In this lesson, students will do an activity that will use the data on heights and weights which were collected in Lesson 2. They will construct box plots and calculate the summary measures they have learned in previous lessons. These computed summary measures and constructed boxplot will be used to describe fully the data set so as to provide simple analysis of the data at hand.

1. More on Describing Data
Summary Measures and Graphs

2. Learning Outcomes
Construct and interpret box plots; and
Provide simple analysis of a data set based on
its descriptive measures.

3. GROUPINGS
The class will be divided into three groups.

4. What is BMI?
The BMI, devised by Adolphe Quetelet, is defined as
the body mass divided by the square of the body
height, and is universally expressed in units of kg/m2,
using weight in kilograms and height in meters. When
the term BMI is used informally, the units are usually
omitted. A high BMI can be an indicator of high body
fatness. The BMI can be used to screen for weight
categories that may lead to health problems

5. What is BMI?
 The BMI provides a simple numeric measure of a person's thickness or
thinness, allowing medical and health professionals to discuss weight
problems more objectively with the adult patients. The standard weight
status categories associated with BMI ranges for adults are listed below:

6. QUESTIONS
Are the heights, weights, and BMI of males and
females the same or different?
What are some other factors besides sex that
might affect heights, weights and BMI?

7. GROUP ASSIGNMENT
GROUP 1 will be assigned for HEIGHT
GROUP 2 will be assigned for WEIGHT
GROUP 3 will be assigned for BMI

8. TASKS
Compute the descriptive measures for the whole class and
also for each subgroup in the data set with sex as the
grouping variable. The descriptive measures to compute
include the measures of location such as minimum, maximum,
mean, median, first and third quartiles; and measures of
dispersion such the range, interquartile range (IQR) and
standard deviation.
With the computed descriptive measures, write a textual
presentation of the data for thevariable assigned to the group.

9. TABLE FORMAT

10. EXAMPLE

11. Possible textual presentation of the data on
heights:
Based on Table 9.2, on the average, a student of this class is 1.582
meters high. The shortest student is just a little bit over one meter
while the tallest is 1.79 meters high resulting to a range of 0.77
meter. The median which is 1.585 is almost the same as the mean
height.
Comparing the males and female students, on the average male
students are taller than female students but the dispersion of the
heights of the female students is wider compared to that of the
male students. Thus, male students of this class tend to be of same
heights compared to female students.

12. EXAMPLE

13. Possible textual presentation of the data on
weights:
Using the statistics on Table 9.3, on the average, a student of this
class weighs 55.8 kilograms. The minimum weight of the students in
this class is only 27 kilograms while the heaviest student of this class
is 94 kilograms. There is a wide variation among the values of the
weights of the students in this class as measured by the range which
is equal to 67 kilograms. The median weight for this class is 51.5
kilograms which is quite different from the mean as the value of the
latter was pulled by the presence of extreme values.

14. Possible textual presentation of the data on
weights:
Comparing the males and female students, on the average male
students are heavier than female students. The extreme values
observed for the class are both coming from male students. The
wide variation observed on the students’ weights of this class was
also observed among the weights of the male students. In fact, the
standard deviation of the weights of the male students is more than
double the standard deviation of the weights of female students.

15. EXAMPLE

16. Possible textual presentation of the data on
BMIs:
 Table 9.4 shows that the minimum BMI of the students in the class is 9 while
the maximum is 58 kg/m2. On the average, a student of this class has a BMI
of 22.9. Also, the median BMI for this class is 21.5 which is near the value of
the mean BMI. The variability of the values is also not that large as a small
standard error value of 8.3 was obtained.
 Comparing the males and female students, on the average, the BMI of the
male and female students are near each other with numerical values equal to
23.6 and 22.2, respectively. But there is a wider variation among the BMI
values of the female students compared to that of the male students. The
standard deviation of the BMIs of the male students is less than that of the
female students

17. TABLE FORMAT

18. CONSTRUCTION OF A
BOX-PLOT

19.  Draw a rectangular box (horizontally or vertically) with the first and third
quartiles as the endpoints. Thus the width of the box is given by the IQR
which is the difference between the third and first quartiles.
 Locate the median inside the box and identify it with a line segment.
 Compute for 1.5 IQR. Use this value to identify markers. These markers are
used to identify outliers. The lowest marker is given by Q1 – 1.5IQR while
the highest marker is Q3+ 1.5IQR.Values outside these markers are said to
be outliers and could be represented by a solid circle.
 One of the two whiskers of the box-plot is a line segment joining the side
of the box representing Q1 and the minimum while the other whisker is a
line segment joining Q3 and the maximum. This is for the case when the
minimum and maximum are not outliers. In the case that there are
outliers, the whiskers will only be line segments from the side of box and
its corresponding marker.

20. EXAMPLE

21. EXAMPLE

22. EXAMPLE

23. EXAMPLE

24. EXAMPLE

25. EXAMPLE

26. KEY POINTS
Descriptive measures are important statistics required
in simple data analysis.
Groups of data could be compared in terms of their
descriptive measures.
A box-plot is an approach to compare visually data
distributions.