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Statistics - Important Questions

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1
Exercise 15.1
Find the mean deviation about the mean for the data: 4, 7, 8, 9, 10, 12, 13, 17.
▶ Show Detailed Solution
Mean x̄ = (4+7+8+9+10+12+13+17)/8 = 80/8 = 10
Deviations |x - x̄|: 6, 3, 2, 1, 0, 2, 3, 7
Sum of deviations = 24
MD about mean = 24/8 = 3
2
Exercise 15.1
Find the variance and standard deviation of the data: 6, 8, 10, 12, 14.
▶ Show Detailed Solution
Mean x̄ = 50/5 = 10
Deviations: -4, -2, 0, 2, 4
Squares: 16, 4, 0, 4, 16; sum = 40
Variance = 40/5 = 8
Standard deviation = √8 = 2√2 ≈ 2.83
3
Exercise 15.1
The scores of two players in 5 matches are given. Calculate the standard deviation of each set:<br>Player A: 42, 48, 60, 65, 75<br>Player B: 50, 55, 60, 65, 70<br>Who is more consistent?
▶ Show Detailed Solution
Player A: mean = 290/5 = 58
Deviations: -16, -10, 2, 7, 17; squares: 256, 100, 4, 49, 289; sum = 698
σA = √(698/5) = √139.6 ≈ 11.8

Player B: mean = 300/5 = 60
Deviations: -10, -5, 0, 5, 10; squares: 100, 25, 0, 25, 100; sum = 250
σB = √(250/5) = √50 ≈ 7.07

Player B has smaller SD, so Player B is more consistent.
4
Exercise 15.1
Find the standard deviation for the grouped data: 0-10: 2, 10-20: 3, 20-30: 5 (using class marks).
▶ Show Detailed Solution
Class marks: 5, 15, 25.
Mean x̄ = (5×2 + 15×3 + 25×5)/10 = (10+45+125)/10 = 18
Deviations: -13, -3, 7
Squares × frequency: 169×2 + 9×3 + 49×5 = 338 + 27 + 245 = 610
Variance = 610/10 = 61
SD = √61 ≈ 7.81
5
Exercise 15.1
The mean of 100 observations is 40. Later it was found that an observation 53 was misread as 35. Find the correct mean.
▶ Show Detailed Solution
Sum = 100 × 40 = 4000
Correction: replace 35 with 53, add 18.
Corrected sum = 4000 + 18 = 4018
Corrected mean = 4018/100 = 40.18