Analyzing Measures of Central Tendency Using Excel for Statistics

This assignment explores the measures of central tendency, including mean, median, and mode, and their application in statistical analysis using Excel. The solution demonstrates how to calculate these measures for a given dataset and interpret the results. It explains the process of using the data analysis tool in Excel to compute descriptive statistics, including mean, median, mode, standard deviation, variance, skewness, and kurtosis for three different factors. The assignment further discusses how the mean is used to determine variance, standard deviation, and skewness, and how these values can be used to identify outliers and understand data distribution. References to relevant statistical concepts and formulas are provided, offering a comprehensive overview of central tendency and its importance in data analysis. The assignment emphasizes the practical application of Excel in statistical analysis, making it a valuable resource for students learning about descriptive statistics. The student's work is available on Desklib, a platform providing study resources.

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Measures of Central Tendency and How to Use Excel
Student’s Name
Institution Affiliation

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Measures of Central Tendency and How to use Excel
The measures of central tendency include the mean, mode, median. These measurements
help in explaining more characteristics about a particular data set. The means is computed by
adding up all the observed values and diving the total amounts by the total number of
observations. Mode represents the number that appears with a higher frequency amongst all the
observed values. The median is the boundary between the upper and the lower set of the data
(Dretzke, 2013).
In excel, the measures of central tendency are calculated by utilizing the data analysis
tool Pak and then selecting the descriptive statistics options. With reference to factor data with
three groups. The procedure of analyzing the data in excel entails following the procedure below.
After the data is manually keyed -in excel, the analysis is conducted by clicking on the
data analysis tab. A pop-up widow appears as shown below.
After clicking okay, one is prompted to input the range of the data as shown in the pop-up
window.

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A selection of “Labels int first row” allows the inclusion of data headers in the analysis. The
summary statistics allows for calculation of descriptive statistic and after clicking okay the
results in the table below was generated.
Factor 1 Factor2 Factor3
Mean
85.8571
Mean
82.1429
Mean
85.1429
Median
86.0000
Median
82.0000
Median
82.0000
Mode
86.0000
Mode
77.0000
Mode
79.0000
Standard
Deviation 4.0178
Standard
Deviation 4.9809
Standard
Deviation 8.5133
Sample
Variance 16.1429
Sample
Variance 24.8095
Sample
Variance 72.4762
Kurtosis
2.1863
Kurtosis
(0.9533)
Kurtosis
(1.4694)
Skewness
(1.3652)
Skewness
0.5611
Skewness
0.4200
Range
12.0000
Range
13.0000
Range
23.0000
Minimum
78.0000
Minimum
77.0000
Minimum
75.0000
Maximum
90.0000
Maximum
90.0000
Maximum
98.0000
Sum
601.0000
Sum
575.0000
Sum
596.0000
Count
7.0000
Count
7.0000
Count
7.0000

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From the table above, the analysis of central tendency for the 3 factors is as shown in the table
below.
Factor 1 Factor2 Factor3
Mean 85.857
1
Mean 82.142
9
Mean 85.1429
Median 86.000
0
Median 82.000
0
Median 82.0000
Mode 86.000
0
Mode 77.000
0
Mode 79.0000
The mean of factor 1 (85.8571) is higher than the mean of factor 2(82.1429) and the
mean of factor 3 (85.1429). The number of observations that appeared more times was 86,77,79
for factors 1, factor 2 and factor 3 respectively as shown by the mode in the table above. Lastly
the median, which is the middle term dividing the data at the lower and upper level in the dataset
was 86,82 and 82 for factors 1, factor 2 and factor 3.
Once the mean is calculated, it is used to determine the variance and standard deviation
of the data (Aldous, 2016). The sum of the squared differences between the mean and the
observed values are used in computing the variance. The square root of the variance gives the
standard deviation of the data. The standard deviation explains how far an observe value is from
the calculated mean (Silver, 2007). This is used to determine whether an observed value is an
outlier or not. Therefore, the mean is a key value is statistic as it is used to determine other
characteristic of observed data.
When calculating skewness, the means is also used to determine whether the data is
positively or negatively skewed (Dimitriadis, Patton & Schmidt, 2019). Negatively skewed data
has a longer tail at the left of the mean while positively skewed data has the longer tail on the
right-hand side of the mean. According to Dretzke & Larson (2000), the position of the mode,

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mean and the median in negatively skewed data, and positively skewed data. The mode, is
identifiable from the highest point of the skewness curve, and the median position is either right
or left of the skewness curve depending on how the observed values are distributed on the right
hand-side or left-hand side of the skewness curve (Berényi, 2003).
This analysis helps in informing the analyst or the user of the information about
characteristics of information contained in the dataset. Other values calculated by descriptive
statistics test shows that are minimum values and maximum values in each factor, sum which is
the total of adding up all the observed values, counts which represents the number of
observations. The range represents the difference between the largest and the smallest value in
the dataset.

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References
Aldous, D. (2016). Descriptive statistics. New Rochelle, N.Y: Magnum Publishing.
Berényi, Z. (2003). Risk and performance evaluation with skewness and kurtosis for
conventional and alternative investments. Frankfurt am Main: Peter Lang.
Dimitriadis, T., Patton, A., & Schmidt, P. (2019). Testing Forecast Rationality for Measures of
Central Tendency. SSRN Electronic Journal. doi: 10.2139/ssrn.3466442
Dretzke, B. (2013). Statistics with Microsoft Excel (5th ed.). Prentice Hall.
Dretzke, B., & Larson, R. (2000). The Microsoft Excel manual, Elementary statistics: picturing
the world [by] Larson, Farber. Upper Saddle River, N.J.: Prentice Hall.
Silver, G. (2007). Operational measures of central tendency. Applied Mathematics And
Computation, 186(2), 1379-1384. doi: 10.1016/j.amc.2006.07.130