Answer:
(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.
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.