The frequency table below shows the percentages obtained in a Biometry test for a random sample of 60 students:
Interval fi xi F
[30 – 40) 5 b1 c1
[40 – 50) 12 b2 c2
[50 – 60) 18 b3 c3
[60 – 70) 15 b4 c4
[70 – a1) 7 b5 c5
[a1 – 90) 2 b6 c6
[90 – 100) 1 b7 c7
For the percentages obtained, find the sample standard deviation.
A)11.39
B)16.89
C)15.69
D)13.29
To find the sample standard deviation, we first need to calculate the mean of the data. The mean is calculated by adding up all the xi values multiplied by their corresponding frequencies, and then dividing by the total number of observations (60 in this case).
Mean = (5*b1 + 12*b2 + 18*b3 + 15*b4 + 7*b5 + 2*b6 + b7) / 60
Next, we calculate the squared deviations from the mean for each interval. This is done by taking the difference between the xi value and the mean, squaring it, and then multiplying by the frequency of that interval.
Sum of squared deviations = (5*(b1 - Mean)^2 + 12*(b2 - Mean)^2 + 18*(b3 - Mean)^2 + 15*(b4 - Mean)^2 + 7*(b5 - Mean)^2 + 2*(b6 - Mean)^2 + (b7 - Mean)^2)
Finally, the sample standard deviation is calculated by taking the square root of the sum of squared deviations divided by the total number of observations minus 1.
Sample standard deviation = sqrt((Sum of squared deviations) / (60-1))
Now, substitute the values you found for Mean and Sum of squared deviations to find which option is the correct sample standard deviation value.