Data collected from students How can we compare?

Approximately how many times did you get Number of Frequency

Number of Frequency
angry with anyone in the last 7 days? times being
times being
angry
angry
Responses from 10 undergraduate and 10 1 1
1 2
2 4
graduate students: 2 2
3 5
3 2
Undergraduate students’ responses: Graduate students’ responses: 4 2
4 3
5 2
5 4
4, 5, 2, 4, 6, 6, 7, 6, 6, 2, 5, 4, 3, 1, 3, 5, 2, 4, 2 , 2, 3, 1, 6, 3, 2, 3, 3, 4, 1, 6 1
5, 5 5, 3 6 3
7 0
7 1

We want to compare: who gets angry more Undergraduate Students Graduate students
often? Undergrads or grads?

Graduate students
No of students (frequency)

Graduate students
No of students (frequency)

Undergraduate students

Organizing data
0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8
No. of times getting angry No. of times getting angry Dr. Sumera Ahsan
 Content Data
• Raw data and organized data Data (plural) are measurements or observations.
• Preparing Tables A data set is a collection of measurements or
• Frequency Distribution: Simple and for observations. A datum (singular) is a single
grouped data measurement or observation and is commonly
called a score or raw score.

Frequency Distribution Table Frequency Distribution

With an ordinal, interval, or ratio scale, the
X f categories are listed in order (usually highest A frequency distribution is an organized tabulation
8 2 to lowest). For a nominal scale, the categories of the number of individuals located in each
can be listed in any order.
7 0 category on the scale of measurement.
6 4 By adding up the frequencies, you obtain the
total number of individuals
5 3 A frequency distribution can be structured either as
4 1 Notice that the X values in a frequency a table or as a graph, but in either case, the
distribution table represent the scale of
measurement, not the actual set of scores. distribution presents the same two elements:
In-course number
The frequency associated with each score is
1. The set of categories that make up the original
recorded in the second column. measurement scale.
∑f=N
2. A record of the frequency, or number of
individuals in each category.
 ∑X
Proportion
• What will be the ∑X? • P= f/N
X f fX
Proportion measures the fraction of the total group that
is associated with each score.
8 2 16
7 0 0 X f fX
6 4 24 8 2 16 for the score x= 8,
5 3 15 7 0 0 p= 2/10= 1/5=.20
4 1 4 6 4 24
∑fX=59 5 3 15
4 1 4
∑X= 8+8+6+6+6+6+5+5+5+4=59 10 ∑fX=59

• What will be the ∑X2?= Because proportions describe the frequency (f) in relation
82+82+62+62+62+62+52+52+52+42 to the total number (N), they often are called relative
frequencies.

Percentage
Grouped frequency Distribution Table
percentage associated with each
X f fX • When a set of data covers a wide range of values, it is unreasonable
8 2 16
score, you first find the to list all the individual scores in a frequency distribution table. For
example, a set of exam scores that range from a low of 41 to a high
7 0 0 proportion (p) and then multiply of 96. These scores cover a range of more than 50 points.
6 4 24 by 100: • Although this would organize the data, the table would be long and
5 3 15 cumbersome.
4 1 4 percentage p (100)=(f/N)100 Remember: The purpose for constructing a table is to obtain a
relatively simple, organized picture of the data.
10 ∑fX=59 • This can be accomplished by grouping the scores into intervals and
then listing the intervals in the table instead of listing each
for the score x= 8, individual score.
• The result is called a grouped frequency distribution table because
p(100)= (2/10)100=.20×100=20% we are presenting groups of scores rather than individual values.
The groups, or intervals, are called class intervals.
Preparing Grouped frequency Distribution Guidelines
Raw scores:
• The grouped frequency distribution table should have
82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, about 10 class intervals. Why not many? OR why not
89, 75, 80, 73, 78, 60 only several?
How many rows: When the scores are whole numbers, the total • The width of each interval should be a relatively
number of rows can be obtained by finding the difference between simple number. For example, 2, 5, 10, or 20 would be a
the highest and the lowest scores and adding 1: good choice for the interval width.
Highest score – lowest score+ 1; 94-53+1=42 (we need 42 rows!!) • The bottom score in each class interval should be a
multiple of the width. If you are using a width of 10
The best method for finding a good interval width is a systematic trial- points, for example, the intervals should start with 10,
and-error approach 20, 30, 40, and so on.
Width of interval Number of Intervals Needed • All intervals should be the same width. They should
to Cover a range of 42 points
cover the range of scores completely with no gaps and
2 21 no overlaps, so that any particular score belongs in
5 9 exactly one interval.
10 5

Preparing Grouped frequency Distribution Preparing Grouped frequency Distribution

• The next step is to actually identify the intervals. X f Raw scores:
• The lowest score for these data is X 53, so the lowest 90-94 3 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61,
91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60
interval should contain this value. Because the interval 85-89 4
should have a multiple of 5 as its bottom score, the 80-84 5
interval should begin at 50. The interval has a width of 75-79 4
This grouped frequency distribution table
5, so it should contain 5 values: 50, 51, 52, 53, and 54. 70-74 3 shows the data from Example 2.4. The original
Thus, the bottom interval is 50–54. 65-69 1 scores range from a high of X 94 to a low of X
• The next interval would start at 55 and go to 59. Once 60-64 3
53. This range has been divided into 9 intervals
with each interval exactly 5 points wide. The
the class intervals are listed, you complete the table by 55-59 1 frequency column (f) lists the number of
adding a column of frequencies. The values in the individuals with scores in each of the class
50-54 1
frequency column indicate the number of individuals intervals
who have scores located in that class interval.
 Explain with example Exercise
• After the scores have been placed in a • Please complete the exercise that will be
grouped table, you lose information about the posted in google classroom
specific value for any individual score
• The wider the class intervals (width) are, the
more information is lost.