PART B: DESCRIPTIVE STATISTICS (60 points) Note: Please round your results to 2

ID: 3124278 • Letter: P

Question

PART B: DESCRIPTIVE STATISTICS (60 points)

Note: Please round your results to 2 decimals; When the 3rd decimal is 5 or more you round up, otherwise you round down.

For example: 0.398 I rounded to 0.40; 0.3923 is rounded to 0.39

For two of the below problems, COMPUTE ALL DESCRIPTIVE STATISTICS (WITHOUT using the excel’s tool “descriptive statistics”) – mean, median, mode, quartiles, range, inter-quartile range, variance, standard deviation, coefficient of variation.

An example of solution is given in problem 1 solution.

Remember two important things about typing in Excel: (1) to start typing, just click on the desired cell; (2) if what you type starts with “=”, it tells Excel to compute something instead of just displaying a value. When you want to enter a formula type “=” first. If you use an excel function, don’t type “=”; just click on the cell and next choose the excel function from the list of functions.

For the rest of the problems COMPUTE ALL DESCRIPTIVE STATISTICS using the tool of your choice. If you use the excel tool “descriptive statistics” be sure you complete your solution by given the missing descriptive statistics (inter-quartiles, coefficient of variation). Double check the mode value(s). The excel tool gives only one mode value even if the set is multimode. Show the Excel output.

For only one of the problems (of your choice) convert the data to Z-scores.

You should always explain (comment, justify) the answers of your homework.

Pay attention to the solution of problem 1

PROBLEM 1: #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: Zi = (Xi - 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.

Below 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.

Column1

Mean

Standard Error

0.560112

Median

Mode

Standard Deviation

2.376354

Sample Variance

5.647059

Kurtosis

1.497461

Skewness

0.887652

Range

Minimum

Maximum