Question

The systolic blood pressures of a sample of 32 patients in Canada are shown below:
77 86 84 90 94 100 81 85 81 90 78 106 84 94 99 91
85 99 78 90 108 90 93 94 116 101 97 95 99 80 118 73
(a) Construct a frequency distribution and a relative frequency distribution for the
systolic blood pressures of the patients. Use the intervals 70 - 75, 75 - 80, 80 - 85
etc.
(b) Create a histogram for the systolic blood pressures of the patients. Use the same
intervals that you used for the frequency distribution.
(c) Comment on the main features of the distribution of 32 systolic blood pressures?

Answer 1

First, order the data:

73, 77, 78, 78, 80, 81, 81, 84, 84, 85, 85, 86, 90, 90, 90, 90, 91, 93, 94, 94, 94, 95, 97, 99, 99, 99, 100, 101, 106, 108, 116, 118.
Frequencies below are shown in brackets.
Frequency distribution:

73 (1); 77 (1); 78 (2); 80 (1); 81 (2); 84 (2); 85 (2); 86 (1); 90 (4); 91 (1); 93 (1); 94 (3); 95 (1); 97 (1); 99 (3); 100 (1); 101 (1); 106 (1); 108 (1); 116 (1); 118 (1).

Relative frequency distribution:

A-71-75: (1); B-76-80: (4); C-81-85: (6); D-86-90: (5); E-91-95: (6);

F-96-100 (5); G-101-105: (1); H-106-110: (2); I-111-115: (1); J-116-120: (1).

In a histogram, there are 10 bands (x axis), A to J. The maximum height is 6 (y axis), the highest frequency:

6                

5           

4      

3      

2           

1 

     A  B   C  D   E  F   G   H   I   J

The histogram shows that most readings are between bands B and F, 76-100, (26/32 or 81%) and the distribution is skewed to the left, with a steeper rise in frequency on the lower side than the higher side of the distribution. The peak readings are between 81 and 95 (17/32 or 53%).