in addition show the formula and working out of how you arrived with the Standard deviation As well as the Formula for the Mean
show all working out
Transcribed Image Text:Many students at popular school in Timbuktu have been complaining that there seems
to be some level of inconsistency with the marking of essays among teachers. To
verify if there is any truth to this, a group of students submitted the same essay to
different teachers. The grade awarded by each teacher for each essay was recorded.
Use the data below to answer the questions that follow.
Essay
Quarrie
Taylor
Wilson
Forbes
1
62
63
65
68
58
60
61
64
3
63
68
72
58
4
64
65
65
61
60
63
66
67
6.
62
66
65
59
7
57
67
71
60
8.
58
68
65
67
9.
59
69
64
62
10
63
60
67
66
11
65
64
62
63
12
61
61
73
64
13
60
62
65
68
14
59
68
68
70
15
57
66
69
71
16
56
63
60
68
17
62
60
61
69
* The above data is also available in excel format on the course page.
Transcribed Image Text:Calculate one (1) appropriate
measure of central tendency
using the data for each teacher
and explain your choice.
4
*There are a total of four
teachers, so there should be a
total of four measure of central
tendencies.
Use the data to generate any
three (3) appropriate graphs.
*You answer should include a
total of three graphs.
5
Is the mean score for each teacher
the best measure of central
tendency to confirm whether or
not there is inconsistency with the
marking of essays among
teachers?
Compute and explain skewness
of the grades for any two (2)
teachers using Pearson's 1st
7
measure of skewness.
*This means that you should
have only two sets of
calculations for this part of the
question.
*A total of two (curves).
Hand-drawn curves are
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 + ...
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