Question

The IQ of 50 students in the fifth grade of a special school was measured. The results are as follows: IQ score Frequency 71 - 79 2 80 - 88 8 89 - 97 10 98 - 106 12 107 - 115 6 116 - 124 8 125 - 133 4Compute the sample variance and sample standard deviation.

Answer 1

Answer:

variance 221.37

standard deviation 14.88

Step-by-step explanation:

We need to determine the midpoint of the IQ scores:

$=(71+79)/2=75$

Determine for each IQ score range:

$75,84,93,102,111,120,129$

We square the midpoints:

$=75^2=375$

For each I! range:

$375,7056,8649,10404,12321,14400,16641$

Now we determine the grouped mean by taking the sum of the product of midpoints and frequency:

$=102.36$

We must now determine the sum of squared values of the midpoints subtracted from the mean:

$=(75-102.36)^2=748.57$

Do for all sets:

$748.57,337.09,87.61,0.1296,74.65,311.17,709.69$

We must multiply the frequency with the above values:

$=748.57\cdot{2}=1497.14$

For all IQ ranges:

$1497.14,2696.72,876.1,1.56,447.9,2489.36,2838.76$

The sum of the values are 10847.54

The formula of the standard deviation is:

$s^2=(sum(f(x_i-mean)^2))/(n-1)=10847.54/(50-1)=221.37$

$s=14.88$