Calculate mean and standard deviation from the following distribution: (20)
Class Interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 2 4 4 8 6 3 2
Answers
Answer:
Mean = 45
Standard deviation = 15.97
Explanation:
Class Interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Mean of class intervals 15 , 25 , 35 , 45 , 55 , 65 , 75
Frequency 2 , 4 , 4 , 8 , 6 , 3 , 2
Total sum = 15*2 + 25*4 + 35*4 + 45*8 + 55*6 + 65*3 + 75*2
= 30 + 100 + 140 + 360 + 330 + 195 + 150
= 1305
Total Frequency = 2 + 4 + 4 + 8 + 6 + 3 + 2 = 29
Mean = 1305/29
=> Mean = 45
Mean of class intervals² 15² , 25² , 35² , 45² , 55² , 65² , 75²
Frequency 2 , 4 , 4 , 8 , 6 , 3 , 2
∑ f *(class interval Mean)² = 66125
Standard deviation² = Variance = ∑ f *(class interval Mean)² /n - (mean)²
= 66125/29 - (45)²
= 2280.17 - 2025
= 255.17
Standard deviation = √255.17 = 15.97