StatisticsAssignment: Descriptive Statistics

StatisticsAssignment: Descriptive Statistics

Measuresof Central Tendency and Variation

Measuresof central tendency and variation are characteristic figures for anydistribution of probability. They are also referred to as the centersof particular distributions, or averages. Examples of such measuresinclude mean, also referred to as average, mode, and the median value*(Comparing Measures of Central Tendency*,2016).In essence, the measures can be computed for either a predeterminedset of figures or values. Additionally, they can be calculated for adistribution, which is hypothetical. Fundamentally, the normalprobability distribution, which is also referred to as the Gaussiandistribution, is an example of such a distribution.

Asaforementioned, there are many measures of central tendency.Arithmetic mean is the total of all the available set of data dividedby the total observations in the data set. Conversely, median is thevalue, which is at the center of a given data set provided that thedata is arranged in an ascending or descending pattern.Intrinsically, it is used in instances where the data is of ordinalnature. Unlike mean and median, mode is the most repeated value thismeasure is only used when the data is of nominal nature. Essentially,means may be geometric, harmonic weighted, trimmed, or interquartile.

Conversely,a measure of variation, also known as a measure of dispersion, is apositive quantity that is usually naught when all the data set issame. Notably, it rises as the data turns to be more varied. Themajority of such measures usually have similar components as theamount, which is being measured, which means that if the units of thedata are in kilometers, then the measures should be quoted using asimilar system*(Grouped and Ungrouped Data | TutorVista.com*,2016).Examples of measures of variation are standard deviation, range,variance, the interquartile range, the gini mean, the distancestandard deviation, and the median absolute deviation among others.Nevertheless, the measures may differ if the type of the distributionis skewed. The following is an example of a skewed distributionithas a skew, which is non-negative as shown below.

Figure1: Non-negative skew (*SkewedData*,2016)

Negativelyskewed data is as follows:

Figure2: Negatively skewed data (*SkewedData*,2016).

Adistribution, which has no skew is as in the following graph:

Figure3: Distribution with no skew (*SkewedData*,2016).

Question2

Theleader should consider selling the shares to the public as they arenot profitable to him/her. If the median, which is the center of thedata is found to be $3000, this shows that there are other values,which are approximately 20000 in the data set. Essentially, this ismuch less tan $3000 hence, there is no profit to the leader.

Question3

Itis not possible for one to calculate the mean and median for theprovided grouped data. In principle, the interval in the sixth groupis different than that of the other groups therefore, this makes themeasures impossible to compute.

References

*ComparingMeasures of Central Tendency*.(2016). *Onlinestatbook.com*.Retrieved 5 September 2016, fromhttp://onlinestatbook.com/2/summarizing_distributions/comparing_measures.html

*Groupedand Ungrouped Data | TutorVista.com*.(2016). *Tutorvista.com*.Retrieved 5 September 2016, fromhttp://www.tutorvista.com/math/grouped-and-ungrouped-data

*SkewedData*.(2016). *Mathsisfun.com*.Retrieved 5 September 2016, fromhttp://www.mathsisfun.com/data/skewness.html