Lesson in Statistics and Probability Grade 11

1. LESSON 7: OTHER MEASURES OF
LOCATION

2. LEARNING OUTCOME(S): AT THE END OF
THE LESSON, THE LEARNER IS ABLE TO
 Calculate measures of location other than the
measure of central tendency, and
 Provide a sound interpretation of these summary
measures.

3. A. MOTIVATION

4. QUESTIONS:
1. What is the highest score? Lowest score?
2. What is the most frequent score?
3. What is the median score?
4. What is the average or mean score?
5. What is the score where at most 75% of the 150
students scored less or equal to it?
6. Do you think the long test is easy since 75
students have scores at most 33 out of 50?
7. Do you need to be alarmed when 10% of the class
got a score of at most 20 out of 50?

5. B. MEASURES OF LOCATION: MAXIMUM,
MINIMUM, PERCENTILES, DECILES AND
QUATILE
Terms
a. Maximum -as a measure of location that pinpoints
the highest value in the data distribution.
b. Minimum- locates the lowest value.
c. Percentile- is a measure that pinpoints a location
that divides distribution into 100 equal parts. It is
usually represented by Pj, that value which
separates the bottom j% of the distribution from the
top (100-j)%.

6. The steps in finding the jth percentile (Pj)
Step 1: Arrange the data values in ascending order of
magnitude.
Step 2: Find the location of Pj in the arranged list by
computing L= , where N is the total number
of observations in the data set.
Step 3: a. If L is a whole number, then Pj is the
mean or average of the values in the Lth and
(L+1)th positions.
b. If L is not a whole number, then Pj is the
value of the next higher position.

7. c. Percentile divides the distribution into
100 equal parts,
d. Deciles divide the distribution into 10
equal parts while
e. Quartiles divide the distribution into 4
equal parts.

9. Using the data, find the following,
1. P30
2. P75
3. Q2
4. D7
5. P80

10. Generalization
• There are other measures of location that
could further describe the distribution of
the data set.
• The maximum and minimum values are
measures of location that pinpoints the
extreme values which are the highest
and lowest values, respectively.
• Percentiles, quartiles and deciles are
measures of locations that divide the
distribution into 100, 4 and 10 equal
parts, respectively.