IX SAII MATHS STATISTICS ASSIGNMENT

1.       The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1	98.6	99.2	90.3	86.5	95.3	92.9	96.3	94.2	95.1
89.2	92.3	97.1	93.5	92.7	95.1	97.2	93.3	95.2	97.3
96.2	92.1	84.9	90.2	95.7	98.3	97.3	96.1	92.1	89

                (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.

                (ii) Which month or season do you think this data is about?

                (iii) What is the range of this data?

2.       100 surnames were randomly picked up from a local telephone directory and a frequency             distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	1 - 4	4 - 6	6 - 8	8 - 12	12 - 20
Number of surnames	6	30	44	16	4

                (i) Draw a histogram to depict the given information.

                (ii) Write the class interval in which the maximum number of surnames lie.

3.       The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:                      

Length (in mm)	118 - 126	127 - 135	136 - 144	145 - 153	154 - 162	163 - 171	172 - 180
Number of leaves	3	5	9	12	5	4	2

                (i) Draw a histogram to represent the given data.

                (ii)Also represent by a polygon ( Separately )

                (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

4.       Find out mean, mode  ( Calculate).

Marks	10	20	30	40	50	60	70
Number of students	7	10	10	17	23	15	8

5.       Find the value of p if mean is 7.5

Marks	3	5	7	9	11	13
Number of students	6	8	15	p	8	4

6.       Find the value of  ‘m’ and ‘n’  if mean is 50 and total observations are 90.

Class Marks	10	30	50	70	90
Number of students	17	m	32	n	19

7.       Find median of 

20,26,8,18,24,18,46,23,62,55,70,44

8.       The class mark for a certain continuous frequency distribution are . find class intervals and draw hisrogram.

Class Marks	6	12	18	24	30
Number of students	12	15	20	9	16

9.       The mean of a data is 46. Find the new mean if  each of the observation of a data is

(a) increased by 3   (b) decreased by 2         (c) multiplied by 0.5

10.   Find less than and more than cumulative frequency.

Number of letters	0 - 4	4 - 8	8 - 12	12 - 16	16 - 20
Number of surnames	6	17	23	13	11

IX M SAII QUADRILATERALS ASSIGNMENT 3

IX M SAII QUADRILATERALS ASSIGNMENT 2

IX M SAII QUADRILATERALS ASSIGNMENT 1

Prove the followings:

1. A diagonal of a parallelogram divides it into two congruent triangles. 
2. In a parallelogram, opposite sides and angle are equal. 
3. If each pair of opposite sides of quadrilateral is equal, then it is a parallelogram. 
4. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. 
5. The diagonals of a parallelogram bisect each other. 
6. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. 
7. A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. 
8. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side. 
9. The line segment joining the mid- points of the two sides of a triangle is parallel to the third side. 
10. Show that each angle of a rectangle is a right angle. 
11. Show that the diagonal of a rhombus are perpendicular to each other. 
12. Show that the bisectors of the angles of a parallelogram form a rectangle. 
13. ABCD is a parallelogram (||gm) in which P and Q are mid-points of opposite side AB and CD. If AQ intersects DP at S and BQ intersects CO at R, show that

(i) APCQ is ||gm                              (ii)DPBQ is ||gm                             (iii) PSQR is ||gm

14. In Triangle ABC, D, E and Fare respectively the mid points of sides AB, BC and CA. Show that triangle ABC is divided into four congruent triangle by joining D, E and F
15. If the diagonal of a parallelogram are equal, then show that it is a rectangle. 
16. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. 
17. Show that the diagonals of a square are equal and bisect each other at right angles. 
18. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. 
19. In Δ ABC and Δ DEF, AB=DE, AB||DE, BC=EF and BC||EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that:

(i) Quadrilateral ABCD is a parallelogram.

(ii) Quadrilateral BEFC is a parallelogram.

(iii) AD||CF and AD=CF

(iv) Quadrilaterals ACFD is a parallelogram

(v) AC=DF

(vi) Δ ABC ≅ Δ DEF. 

20. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that:

(i) SR||AC and SR =1/2 AC                          (ii) PQ=SR                          (iii) PQRS is a parallelogram. 

21. ABCD is a rhombus and P, Q, R and S are the mid- point of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. 
22. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. 
23. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. 
24. ABC is a triangle right angle at C. A line through the mid-points M of hypotenuse AM and parallel to BC intersects AC at D. Show that

(i) D is the mid –point of AC                      (ii) MD ┴ AC                      (iii) CM=MA=1/2 AB.