources. # The data have already been collected for other purposes.
Q6. What are the steps for a project.
1.Identifying a problem 2. Choice of target group 3. Collection of data 4. Presentation of data 5. Analysis and
interpretation 6. Conclusion 7. Bibliography
Q7. Distinguish between quantitative and qualitative data.
The data which can be expressed numerically are called as quantitative data. For example, income, age,
height, weight etc...But the data which can not be expressed numerically are known as qualitative data. For
example, beauty, attitude, behaviour, sex etc...
Q8. What is meant by sampling errors.
Two types.
1. Sampling errors
2. Non sampling errors
1. Sampling errors:-
Mathematical errors. Such errors are related to the size of
the sample. Such errors can be minimised by increasing the size of sample.
2. Non – sampling errors:-
Such errors arise due to; * mistakes in data acquisition * mistakes in copy writings * non-response
etc....
Q9. Explain the uses of index numbers.
> Helps to measure the cost of living
> Helps to calculate purchasing power of money.
> Measures real wage rate.
> Measures rate of inflation
Statistics Objective type
1. The mid point of ‘10 – 15’ is ........
Ans: 12.5
2. Which of the following is a discrete variable?
( rainfall, population, temperature, none of the above)
Ans: population
3. Which is a graphical method of studying correlation?
Ans: scatter diagram
4. Which of the price index depends on base period quantity?
Ans: Laspeyer’s price index
5. Data collected from a news paper is an example of ........ data.
Ans: secondary data
6. Tally marks of a distribution represents
Ans: class frequency
7. Pre-testing of questionnaire is known as ....
Ans: pilot survey
8. Which average is affected most by the presence of extreme items?
Ans: median
9. Population classified on the basis of gender is an example of
Ans: qualitative classification
10. Population in statistics means
Ans; Totality of the items under study
11. Which of the following is a frequency diagram?
a) histogram b) pie-diagram c) simple bar diagram d) multiple bar diagram
Ans: histogram
12. The measure of central tendency which divides the series into two equal parts
Ans: median
13. Which is the most frequently observed value in a series?
Ans; mode
14. Which index number is known as cost of living index?
Ans: consumer price index
15. The value of mode is obtained from
Ans; histogram
16. The sum of deviations of items from arithmetic mean is…..
Ans; zero
Prepared by Academic Council DETA KOZHIKODE
Kiran Kumar; Medical College Campus GHSS ,Kozhikode
Mustafa K.T.M ; Ferook College HSS, Ferook
Deepa.K.T ; GHSS Payyoli.
Prajish Manhaladathil; R.N.M.HSS Narippatta.
Divya Ramachandran; GHSS Puthuppady.
Aneesh Kumar.K.; CKGM HSS Chingapuram, Koyilandy.
Shameem.P.K; Sevamandir HSS Ramanattukara.
Shamil .P.K. ; Nochad HSS,Nochad.
Saleem Melmuri; VMHM HSS Anayamkunnu, Mukkam
Ramachandran.K; GHSS Kokkallur.
