Question

In: Math

Scores: 57, 49, 53, 60, 58, 59, 48, What is the mean of these scores? (round your...

Scores: 57, 49, 53, 60, 58, 59, 48,

What is the mean of these scores? (round your answer to 2 decimal places)
What is the median?
What is the estimated standard deviation of the population based on this sample? (round your answer to 2 decimal places)

Expert Solution

Solution:

Given that

x	x2
57	3249
49	2401
53	2809
60	3600
58	3364
59	3481
48	2304
∑x=384	∑x2=21208

a ) The sample mean is

Mean = (x/ n) )

= ( 57+49+ 53+ 60+ 58+ 59,+48 / 7 )

= 384 / 7

= 54.8571

Mean = 54.8571

b ) Median :
Observations in the ascending order are :
48,49,53,57,58,59,60

Here, n = 7 is even

M = Value of ( n + 1 / 2) Observation.

= Value of ( 7 + 1 / 2) Observation.

= Value of 4^th Observation.

= 57

Median = 57

c ) Population standard deviation =

= ( x² ) - (( x )² / n ) / n )

= 21208- ( 384 /7 )² / 7

= 21208-- 21065.1429 / 7

= 142.8571 / 7

= 2040.82

= 4.5175

Population standard deviation = 4.5175

milcah answered 10 months ago

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