Lesson in Statistics and Probability Grade 11

1. LESSON 9: MORE ON DESCRIBING
DATA: SUMMARY MEASURES AND
GRAPH

2. LEARNING OUTCOME(S): AT THE END OF
THE LESSON, THE LEARNER IS ABLE TO
• Provide simple analysis of a data set based on its
descriptive measures.

3. A. PRELIMINARIES
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.

4. 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. B. MOTIVATION: THE STUDENT’S HEIGHT AND
WEIGHT AND CORRESPONDING BMI
Questions
1. Are the heights, weights, and BMI of males and
females the same or different?
2. What are some other factors besides sex that
might affect heights, weights and BMI? (Possible
factors that could be studied are age, location
where person resides, and year the data was
collected.)

7. GROUP ACTIVITY
o The first group for the variable ‘height’;
o The second group for the variable ‘weight’; and
o The third group for the variable ‘BMI’

8. EXAMPLE

9. 1. 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. Each
group could use the following format of the
table to present the computed measures:

11. 2. With the computed descriptive measures, write a
textual presentation of the data for the variable
assigned to the group.

13. 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.

15. 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.
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.

17. 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.