Question

Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.

• Researcher 1: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

• Researcher 2: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Compute the mean, median, mode, range, and standard deviation for the data sets for each researcher.

Answer 1

For Researcher 1:

1. Mean :  

(3+4+11+15+16+17+22+44+37+16+14+24+25+15+26+27+33+29+35+44+13+21+22+10+12+8+40+32+26+27+31+34+29+17+8+24+18+47+33+34) / 40 = 23.575

2. Median :

24 (Rearrange this in ascending order we have 3,4,8,8,10,11,12,13,14,15,15,16,16,17,17,18,21,22,22,24,24,25,26,26,27,27,29,29,31,32,33,33,34,34,35,37,40,44,44,47

Then median will be (40/2)+1 = 21st value because total number of observation is 40 which is 24.)

3. Mode : 8,15,16,17,22,24,26,27,29,33,34,44. (Since they all have the highest frequency which is 2.)

4. Range : maximum - minimum = 47 - 3 = 44.

5. Standard Deviation : (1/40) * [ (3-23.575)^2 + (4-23.575)^2 + ........... + (33-23.575)^2 +(34-23.575)^2 ] = 11.11730071

For Researcher 2:

1. Mean :

(3+14+11+5+16+17+28+41+31+18+14+14+26+25+21+22+31+2+35+44+23+21+21+16+12+18+41+22+16+25+33+34+29+13+18+24+23+42+33+29) / 40 = 22.775

2. Median :

22 (Rearrange this in ascending order we have 2,3,5,11,12,13,14,14,14,16,16,16,17,18,18,18,21,21,21,22,22,23,23,24,25,25,26,28,29,29,31,31,33,33,34,35,41,41,42,44.)

3. Mode : 14,16,18,21 (Since they all have the highest frequency which is 3.)

4. Range : maximum - minimum = 44 -2 = 42

5. Standard Deviation : (1/40) * [ (3-22.775)^2 + (14-22.775)^2 + ........... + (33-22.775)^2 +(29-22.775)^2 ] = 10.24814008