Statistics Case Study Examples

Frequency table

Figure 1 illustrates the frequency table.
Figure 1. The frequency table
The values are distributed among the range, and only the values 8.9 and 10.1 are repeated twice.

Histogram

The histogram displays the frequencies of the grouped values.
Figure 2. The histogram
The value of the highest bar indicates the mean value, which is about 12 $ million. The distribution is left asymmetric, namely the majority of the values are at the left side of the distribution.

Stem and leaf plot

Figure 3. The stem and leaf plot for the data

Apparently, the values close to 10 and 11 are the most frequent.

Sample mean and median
The mean calculates as the sum of all the values, divided by 25:
Mean= 38.6+34.1+16.4+16.3+15.7++8.9+8.925=13.85.
The median is the number that separates the higher half from the lower half. To calculate the median, we need to arrange the data in increasing order. The 13th value is the median
8.9; 8.9; 9.1; 9.4; 9.6; 10; 10.1; 10.1; 10.5; 11; 11.1; 11.5; 11.6; 11.8; 11.9; 12.4; 12.8; 14.7; 14.8; 14.9; 15.7; 16.3; 16.4; 34.1; 38.6.
Thus, median is 11.6.

Sample standard deviation

The standard deviation calculates as:
Std=(x1-mean)2+(x2-mean)2+(x3-mean)2++(x25-mean)225-1.
Std=(38.6-13.85)2+(34.1-13.85)2+(16.4-13.85)2++(8.9-13.85)225-1=7.19.

Conclusion

Using the statistical methods, the data of the highest paid women were analyzed. The mean compensation among the most paid women is 13.85 $ million, and the median is 11.6 $ million.
The salaries are not normally distributed, the distribution is characterized by the left asymmetry. The most frequent values are about 10 and 11 million.