__Descriptive Statistic__

Based on your skew value and histogram, discuss the best measures of central tendency and dispersion of your data. Justify your selection

Skew is the measure of symmetry in a data set, data can be positively skewed or negatively skewed, positively skewed or data skewed to the right means that more observations are concentrated on the lower measures of the data, negative skewed or data skewed to the left data means that more observations are concentrated on the higher measures of the data.

The following diagrams shows positive and negative skewed data

However data may be symmetrical which means it will take a bell shaped *form* of diagram and therefore this is a normal distribution where the mean it is at the centre and data deviates with the same standard deviation.

In our case we have to series of data as follows:

A

B

**Descriptive Statistic**

MIN

2

0

MAX

20

1

RANGE

18

1

MEAN

**Descriptive Statistic**

10.3

0.43

STD DEV

18.45

0.25

POP VARIANCE

18.14

0.25

From the above data collected the column A represents high ATM usage while B represents debit card usage, the first data n high ATM usage has a mean value of 10.3 and the minimum amount is 2 and maximum amount of 20, the standard deviation is 18.45 and for this reason the data is negatively skewed

The above chart shows negative skew for the high ATM usage, this states that more of the data observations lie on the lower measures of the data; less data on the other hand lies on the

Descriptive Statistic

higher measure of the data.

For the debit card usage the data is as follows:

The data on debit card usage is also negatively skewed and this means that more of the data *observations* lies on the lower measures of the data, less data on the other hand lies on the higher measure of the data.

The mean:

The mean of high ATM usage is 10.3 showing that there are more individuals using ATM, the mean of debit card usage is 0.43 showing that less people use debit cards. The mean is a measure of central tendencies of the data and **they** give us the probability of expected turnout. Therefore from this measure it is clear that **more** people use ATM but less people use Debit cards.

Standard deviation:

The standard deviation is a measure of dispersion from the mean, the higher the standard deviation then the higher is the dispersion from the mean, however the lower the standard deviation then the lower is the standard deviation. In our case the ATM usage standard deviation is 18.45 and this is higher than the deviation of debit card usage which is 0.25.

*Descriptive Statistic*

Population standard deviation:

The population standard deviation is a measure of dispersion from the mean for the entire population, In this case the ATM usage population standard deviation is 18.14 and the population standard deviation for debit card usage is 0.25, the population standard deviation helps us to determine the validity of data analysis of the sample because a sample should be a representative of the entire population, therefore our sample is not biased and therefore represents the entire population due to the low errors on central measures.

Median and mode:

The median and the mode are also measures of central tendencies of the data, the mode measures the highest recorded frequencies of data measures, and it helps us to determine where most of the data lie while the median helps us to determine the quartile range and the skew of the data.

Minimum and maximum:

**Descriptive Statistic**

The minimum and the maximum values of data represents the lowest and highest value of data respectively, they are important measures in that they aid in the calculation of the range of data and quartile range for the data.

All the above measures aid in the analysis of data and they help in the description of data collected, they help in the description of data giving information regarding skew, range, mean, median and mode all which are important in the description of data.

References:

D. Bridge (1993) Statistics: An Introduction to Quantitative Research, Rand McNally publishers, Michigan

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