How to Use Histograms and Descriptive Statistics to Understand Data

Section 1: Histograms 

The following graph is an histogram of male and female students. 

Skew 

For the histogram of the female and male students, the distribution is more symmetrical as the halves appear as mirror images of one another. 

Kurtosis 

The first histogram is light tailed compared to the second one. This therefore means that the second histogram has a higher kurtosis as compared to the first one. The value of kurtosis of the first histogram is expected to be near 3. 

Outlier 

Both the male and female histogram has outliers. This might have been associated with data entry errors. 

Symmetry 

The male histogram appears symmetrical since the bars are compacted to the centre. The female histogram is skewed to the left therefore appears asymmetrical. 

Modality 

Both the males and the females have single modes. 

Visual interpretation is appealing to the eye but does not give detailed information contained. The following are some of the advantage and disadvantages of visual interpretations. 

Advantages of visual interpretation 

The following are some of the advantages of visual interpretation of data 

Easy to read 

They are visually appealing 

It is easy to handle large data sets using keyed icons. 

Limitations of visual interpretation 

These are some of the disadvantages; 

It is hard to quantify partial icons 

The icons must be of regular size for easy interpretation 

It works best for 2-6 categories 

Very basic 

Section 2: Measures of Central Tendency and Dispersion 

The following table shows the mean, standard deviation, skewness and kurtosis of the id, gender, ethnicity, gpa, quiz3 and total variables. 

Table 1 : Descriptive statistics

Descriptive Statistics
	N	Mean	Std. Deviation	Skewness		Kurtosis
	Statistic	Statistic	Statistic	Statistic	Std. Error	Statistic	Std. Error
Id	105	571366.67	277404.129	-.090	.236	-1.299	.467
Gender	105	1.39	.490	.456	.236	-1.828	.467
ethnicity	105	3.35	1.056	-.451	.236	-.554	.467
Gpa	105	2.9950	.67370	-.317	.236	-.656	.467
quiz3	105	7.06	1.875	-.147	.236	-.134	.467
Total	105	99.65	14.195	-.866	.236	1.201	.467

From the table above, it is possible to interpret the means, standard deviation, skewness and kurtosis for interval scaled variables only i.e. gpa, qiuz3 and total (scaled). However, it is not possible to interpret the ordinal and categorical variables i.e. Id, gender and ethnicity . These categorical variables have no intrinsic ordering to the categories. 

The values of skewness and kurtosis lie in the range between -2 and +2 (Gergia & Mallery, 2003) . From the table above, it can be deduced that gpa,, quiz3 , and total variables are within the range of skewness and kurtosis. 

Gpa, and quiz3 variables are excellent while total variable is accepted but not excellent. This is because the values of gpa and quiz3 are more closer to zero as compared to total variable. 

The mean, standard deviation, skewness and kurtosis of the accepted variables are shown in the table 2 below 

Table 2 : Acceptable Variables

Descriptive Statistics
Variables	N	Mean	Std. Deviation	Skewness	Kurtosis
	Statistic	Statistic	Statistic	Statistic	Statistic
Gpa	105	2.9950	.67370	-.0.053	-0.189
quiz3	105	7.06	1.875	0.089	-0.333
Total	105	99.65	14.195	0.65	1.668

Reference 

Gergia D & Mallery P. (2003). SPSS for Windows Step by Step. Science and Education .