Question

Without using R find the median and the first quartile of the following data taken from a random sample of systolic blood pressures of patients measured in mmHg. What is the interquartile range?

88, 88, 92, 96, 96, 100, 102,102,104,104,105,105,105,107,107,108,110,110,110,111,111, 112,113,114, 114,115,115,116,116,117,117,117, 118,119,120,121,121, 121,121,121,121,122,122,123,123, 123, 123,123,124,124,124,124,125,125,125,126,126,126,126, 124, 125,125,125,126,126,126,126,131,133,134,135,136,136,136,138,138,139,139,141,142,142, 143,144,146,147,155,156.

Create a histogram of these data. What is the mode of the data?

Answer 1

We construct the frequency distribution table

Values	frequency
88	2
92	1
96	2
100	1
102	2
104	2
105	3
107	2
108	1
110	3
111	2
112	1
113	1
114	2
115	2
116	2
117	3
118	1
119	1
120	1
121	6
122	2
123	5
124	5
125	6
126	8
131	1
133	1
134	1
135	1
136	3
138	2
139	2
141	1
142	2
143	1
144	1
146	1
147	1
155	1
156	1
Grand Total	87

Here n=87

median is the (n+1)/2 th value = (87+1)/2th=44th value

median = 123

first quartile is the (n+1)/4 th value = 22th value

first quartile = 112

third quartile is the 3(n+1)/4 th value = 66th value

third quartile = 126

Inter quartile range = third quartile - first quartile = 126 -112 = 14

Mode is the value which has the highest frequency

Mode = 126

For drawing Histogram we create the below table

Lower boundary	Upper boundary	frequency
87.5	97.5	5
97.5	107.5	10
107.5	117.5	17
117.5	127.5	35
127.5	137.5	7
137.5	147.5	11
147.5	157.5	2

Histogram ( we draw the histogram using Excel choosing the appropriate data and using column diagram)