
Descriptive Statistics  Introduction 
8  7  6  9  4  5  3  7  8 
10  7  7  6  4  10  3  6  8 
2  5  4  5  3  8  7  4  6 
3  7  12  4  3  6  6  9  4 
(a) Construct the frequency distribution.
(b) What percentage of recovery times were less than 10 days?
Solutions:
(a) The frequency distribution (the number of times each occurred) of
each recovery times (range from 2 to 12) is:
Recovery Times, x  2  3  4  5  6  7  8  9  10  12  Total 
Frequency, f  1  5  6  3  6  6  4  2  2  1  36 
(b) Sum of frequencies up to and including 9 is 33 so percentage less than 10 is 
Question 2. The owner of a small business wants to analyze the
profits (thousands of dollars) over the past 30 years.
The ordered data from smallest to largest profits are as follows:
15  17  18  19  20  20  20  21  23  23  24  24  24  24  24 
25  25  25  25  25  26  26  27  27  28  29  30  30  31  32 
(a) Complete the grouped frequency distribution table:
Class  Class boundaries  Frequency 
2  17.520.5  
(b) What is the class width?
(c) Compute the relative frequency of each class
(d) What is the median and mode?
Solutions:
(a), (b) and (c) Relative Frequency table  Class width is 20.5  17.5
= 3
Class  Class boundaries  Frequency
(1) 
Relative Frequency
(1) / (2) 
1  14.517.5  2  0.667 
2  17.520.5  5  0.167 
3  20.523.5  3  0.1 
4  23.526.5  12  0.4 
5  26.529.5  4  0.133 
6  29.532.5  4  0.133 

(2) Sum = 30  Sum =1 
(d) The mode is 24 and 25 since they appears the most, 5 times
The median is (24 + 25) /2 = 24.5
Question 3  The following is the world distribution of nuclear
reactors in operation:
United States  109  Russia  29 
France  56  Canada  21 
Japan  51  Germany  20 
United Kingdom  35  Others  116 
(a) Construct a bar graph  (c) Construct a pie chart 
Question 4. From the following data (per 1000 population) for
selected countries:
Compute the statistics required for a boxplot diagram: Ordered Data
4.9  5.1  6.3  6.7  7  7.1  7.8  8.6  8.7  8.8  
8.9  9  9.4  9.4  9.5  9.6  9.9  10  10.1  10.1  
10.1  10.3  10.4  10.7  10.9  11.3  11.6  11.8  14.3 
Solutions: (see programs)
min  25 percentile  median  75 percentile  max 
4.9  8.6  9.5  10.3  14.3 

Question 5 The following grouped frequency distribution represents the ages (in years) of 59 patients of a counseling center.
(a) Compute a frequency polygon and
(b) Compute the mean and standard deviation of the age of the patients.
Class Limits  2127  2834  3541  4248  4955  5662  6369 
Frequency  3  7  12  15  12  7  3 
Solution.
Class Limits  2127  2834  3541  4248  4955  5662  6369 
Class Midpoint  24  31  38  45  52  59  66 
Frequency  3  7  12  15  12  7  3 
(a) Frequency polygon

(b) Weighted Mean and Grouped Standard
Deviations
Weighted Mean = 45 Group variance = 113.2069 Group Standard Deviation = 10.64 
Program Output 
Question 6. The following data gives the average temperatures
per month over a
12month period for two cities A and B.
City A  8  14  25  43  54  64  71  69  58  47  29  16 
City B  56  60  58  62  63  68  69  71  69  67  61  58 
(a) Which of the two cities do you suspect is warmer on average? Which has more temperature variability?
(b) Use the following information and compute the mean and standard deviation for each city.
City A and
City B
and
(a) City B has the larger mean
of 63.5
And City A has a larger variation in temperature with a larger variance of 504.64 
(b) From Formula:
City A and City B and
City A: = 22.46 mean = City B: mean = 63.5 and s=5.11 Variance = 26.09 
Example of calculation for City B 
Question 6 The following data give the time in days from remission
to relapse for 51 patients with an acute illness.
Find the following:
Questions  Solutions from Program 
(a) The first and third quartiles  135.5 and 367 
(b) The inter quartile range  231.5 
(c) The median  249 
(d) The 95th percentile  669.5 
(e) The percentile rank of 111  20% 