Descriptive Statistics and Visual Distributions: Histogram and Kurtosis

Respond to the following post

Post 1

In research, kurtosis is a statistical measure that quantifies the shape of a probability distribution or a dataset. It provides information about the tails and the peakedness of the distribution relative to the normal distribution. Kurtosis is commonly used to understand the departure of a dataset from a normal distribution, also known as the bell curve. A normal distribution has a kurtosis value of 0. Positive kurtosis indicates a distribution with heavier tails and a more peaked center compared to the normal distribution, while negative kurtosis indicates lighter tails and a flatter center.

There are different ways to calculate kurtosis, but one commonly used formula is the Pearson's coefficient of kurtosis, which is calculated as the fourth standardized moment of the distribution. It is defined as the average of the fourth power of the deviation from the mean, divided by the fourth power of the standard deviation. Researchers use kurtosis to gain insights into the characteristics of their data. It helps in understanding the presence of outliers, the concentration of values around the mean, and the overall shape of the distribution. High kurtosis values indicate a more extreme distribution with potential outliers, while low kurtosis values indicate a more moderate and less extreme distribution. Thoughts?

Post 2

How does the histogram look? Does it look skewed one way or another?

The histogram is visibly skewed to the right. This means that it is positively skewed indicating that higher values were more abundant than the average values. The skewness on the histogram above is of -0.172766

Can you visualize its kurtosis – is it flat or peaked?

Kurtosis is -1.114909 therefore it suggests a flat, platykurtic, distribution.

How does the visual of the histogram chart compare to the values that were calculated in the descriptive statistics?

In order to compare the visual of the histogram chart to the values that were calculated in the descriptive statistics there is an increased need to focus on the shape of the distribution and see if this is centered or spread. Also skewness and kurtosis will be a good indicator of the visual. When looking at the histogram, researchers must look at the overall shape and look for its peak and symmetry. Descriptive statistics consider skewness and kurtosis. When looking at kurtosis a positive value will be leptokurtic and a negative value a platykurtic.

Does the histogram, at least visually, look like a normal distribution (bell curve)?

By observing the histogram, there is no normal distribution (bell curve) as the bell curve is usually centered and is exhibits a bell-shaped curve that is symmetric. The curve is skewed to the left.

Post 3

How does the histogram look? Does it look skewed one way or another? Can you visualize its kurtosis – is it flat or peaked?

The histogram is skewed. It is negatively skewed to the left. Kurtosis is peaked but has a moderate peak. I had to adjust the histogram to analyze the characteristics.

How does the visual of the histogram chart compare to the values that were calculated in the descriptive statistics?

The median of the data is higher than the mean. In a left-skewed distribution curve, the median and mode are greater than the mean. Using that example shows that the histogram accurately represents the calculated descriptive statistics.

Does the histogram, at least visually, look like a normal distribution (bell curve)?

It is similar to a normal distribution curve, but it is skewed left. To have a normal distribution, the histogram has to be symmetrical.

Post 3

This histogram has two peaks, so it is not normally distributed. Visually, it resembles bimodal distribution rather than normal distribution. It has two points of equal kurtosis, and the tails are fat which means there are no outliers.

It is easier to visualize the complete distribution of the project grades with the histogram than the descriptive statistics, but the statistical values are more exact. The mean of the project grades is 79.25 which is one of the lower points on the histogram. The median is 81.01 which is within the same 5 point range bar on the histogram. According to the descriptive statistics, the data is negatively skewed; however, that is difficult to see in the histogram. The last bar of the histogram extends to 101.70, but the highest actual score is 99.84 which can be seen as the maximum in the box of descriptive statistics values.

Images are attached and are post 2 and 3 respectively.