question paper module 5
Part A (1 Mark Questions with Answers)
1. What is Statistics?
Statistics is the science of collecting, organizing, presenting, analyzing and interpreting numerical data.
2. What is classification of data?
Classification is the process of arranging data into groups or categories based on common characteristics.
3. What is tabulation?
Tabulation is the systematic presentation of data in rows and columns.
4. What is frequency distribution?
Frequency distribution is a table showing how many times each value occurs in a dataset.
5. What is histogram?
A histogram is a graphical representation of continuous data using adjacent rectangles.
6. What is pie diagram?
A pie diagram is a circular graph that represents the proportion of different categories in a dataset.
7. What is mean?
Mean is the average value obtained by dividing the sum of all observations by the total number of observations.
8. What is median?
Median is the middle value when data are arranged in ascending or descending order.
9. What is range?
Range is the difference between the highest and lowest value in a dataset.
10. What is correlation?
Correlation is a statistical measure that shows the relationship between two variables.
Part B (2 Marks Questions with Answers)
11. Explain the need of statistics in education.
Statistics is needed in education to:
- Analyze students’ performance
- Conduct educational research
- Compare academic achievements
12. Write any two advantages of tabulation.
- It simplifies large data.
- It helps in easy comparison.
13. Differentiate between bar diagram and histogram.
| Bar Diagram | Histogram |
|---|---|
| Used for discrete data | Used for continuous data |
| Bars have gaps | Bars touch each other |
14. What is frequency polygon?
A frequency polygon is a graph obtained by joining the midpoints of the tops of histogram rectangles with straight lines.
15. What are measures of central tendency?
Measures of central tendency are statistical methods used to find the central value of data.
Examples: Mean, Median, Mode.
16. What is standard deviation?
Standard deviation is a measure of variability that indicates how much the values deviate from the mean.
17. What is Spearman’s rank correlation?
Spearman’s rank correlation is a method used to measure the relationship between two variables using ranks.
Formula:
R = 1 - \frac{6\sum d^2}{n(n^2-1)}
18. Write two characteristics of normal probability curve.
- The curve is bell shaped.
- Mean, Median and Mode are equal.
Part C (4 Marks Problems with Answers)
19. Calculate Mean
| X | 5 | 10 | 15 | 20 | 25 |
|---|---|---|---|---|---|
| f | 2 | 3 | 5 | 4 | 1 |
Solution:
| X | f | fX |
|---|---|---|
| 5 | 2 | 10 |
| 10 | 3 | 30 |
| 15 | 5 | 75 |
| 20 | 4 | 80 |
| 25 | 1 | 25 |
Σf = 15
ΣfX = 220
Mean formula
Mean = \frac{\Sigma fX}{\Sigma f}
Mean = \frac{220}{15} = 14.67
Mean = 14.67
20. Find Median
| X | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|
| f | 3 | 7 | 9 | 5 | 1 |
Solution:
| X | f | Cumulative f |
|---|---|---|
| 4 | 3 | 3 |
| 6 | 7 | 10 |
| 8 | 9 | 19 |
| 10 | 5 | 24 |
| 12 | 1 | 25 |
Total frequency N = 25
Median position
\frac{N+1}{2} = \frac{26}{2} = 13
13th value lies in X = 8
Median = 8
21. Find Range
Data:
10, 15, 18, 20, 25, 30
Formula
Range = Highest - Lowest
Range = 30 - 10
Range = 20
22. Find Spearman Rank Correlation
| X | Y |
|---|---|
| 10 | 8 |
| 20 | 18 |
| 30 | 28 |
| 40 | 35 |
| 50 | 45 |
| Rank X | Rank Y | d | d² |
|---|---|---|---|
| 1 | 1 | 0 | 0 |
| 2 | 2 | 0 | 0 |
| 3 | 3 | 0 | 0 |
| 4 | 4 | 0 | 0 |
| 5 | 5 | 0 | 0 |
Σd² = 0
n = 5
Formula
R = 1 - \frac{6\sum d^2}{n(n^2-1)}
R = 1
Correlation = 1 (Perfect positive correlation)
Part D (10 Marks Question with Answer)
23. Explain the importance of statistics in education.
Statistics plays an important role in education.
1. Evaluation of students
It helps teachers measure students’ performance through tests and examinations.
2. Educational research
Statistics helps researchers collect and analyze data in research studies.
3. Comparison of performance
It helps compare achievements of students, classes and schools.
4. Decision making
Educational administrators use statistical data for planning and policy making.
5. Presentation of data
Statistical data can be presented through tables, charts and graphs.
6. Measurement of learning outcomes
Teachers can measure learning outcomes effectively using statistical methods.
Thus statistics is very important in teaching, evaluation and educational research.
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