13. Statistics
- 1. REAL NUMBERS
- 2. POLYNOMIALS
- 3. PAIR OF LINEAR EQUATIONS IN TWOVARIABLES
- 4. QUADRATIC EQUATIONS
- 5. ARITHMETIC PROGRESSIONS
- 6. TRIANGLES
- 7. COORDINATE GEOMETRY
- 8. TRIGONOMETRY
- 9. APPLICATIONS OF TRIGONOMETRY
- 10. CIRCLES
- 11. AREAS RELATED TO CIRCLES
- 12. SURFACE AREAS AND VOLUMES
- 13. STATISTICS
- 14. PROBABILITY
- 1APPENDIX A1 PROOFS IN MATHEMATICS
- APPENDIX A2 MATHEMATICAL MODELLIING
13.1 Introduction
13.2 Mean of Grouped Data
Example 1:
The marks obtained by 30 students of Class X of a certain school ina a Mathimatics paper containing of 100 marks are presented in table below. Find the mean of the marks obtained by the students.
| Marks obrtained (xi) | 10 | 20 | 36 | 40 | 50 | 56 | 60 | 70 | 72 | 80 | 88 | 92 | 95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Number os students (fi) | 1 | 1 | 3 | 4 | 3 | 2 | 4 | 4 | 1 | 1 | 2 | 3 | 1 |
Example 2:
The table below gives the percentage distribution of female teachers in athe primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section.
| Marks obrtained (xi) | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 |
|---|---|---|---|---|---|---|---|
| Number os students (fi) | 6 | 11 | 7 | 4 | 4 | 2 | 1 |
Example 3:
The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What dows the mean signify?
| Marks obrtained (xi) | 20 - 60 | 60 - 100 | 100 - 150 | 150 - 250 | 250 - 350 | 350 - 450 |
|---|---|---|---|---|---|---|
| Number os students (fi) | 7 | 5 | 16 | 12 | 2 | 3 |
EXERCISE 13.1
1. A survey was conducted by a group of students as a part os their environment awareness programme, in whick they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
2.3. Relationship between Zeroes and Coefficients of a Polynomials.
Example 2:
Find the zeroes of the quadratic polynomials x2+ 7x + 10, and verify the relationship between the zeroes and the coefficients.
Example 3:
Find the zeroes of the polynomials x2- 3, and verify the relationship between the zeroes and the coefficients.
Example 4:
Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.
Example 5:
Verify that 3, -1, -1/3 are the zeroes of the cubic polynomial p(x) = 3x3 - 5x2 - 11x - 3, and then verify the relationship between the zeroes and the coefficients.
Exercise 2.2
1. Find the zeroes of the following quadratic and verify athe relationship between the zeroes and the coefficients.
(i) x2 - 2x - 8 (ii) 4s2 - 4s + 1 (iii) 6x2 -3 - 7x (iv) 4u2 + 8u (v) t2 - 15 (vi) 3x2 - x - 4
2. Find a quadratic polynomial each with the given numbers as the sum and product of it's zeroes respectively.
(i) 1/4, 1 (ii) √2, 1/3 (iii) 0,√5 (iv) 1, 1 (v) -1/4, 1/4 (vi) 4, 1
3. Plotting a cubic polynomials in a graph.