This document discusses different types of graphs that can be used to present data graphically: pie charts, bar graphs, histograms, frequency polygons, and cumulative frequency polygons. It also discusses stem and leaf plots and dot plots. Additionally, it covers measures of central tendency including the mean, median, and mode. It provides examples of calculating each measure and includes sample problems for students to practice finding the mean, median, and mode.

1. Graphical Presentation of
Data
Prepared by: Ms. Jenny Tuazon

2. Commonly used graphs:
PIE CHART
BAR GRAPH
HISTOGRAM
FREQUENCY POLYGON

3. Pie Chart
A circular graph that shows how
measurements are distributed
among the categories

4. Bar Graph
Shows the distribution of
measurements among the
categories through the height of the
bar, which determines how often a
particular category is observed

5. Histogram
Also known as frequency histogram
Graph represented by vertical bars whose
bases represent the class marks and whose
heights represents the class frequency
RELATIVE FREQUENCY HISTOGRAM the
height represents the relative frequency of a
class

6. FREQUENCY POLYGON
Line graph of a frequency distribution.
The number of observation in each
class is represented by a dot above the
class mark, whose height is the
frequency of the class inerval

7. Cumulative Frequency
Polygon
Also called an ogive.
Formed by plotting the cumulative
frequency against the class
boundary and joining all the
consecutive points by a straight line
segments

8. Stem and Leaf Plot and
Dot

9. STEM AND LEAF PLOT
A simple way to show the
distribution of a set of
quantitative data.

10. Dot Plot
A graphical representation of a set
of data which shows a dot for
each value in a data set along the
number line.

11. Measures of
Central
Tendency

12. Measures of Central
Location/Tendency
Any measure indicating the
center of a set of data, which is
arranged in increasing or
decreasing order.

13. Arithmetic Mean
Average of a set of
measurements and is one of the
most common and useful
measures of central tendency.
MEAN/Average

14. Relevant Notation/Symbols
- mean of the population
x̄ - mean of a sample
N - population size
- sum
N – Population size
n – Sample Size
Formula in finding the Mean
𝝁 =
𝒙=𝒊
𝑵
𝒙𝒊
𝑵
𝒙 =
𝒙=𝒊
𝒏
𝒙𝒊
𝒏

15. Example
Determine the mean of the
following set of samples:
5,2,1,3,4

16. Example
Suppose a population
consists of observations with
the following values:
1,1,2,1,4,3,4,3,4,5,2, and 1.

17. Median
The value of x in the middle of a set of n
measurements.
Steps in finding the Median
1. Arrange the data from smallest to largest.
2. When the number of data is odd, use the
formula: 𝑥 = 0.5 𝑛 + 1
3. When the data is even, get the average of
the two values in the middle.

18. Examples
1. Determine the mean of the
following set of samples: 5,2,1,3,4
2. Suppose a sample data has the
following values:
2,4,5,3,2, and 4.

19. Mode
The value that occurs most
frequently in a set of observations.
If the set of data contains only one
mode – unimodal and if it has two
modes – bimodal distribution
Bimodal Distribution – two
different values in the data set occur
frequently.

20. Exercises/Seatwork
Find the MEAN, MEDIAN, and MODE.
1. The marks scored obtained by 20 students in an
examination are as follows:
25, 37, 8, 40, 45, 29, 42, 12, 25, 16, 20, 36, 30, 33, 24, 24,
11, 35, 30, 45
2. The shoe sizes of 10 people in a survey are:
8, 9, 9, 7, 10, 6, 7, 8, 9, 7
3. The number of incorrect answers on a true-false
competency test for a random sample of 15 students were
recorded as follows: 2, 1, 3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4, and
2.

21. QUIZ (Measures of Central Tendency)
1. The number of building permits issued last month to 12
construction firm in a small Midwestern city were 4, 7, 0, 7, 11, 4,
1, 15, 3, 5, 8, and 7. Treating the data as a population, find a.) the
mean; b.) the median; and c.) the mode.
2. The reaction times for a random sample of 9 subjects to a stimulant
were recorded as 2.5,3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1, and 3.4 seconds.
Calculate a.) the mean; and b.) the median.
3. The employees of a local manufacturing plant pledged the
following donations, in dollars to the United Fund: 10, 40, 25, 5, 20,
10, 50, 30, 10, 5, 15, 25, 50, 10, 30, 5, 25, 45, and 15. Treating the
data as a population, calculatea.) the mean; and b.) the mode c.)
median