Question

A teacher sets a test for a class of students. The teacher decides to analyse the test results using statistical analysis techniques. Given the table of results below, complete the following tasks:

CLASS RESULTS

STUDENTS                       TEST SCORE%

Thomas                               74

Charles                                55

Sarah                                   81

Mathew                               68

James                                   71

Jessica                                  74

Daniel                                  86

Jack                                      66

Emma                                  73

Laura                                    72

Joshua                                 84

Alice                                     68

Samantha                           70

a). Calculate the Mean of the test scores.

b). Calculate the Median of the test scores.

c). Calculate the Mode of the test scores.

d). Calculate the Range of the test scores.

e). Calculate the Variance of the test scores.

f). Calculate the Standard Deviation of the test scores.

g). Grade the scores based on the following criteria:

- A student scoring greater than two standard deviations above the mean is assigned a grade of A+ .

- A student scoring between one standard deviation above the mean and two standard deviations above the mean is assigned a grade of A.

- A student scoring between the mean and one standard deviation above the mean is assigned a grade of B

- A student scoring between the mean and one standard deviation below the mean is assigned a grade of C

- A student scoring between one standard deviation below the mean and two standard deviations below the mean is assigned a grade of D.

- A student scoring more than two standard deviations below the mean fails the test.

h). Construct a Histogram (i.e. frequency versus score) of the class results using the scheme specified in part (g)

i). Construct a relative frequency versus score graph for the class results using the scheme specified in part (g)

I have completed this question till (F), Please solve g, h and i. This is really urgent. i will give you great review. Thanks!

Answer 1

Solution-:

Let, x=Test Score

By using R-Software:

> x=c(74,55,81,68,71,74,86,66,73,72,84,68,70)
> #(a) for mean of the test scores
> Mean=mean(x);Mean
[1] 72.46154
> #(b) for median of the test scores
> med=median(x);med
[1] 72
> #(c) for mode of the test scores
> tx=table(x);
> m=which(tx==max(tx))
> stx=sort(unique(x))
> Mode=stx[m];
> Mode
[1] 68 74
> #(d) for range of the test scores
> min=min(x);min
[1] 55
> max=max(x);max
[1] 86
> range=max-min;range
[1] 31
> #(e) for variance of the test scores
> n=13
> v=var(x);v
[1] 65.76923
> var=((n-1)/n)*v;var
[1] 60.71006
> #(f) for Standard deviation of the test scores
> sd=sqrt(var);sd # Standard Deviation
[1] 7.791666

R-Code:
x=c(74,55,81,68,71,74,86,66,73,72,84,68,70)
#(a) for mean of the test scores
Mean=mean(x);Mean
#(b) for median of the test scores
med=median(x);med
#(c) for mode of the test scores
tx=table(x);
m=which(tx==max(tx))
stx=sort(unique(x))
Mode=stx[m];
Mode
#(d) for range of the test scores  
min=min(x);min
max=max(x);max
range=max-min;range
#(e) for variance of the test scores
n=13
v=var(x);v
var=((n-1)/n)*v;var
#(f) for Standard deviation of the test scores
sd=sqrt(var);sd # Standard Deviation