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#### Q. 1.     What cross-sections do you get when you give a             (i) vertical cut          (ii) horizontal cut             to the following solids?             (a) A brick        (b) A round apple          (c) A die     (d) A circular pipe        (e) An ice cream cone

a )  A brick

i ) Vertical cut

A vertical cut gives a square or rectangular crossection

ii )  The horizontal cut  gives rectangular crossection

b ) A round apple

In both, the case crossection will be circular in shape approximately

c ) A die

both the cut will give a square shape

d ) A circular pipe

i ) A vertical cut will give a circular shape

ii ) The horizontal cut  gives a rectangular shape

e ) An ice cream cone

i) The vertical cut gives a triangular shape

ii) The horizontal cut gives a circular shape

#### 5. The sum and sum of squares corresponding to length (in cm) and weight (in gm) of 50 plant products are given below:                     Which is more varying, the length or weight?

For length x,

Mean,

We know, Variance,

We know,  Standard Deviation =

C.V.(x) =

For weight y,

Mean,

Mean,

We know, Variance,

We know,  Standard Deviation =

C.V.(y) =

Since C.V.(y) > C.V.(x)

Therefore, weight is more varying.

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#### 4.  The following is the record of goals scored by team A in a football session: No. of goals scored 0 1 2 3 4 No. of matches 1 9 7 5 3 For the team B, mean number of goals scored per match was 2 with a standard deviation    goals. Find which team may be considered more consistent?

 No. of goals scored Frequency 0 1 0 0 0 1 9 1 9 9 2 7 4 14 28 3 5 9 15 45 4 3 16 12 48 =N = 25 = 50 =130

For Team A,

Mean,

We know, Variance,

We know,  Standard Deviation =

C.V.(A) =

For Team B,

Mean = 2

Standard deviation,  = 1.25

C.V.(B) =

Since C.V. of firm B is more than C.V. of A.

Therefore, Team A is more consistent.

#### 3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:   Firm A Firm B No. of wage earners Mean of monthly wages Variance of the distribution of wages (ii) Which firm, A or B, shows greater variability in individual wages?

Given, Variance of firm A = 100

Standard Deviation =

Again, Variance of firm B = 121

Standard Deviation =

Since , firm B has greater variability in individual wages.

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#### 3.      An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:     Firm A Firm B No. of wage earners Mean of monthly wages Variance of the distribution of wages (i) Which firm A or B pays larger amount as monthly wages?

Given, Mean of monthly wages of firm A = 5253

Number of wage earners = 586

Total amount paid = 586 x 5253 = 30,78,258

Again, Mean of monthly wages of firm B = 5253

Number of wage earners = 648

Total amount paid = 648 x 5253 = 34,03,944

Hence firm B pays larger amount as monthly wages.

#### 2   From the prices of shares X and Y below, find out which is more stable in value:       X 35 54 52 53 56 58 52 50 51 49 Y 108 107 105 105 106 107 104 103 104 101

 X() Y() 35 108 1225 11664 54 107 2916 11449 52 105 2704 11025 53 105 2809 11025 56 106 8136 11236 58 107 3364 11449 52 104 2704 10816 50 103 2500 10609 51 104 2601 10816 49 101 2401 10201 =510 = 1050 =26360 =110290

For X,

Mean ,

Variance,

We know,  Standard Deviation =

C.V.(X) =

Similarly, For Y,

Mean ,

Variance,

We know,  Standard Deviation =

C.V.(Y) =

Since C.V.(Y) < C.V.(X)

Hence Y is more stable.

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#### 1.From the data given below state which group is more variable, A or B? Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7

The group having a higher coefficient of variation will be more variable.

Let the assumed mean, A = 45 and h = 10

For Group A

 Marks Group A Midpoint 10-20 9 15 -3 9 -27 81 20-30 17 25 -2 4 -34 68 30-40 32 35 -1 1 -32 32 40-50 33 45 0 0 0 0 50-60 40 55 1 1 40 40 60-70 10 65 2 4 20 40 70-80 9 75 3 9 27 81 =N = 150 = -6 =342

Mean,

We know, Variance,

We know,  Standard Deviation =

Coefficient of variation =

C.V.(A) =

Similarly,

For Group B

 Marks Group A Midpoint 10-20 10 15 -3 9 -30 90 20-30 20 25 -2 4 -40 80 30-40 30 35 -1 1 -30 30 40-50 25 45 0 0 0 0 50-60 43 55 1 1 43 43 60-70 15 65 2 4 30 60 70-80 7 75 3 9 21 72 =N = 150 = -6 =375

Mean,

We know, Variance,

We know,  Standard Deviation =

Coefficient of variation =

C.V.(B) =

Since C.V.(B) > C.V.(A)

Therefore, Group B is more variable.

#### Q.2 Draw a graph for the following(ii)Is it a linear  graph?

(ii)

From above graph,we conclude that graph is not linear.

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#### Q.2 Draw a graph for the following Is it a linear graph (i)

(i)

From the above graph ,we conclude that graph is linear.

#### Draw a graph for the following

The question is incomplete.