Modality Skew Standard Deviation in Histogram

Histograms and Visual Interpretation

Histogram 1 shows the total scores of females. Histogram 2 shows the total scores of males.

Both histograms display negative skew with longer tails on the left than on the right. The kurtosis is flatter among males than among females, which shows a sharp increase around the median; thus the histogram of female totals is mesokurtotic and the histogram of males is more playkurtotic. The modality is different for the two as well: the female histogram is multimodal and the male histogram is bimodal. There appear to be outliers but this could also be judged as the tail of normal distribution and were they removed it would look like an amputee distribution perhaps. Both histograms show significant symmetry with slightly more modality on the right because of the skew.

The strengths of visually interpreting histograms is that it provides a general feel for the shape of the curve and the make-up of the variable, in this case males and females and how they round out as a whole. The weakness of visually interpreting histograms is that it does not provide an exact numerical interpretation for measurement purposes.

Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Skewness

Kurtosis

Statistic

Statistic

Statistic

Statistic

Statistic

Statistic

Std. Error

Statistic

Std. Error

id

106484

988808

571366.67

277404.129

-.090

.236

-1.299

.467

gender

1

2

1.39

.490

.456

.236

-1.828

.467

ethnicity

1

5

3.35

1.056

-.451

.236

-.554

.467

gpa

1.14

4.00

2.7789

.76380

-.052

.236

-.811

.467

quiz3

0

10

8.05

2.322

-1.177

.236

.805

.467

total

51

15.299

-.837

.236

.943

.467

Valid N (listwise)

Section 2: Calculating and Interpreting Measures of Central Tendency and Dispersion

The variables for which mean, s.d., skewness and kurtosis have no meanings are: id, gender, and ethnicity.

The variables for which mean, s.d., skewness and kurtosis are interpretable are gpa, quiz 3, and total scores, because these three variables offer numeric data that represents the class which can be graphed and assessed using these measures.