Question

2. Professor Antonia Giovanni from Colorado State University collected the following age data from a sample of six students from her Principles of Philosophy course: 21, 27, 35, 29, 20, and 36. (a) Compute the range. (b) Compute the variance. (c) Compute the standard deviation.

Answer 1

A. Range is calculated by subtracting the minimum value that occurs in the data set from the maximum value.

Range= maximum value- minimum value

In the given data set,

Range = 36-20= 16

B. Variance is a measure used to know how far the values in data set, on average, lie from the mean.

Variance= $\sum (xi- \mu)^2/N$

Where $\sum$ means sum, $\mu$ means mean ,
T2
denotes the values in the data set, is the sample size.

We first calculate mean,

$\mu = \sum xi/N$

$\mu =$( 21+27+35+29+20+36)/6= 168/6 = 28

Now,

Variance= [(21-28)²+(27-28)²+(35-28)²+(29-28)²+(20-28)²+(36-28)²]/6

Variance= -7²+(-1)²+7²+1²+(-8)²+8²/6

Variance= (49+1+49+1+64+64)/6

Variance= 228/6= 38

C. Standard deviation is the square root of variance.

Hence, standard deviation = √38= 6.16

Answer 2

A. Range is calculated by subtracting the minimum value that occurs in the data set from the maximum value.

Range= maximum value- minimum value

In the given data set,

Range = 36-20= 16

B. Variance is a measure used to know how far the values in data set, on average, lie from the mean.

Variance= $\sum (xi- \mu)^2/N$

Where $\sum$ means sum, $\mu$ means mean ,
T2
denotes the values in the data set, is the sample size.

We first calculate mean,

$\mu = \sum xi/N$

$\mu =$( 21+27+35+29+20+36)/6= 168/6 = 28

Now,

Variance= [(21-28)²+(27-28)²+(35-28)²+(29-28)²+(20-28)²+(36-28)²]/6

Variance= -7²+(-1)²+7²+1²+(-8)²+8²/6

Variance= (49+1+49+1+64+64)/6

Variance= 228/6= 38

C. Standard deviation is the square root of variance.

Hence, standard deviation = √38= 6.16