Question

In: Statistics and Probability

Without using R find the median and the first quartile of the following data taken from...

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?

Solutions

Expert Solution

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)


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