What is the difference between estimated mean and population mean? Thank you
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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What is the difference between estimated mean and population mean? Thank you
Transcribed Image Text:Answer to Problem 8TY
The estimated mean of points scored by 51 winning teams is 30.04 points.
The estimated mean and mean 30.2 is very close.
Explanation of Solution
Given info:
The data set provides the points scored by 51 winning teams. The mean of original data set is 30.2 points.
Calculation:
The frequency distribution of points scored by 51 winning team is as follows:
Class Frequency f
14-20 8
21-27 15
28-34 14
35-41 7
42-48 4
49-55 3
Σf=51
Midpoint:
The midpoint for each class is obtained by using the below formula.
(Lower limit) + (Upper limit)
2
X =
Transcribed Image Text:↑
EXPERT
SOLUTION &
ANSWER
The midpoint for each class is obtained by using the below formula.
(Lower limit)+(Upper limit)
2
Thus, the midpoint for each class is tabulated below:
Class Frequency
X =
14-20 8
21-27 15
28-34 14
35-41 7
42-48 4
49-55 3
n =
Class Frequency f
14-20 8
21-27 15
Σ1 - 51
Mean of the frequency distribution:
The formula is,
3=24
The sum of products of midpoints and frequencies which is denoted as xfis obtained as shown in the
below table:
28-34 14
35-41 7
42-48 4
Midpointx
14,2017
=
21127 = 24
49-55 3
28134
= 31
35141 = 38
42148
2
(8 x 17) = 136
(15 x 24) = 360
(14 x 31) = 434
(7 x 38) = 266
(4 x 45) = 180
(3 x 52) = 156
||n= Σf=51
|Σ x = 1,532
Substitute n as 51 and xf as 1,532 in the formula
49,35 = 52
Midpoint
17
24
= 45
31
38
45
52
xf²
1.532
X=
51
= 30.0392
Thus, the estimated mean is 30.04.
Justification:
The estimated mean is 30.04 and the population mean is 30.2. Thus, the estimated mean is very close the
population mean
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