Statistics Exercise 03
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∑50Xi=212,i=l∑50Xi2=902.8,i=l∑50yi=261,i=l∑50yi2=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 1020 2030 3040 4050 5060 6070 7080 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 = 7010 = 60 Group B Range = 7010 = 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:

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

Calculate the standard deviation for team A.

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

Compare the standard deviation for team A and team B.

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