PROBLEM 3 : Quiz scores L n = 13 students 5 7 9 10 8 9 0 6 7 10 9 10 8 example of how it needs to be answered: PROBLEM: #colds / year n=18 subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3;...

PROBLEM 3: Quiz scores L  n = 13 students

5   7   9   10   8   9   0   6   7   10   9   10   8

example of how it needs to be answered:

PROBLEM: #colds / year      n=18 subjects

10;
8;
5;
2;
3;    3;    3;
6;
4;
2;
 4;    5;
4;    4;
1;
0;
3;   5;

For computations done by hand, data must be ordered.

0      1     2     2    3     3      3    3    4    Median   4     4     4      5    5   5   6    8    10

                           Q1                                                                   Q3

Sample mean =
 =72/18 = 4 colds

Sample median = 4 colds (midpoint of data)

Sample mode = 3 and 4  (the value that occurs most often; this is a bimodal data set)

First Quartile (approximation) =

0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5

à

value is 3

Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5

à

14

à

value is 5

Range = max – min =10 – 0 = 10

IQR = Q3 – Q1 = 5 – 3 = 2

Variance =
s²
=  =
96/17 = 5.64 colds squared

Standard deviation =
s =    =
2.37 colds

Coefficient of variation =
CV =  x 100% =2.37/4 *100% = 59.25%

To convert to a Z-score:   Z_i
= (X_i
-  mean)/s

The 0 becomes (0 – 4) / 2.37 = -1.68;

                                                 the 1 becomes (1 – 4) /2.37 = -1.27;

                                                 the 2 becomes (2- 4)/2.37 =  .84;

                                                 and the 4 becomes a 0; etc.

All values below the mean have negative Z scores and all values above the mean have positive Z scores.

This is the output from MS Excel using the descriptive tool.  For your homework solution an output as the one below (for the excel solution) will be sufficient.

Quartiles are approximations.   A more refined definition is the following:

Please follow the above definitions in calculating the quartiles. There are two distinct situations: set size equal to a power of 4 (L is already a whole number – integer), set size not a power of 4.