Question

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

175; 203; 211; 211; 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

Required:
a. Organize the data from smallest to largest value.
b. Find the median.
c. Find the first quartile.
d. Find the third quartile.
e. Construct a box plot of the data.
f. The middle 50% of the weights are from __________to__________

Answer 1

Kindly check explanation

Explanation:

A.) Rearranged data (ascending order)

174, 175, 178, 184, 185, 185, 185, 185, 188, 190, 200, 203, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302

Size of data, n = 53

B.) median :

1/2*(n+1)th term

1/2 * (53 + 1)

1/2 *54th term = 27 th term

= 241

C.) first quartile (Q1) :

1/4*(n+1)th term

1/4 * (53 + 1)

1/4 *54th term = 13.5

(13 + 14)th term / 2

(205 + 206) /2

= 205.5

D.) third quartile (Q3) :

3/4*(n+1)th term

3/4 * (53 + 1)

3/4 *54th term = 40.5

(40 + 41)th term / 2

(272 + 273) /2

= 272.5