Description

This report looks at a dataset that contains information about gender together with age groups and faculty status and marital status in addition to the number of children. The analysis focuses on summarizing age data through descriptive statistics and graphical displays while creating age group categories for additional examination of their relationship to gender and faculty status.

Analysis

Figure 1 below shows a histogram of the age variable. Most value lie between 30 and 5 it seems like.

Below is table 1 of the age variable, with a \(\bar{x}=35\) and a standard deviation of 7.66. The youngest person is aged 25 and oldest is 52.

Table 1. Descriptive Statistics for Age
Mean SD Min Max
35.18182 7.663372 25 52

Table 2 below shows the descriptive statistics for the recoded age groups (Young, Middle, and Senior). Mean age for the seven young individuals is 27.9 (SD = 1.9). For 10 middle aged people, the mean is 34.4 (SD = 2), and for 5 seniors the mean is 47 (SD = 4.9).

Table 2. Descriptive Statistics for Recoded Age Groups
age_group Count Mean_Age SD_Age
Young (≤30) 7 27.9 1.9
Middle (31–39) 10 34.4 2.0
Senior (40+) 5 47.0 4.9

Table 3 below shows that there is no statistical significant association (\(\chi^2(2, N = 24) = 1.91,\ p = .385\)) between re-coded age group and gender based on the data.

## Warning in stats::chisq.test(x, y, ...): Chi-squared approximation may be
## incorrect
Table 3. Cross-Tabulation of Age Group by Gender
Age Group Female Male
Young (≤30) 2 5
Middle (31–39) 1 9
Senior (40+) 2 3
Chi-Square p-value 0.3852

Table 4 below shows a statistical significant relationship (\(\chi^2(2, N = 24) = 7.48,\ p = .024\)) between age group and faculty status, showing that older individuals are more likely to be faculty than would be expected by chance.

## Warning in stats::chisq.test(x, y, ...): Chi-squared approximation may be
## incorrect
Table 4. Cross-Tabulation of Age Group by Faculty
Age Group No Yes
Young (≤30) 7 0
Middle (31–39) 10 0
Senior (40+) 3 2
Chi-Square p-value 0.0238

Conclusion

The average age is about 35 years, no statistical significance association between recorded age groups and gender. But there was a statistical significant relationship between age group and faculty status, with seniors more likely to be faculty.