Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 1111 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league? 186 229 240 257 187 221 309 293 257 274 221

(a) Mean =243.0909

(b) Median = 240

In other words it is the middle value of the data arranged in order.

(c) Mode =  221  and 257

(d) Mid Range =   247.5

e)

Variance = 1578.5037

Standard Deviation = 39.730

Range = 309-186= 123

(e)  No the results are not  likely to be representative of all players in that sport's league because they are not similar.

Step-by-step explanation:

First arranging the data in ascending order

186 187 221 221 229 240 257 257  274  293    309

(a) Mean = Sum of observations/ No of observations

       = 186 + 187 + 221 +221 + 229 + 240 + 257 + 257 + 274 + 293 + 309 /11

= 2674/11=

= 243.0909

(b) Median for un grouped data is

Here n = 11 and n/2 = 11/2 is not an integer

Median = Results obtained by ([n/2] +1) player

                   = (11/2 +1) = 6th player in ordered data

                = 240

In other words it is the middle value of the data arranged in order.

(c) Mode = Most frequent values.

There are two modes : 221  and 257 . These both values occur repeatedly.

(d) Mid Range = Maximum Value + minimum value/ 2= 186+ 309/2=  247.5

Now we will find the variance and standard deviation

The variance is given by

s² =  (186-243.0909)²+ (187-243.0909)²+ (221-243.0909)²+ (221 -243.0909)²+(229-243.0909)²+ (240-243.0909)²+( 257-243.0909)²+ (257 -243.0909)²+ (274-243.0909)²+ ( 293-243.0909)²+    (309 -243.0909)²/11-1

s²=  3259.370 + 3146.139+ 488.008+ 488.008+ 198.553+ 9.554+ 193.463 + 193.463 + 955.372 +  2509.098 + 4344.009/10

s²= 15,785.037/10= 1578.5037

And Standard Deviation = s= √1578.5037= 39.730

Variance = 1578.5037

Standard Deviation = 39.730

Range = 309-186= 123

(e)  No the results are not  likely to be representative of all players in that sport's league because they are not similar.

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step-by-step explanation: