Question

Find the requested values for the following data set:  214 231 225 227 221 223 227 228 215 233 226 224 220 225 227 219

Round each of these to 2 decimal places. Remember to show any work you may want to submit for any calculations via email for possible partial credit.

Sample Mean:  
Sample Standard Deviation:

Median:  
InterQuartile Range:

Answer 1

Solution:

x	x2
214	45796
231	53361
225	50625
227	51529
221	48841
223	49729
227	51529
228	51984
215	46225
233	54289
226	51076
224	50176
220	48400
225	50625
227	51529
219	47961
∑x=3585	∑x2=803675

Mean ˉx=∑xn

=214+231+225+227+221+223+227+228+215+233+226+224+220+225+227+219/16

=3585/16

=224.0625
Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√803675-(3585)216/15

=√803675-803264.0625/15

=√410.9375/15

=√27.3958

=5.2341


Median :
Observations in the ascending order are :
214,215,219,220,221,223,224,225,225,226,227,227,227,228,231,233

Here, n=16 is even.

M=Value of(n2)thobservation+Value of(n2+1)thobservation2

=Value of(162)thobservation+Value of(162+1)thobservation2

=Value of8thobservation+Value of9thobservation2

=225+2252

=225

Arranging Observations in the ascending order, We get :
214,215,219,220,221,223,224,225,225,226,227,227,227,228,231,233

Here, n=16

Q1=(n+14)th value of the observation

=(174)th value of the observation

=(4.25)th value of the observation

=4th observation +0.25[5th-4th]

=220+0.25[221-220]

=220+0.25(1)

=220+0.25

=220.25

Q3=(3(n+1)4)th value of the observation

=(3⋅174)th value of the observation

=(12.75)th value of the observation

=12th observation +0.75[13th-12th]

=227+0.75[227-227]

=227+0.75(0)

=227+0

=227

InterQuartile Range = Third Quartile - First Quartile

= 227 - 220.25

= 6.75

InterQuartile Range = 6.75