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
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
