# 5-10 Statistics Chapter 5: Practice Comparing Distributions – KEY

```Statistics Chapter 5: Practice Comparing Distributions – KEY
In 1953, N. Keyfitz published a study in the American Journal of Sociology entitled, “A Factorial
Arrangement of Comparisons of Family Size.” Here is some of the data from that study.
Number of children of women who were aged 15–19 when first married
Mother educated for six years or fewer:
14, 13, 4, 14, 10, 2, 13, 5, 0, 0, 13, 3, 9, 2, 10, 11, 13, 5, 14
Mother educated for seven years or more: 0, 4, 0, 2, 3, 3, 0, 4, 7, 1, 9, 4, 3, 2, 3, 2, 16, 6, 0, 13, 6, 6, 5, 9,
10, 5, 4, 3, 3, 5, 2, 3, 5, 15, 5
Question: What can we say about how the number of children compare for these two groups?
Use the example in your book on page 90 as a guide as needed.
Think
I want to compare the number of children of women aged 15 – 19 when first married from two different
groups: mothers educated for six years or fewer, and mothers educated for seven years or more. These
data were collected by N. Kevfitz in 1953.
Quantitative Data Condition: The numbers of children are quantitative. Boxplots are appropriate for
comparing the groups, and numerical summaries of each group are also appropriate.
Min
6 or
fewer
7 or
more
Q1
Med
Q3
Max
IQR
Number of Children
0
0
3
2
10
4
13
6
14
16
18
10
4
Number of Children
Show
16
14
12
10
8
6
4
2
0
LessEducation
MoreEducation
Education
Tell
5-10
The distribution of the number of children of mothers with 6 or fewer years of education is skewed to
the left. In comparison, the distribution of the number of children of mothers with 7 or more years of
education is much more symmetric. Mothers with less education typically had more children, with a
median of 10 children, while mothers with more education had a median of only 4 children.
Additionally, there was much more variability in the distribution of mothers with less education. The
IQR of 10 children is much higher than the IQR of 4 children for the mothers with more education.
With the exception of 3 outliers, all of the families of mothers with more education were smaller than
the median family size of the less educated mothers. It should be noted that the two largest families
were from mothers with more education.