Question

Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year.

177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

Calculate:

a. Median

b. Find the first quartile

c. Find the third quartile

d. Calculate the IQR

Answer 1

Here, we have given that

Xi: weights (in pounds)

n=number of observations= 53

Xi (weights in pounds)	Alphabetically sorted (xi)
177	174
205	177
210	178
210	184
232	185
205	185
185	185
185	185
178	188
210	190
206	200
212	205
184	205
174	206
185	210
242	210
188	210
212	212
215	212
247	215
241	215
223	220
220	223
260	228
245	230
259	232
278	241
270	241
280	242
295	245
275	247
285	250
290	250
272	259
273	260
280	260
285	265
286	265
200	270
215	272
185	273
230	275
250	276
241	278
190	280
260	280
250	285
302	285
265	286
290	290
276	290
228	295
265	302

(A)

we want to find the Median

Q2=median=The middle most observation= 27th observation in sorted data= 241

where Q2 is the second quartile which is also known as the median.

Also, we can find the median using EXCEL software

median =Median(xi)=241

(B)

Now, we can find the first quartile

here, we have total 53 observations i.e. for 5 observation if we make 4 parts i.e. 13*4 approximately 52, i.e lower 25% of data.

Q1= 14th observation = 206

Also, we can find the Q1 using EXCEL software

Q1 =QUARTILE(xi,1)=206

(C)

Now, we can find the third quartile

here, we have total 53 observations i.e. for 5 observation if we make 4 parts i.e. 13*4 approximately 52, i.e upper 25% of data.

Q3= 40th observation = 272

Also, we can find the Q3 using EXCEL software

Q3 =QUARTILE(xi,3)=272

(d)

Now, we want to find the interquartile range (IQR)

IQR= Q3-Q1= 272-206 = 66