Question:

The sum and sum of squares corresponding to length X (in cm ) and weight y (in gm) of 50 plant products are given below: i=l∑50​Xi​=212,i=l∑50​Xi2​=902.8,i=l∑50​yi​=261,i=l∑50​yi2​=1457.6 Which is more varying the length or weight ?

Answer:

Step 1: Calculate the mean of length and weight. Mean of length = 212/50 = 4.24 cm Mean of weight = 261/50 = 5.22 gm

Step 2: Calculate the variance of length and weight. Variance of length = (902.8/50) - (4.24)^2 = 0.44 cm^2 Variance of weight = (1457.6/50) - (5.22)^2 = 0.6 gm^2

Step 3: Compare the variance of length and weight. Since the variance of weight is greater than the variance of length, weight is more varying than length.

Question:

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

Answer:

Step 1: Calculate the range of each group. Group A Range = 70-10 = 60 Group B Range = 70-10 = 60

Step 2: Calculate the variance of each group. Group A Variance = (9+17+32+33+40+10+9)/7 = 24.14 Group B Variance = (10+20+30+25+43+15+7)/7 = 22.71

Step 3: Compare the variance of each group. Group A has a higher variance than Group B, therefore Group A is more variable.

Question:

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

Answer:

Step 1: Calculate the mean of the prices of X.

Mean of X = (35 + 54 + 52 + 53 + 56 + 58 + 52 + 50 + 51 + 49) / 10 = 51.8

Step 2: Calculate the mean of the prices of Y.

Mean of Y = (108 + 107 + 105 + 105 + 106 + 107 + 104 + 103 + 104 + 101) / 10 = 105.1

Step 3: Compare the means of X and Y.

105.1 > 51.8

Therefore, Y is more stable in value.

Question:

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 586 648 Mean of monthly wages Rs 5253 Rs 5253 Variance of the distribution of wages 100 121 (i) Which firm A or B pays larger amount as monthly wages ? (ii) Which firm A or B shows greater variability in individual wages ?

Answer:

(i) Both firms A and B pay the same amount as monthly wages, Rs. 5253.

(ii) Firm B shows greater variability in individual wages, as it has a higher variance of 121, compared to Firm A’s variance of 100.

Question:

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 1.25 goals. Find which team may be considered more consistent ?

Answer:

1. Calculate the mean number of goals scored per match for team A.

2. Calculate the standard deviation for team A.

3. Compare the mean number of goals scored per match for team A and team B.

4. Compare the standard deviation for team A and team B.

5. Based on the comparison of the mean and standard deviation, determine which team may be considered more consistent.