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

Solution :

Researcher 1 : mean = 23.575
median = 24
mode = 24, 27, 29, 22, 33, 17, 16, 15, 34, 44, 8, 26, each appeared 2 times
Range = 44
standard deviation = 11.2589

Researcher 2 :
mean = 911/40 = 22.775
median = 22
mode = 14,16,18,21, each appeared 3 times
Range = 42
standard deviation = 10.3787

Given that 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

Ordering the data from least to greatest, we get:

Researcher 1: 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

Researcher 2: 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

=> Researcher 1 :

mean = sumof the terms/number of the terms = 943/40 = 23.575

median = 24
=> The median is the middle number in a sorted list of numbers =>(24 + 24)/2 = 24

=> The mode of a set of data is the value in the set that occurs most often

range = highest value - lowest value

standard deviation ? = 11.2589