2. MEASURES OF CENTRAL TENDENCY OF
UNGROUPED DATE
PREPARED BY:
CHERRY B. LAGAS
LOVELY MAE L. PORCADILLA
3. Objectives:
At the end of the lesson the students should be
able to:
• define and enumerate measures of the central
tendency of ungrouped data;
• compute the mean of ungrouped data; and
• generate insights from statistical data using
measures of central tendency.
4. Short Review
Identify whether the following data is quantitative or qualitative.
1. general average
2. civil status
3. annual income
4. years in school
5. educational attainment
6. skin color
7. age
8. number of children
9. weight
10.social class
5. Measures of Central Tendency are a single value that attempts to describe a set
of data by identifying the central position within that set of data. As such,
measures of central tendency are sometimes called measures of central location.
Mean is the sum of the data values divided by the number of values. This is also
referred to as the arithmetic mean. The mean is the balance point of a
distribution.
Median is the number that falls in the middle position once the data has been
organized from smallest to largest or largest to smallest.
Mode is the value that appears most frequently in the set of data.
6. In finding the mean of ungrouped data, we find the sum of
values (x) divided by the number of values in the data set
represented by N. We use the formula:
Note: The symbol Σ (sigma) is a Greek letter used to indicate
summation.
7. Example 1:
The grades in Geometry of 10 students are 87, 84, 85, 85, 86, 90, 79,
82, 78, 76. What is the average grade of the 10 students?
Solution:
x=( x)/N
∑
x=(87+84+85+85+86+90+79+82+78+76)/10
=832/10
x = 83.2
Hence, the average grade of the 10 students is 83.2
8. Example 2:
The shoe sizes of the members of the basketball team Liliw
Lakers are 7, 9, 11, 8, 8, 8, 7, 8, 9, 10, 8. Compute for the
mean.
Solution:
Hence, the average shoe size of the members of the
basketball team is 8.45.
9. Example 3:
The weights in kilograms of the runners in the annual district
level marathon are the following: 90.7, 89.5, 93.4, 92.1, 82.6, 92.5,
94.4, 89.5, 86.7, 90.4, 94.4, 97.1, 89.5. Find the mean.
Solution:
Hence, the average weight of runners is 90.98 kg.
10. 1. The number of incorrect answers on a true-or-false test of your
15 classmates were recorded by your teachers as follows: 2, 1, 3, 0,
1, 3, 6, 0, 3, 3, 5, 2, 1, 4 and 2.
2. The number of building permits issued by your municipality last
month were 4, 7, 0, 11, 4, 1, 15, 3, 5, 8, and 7.
3. An experiment was conducted for a random sample of 9 subjects.
A stimulant was applied to each subject and the recorded
reaction time are 2.5, 3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1 and
3.4 seconds.
FIND THE MEAN OF THE
FOLLOWING:
11. How to Calculate Mean in Excel
Step 1: Open MS Excel
Step 2: Select Data
Step 3: Enter AVERAGE Formula
In this method, we are going to use the AVERAGE function which returns the mean of the arguments. For
example, the =AVERAGE(A1:A10) returns the average of the numbers in the range of A1 to A10.
12. Activity 3: Closing the Loop!
Answer the following questions.
1. What are the key concepts of our lesson?
2. Which part of the lesson is the easiest for you?
Why?
3. Which part of the lesson is the hardest for you?
Why?
4. How are we as a class today?
13. Activity 4: Let’s Solve It! Analyze and answer the question that follows.
According to PAG-ASA, last April 30, 2023, the heat index recorded in their 14 monitoring
stations are the following:
Source:
https://mindanews.com/top-stories/2023/05/davao-city-posts-highest-heat-index-in-
mindanao-on-april29-and-30/#gsc.tab=0
14. Questions:
1. Based on the table, what is the mean heat
index?
2. What does the mean imply?
