Question

For the whole city of Columbus, here are the numbers of monthly heroin overdose EMT calls in 2017:

136, 189, 302, 250, 237, 230, 182, 223, 201, 151, 161, 136

(a) The mean of this data is ______.

(b) The standard deviation is ______.

(c) The median of the data is ______.

(d) The Interquartile range, IQR is ______.

Answer 1

We have given data in increasing order is,
136,136,151,161,182,189,201,223,230,237,250,302
Sample size 12
(a) The mean of this data is 199.83
Mean =Sum of all observations /Number of observation
=[136+136+151+161+182+189+201+223+230+237+250+302]/12
(b) The standard deviation is =50.688

(c) The median of the data is =195

...................observation

=6.5th observation

6.5th observation lies between 6th and 7th observation

6th observation=189

7th observation=201

Median =Q2 = 189+0.5(201-189)

=195
(d) The Interquartile range, IQR is 81.75

............observation

=3.25th observation

3.25th observation lies between 3rd and 4th observation

3 rd observation = 151

4th observation = 161

Q1 = 151 + 0.25(161-151)

=153.5

..............observation

=9.75th observation

9.75th observation lies between 9th and 10th observation.

9th observation =230

10th observation =237

Therefore,

Q3 = 230 + 0.75(237-230)

=235.25

Interquartile range = Q3-Q1 = 235.25-153.5=81.75