Post on 18-Jan-2015
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Probability and Statistics
Charts and Frequency Distributions
When the variable of interest is qualitative, the statistical table is a list of the categories being considered along with measure of how often each value occurred. The measure can be presented in the following way:1. The frequency or number of measurements in
each category2. The relative frequency, or proportion of
measurements in each category3. The percentage of measurement in each
category
1. 4000 freshmen were admitted in Don Bosco Technical College in Mandaluyong for the school year 2010-2011. The Students were enrolled in the following program:
Example
Program Number of Students
Architecture 320
Computer Engineering 440
Computer Science 720
Electronics & Communication
1080
Entrepreneurship 800
Information Technology 400
Mechanical Engineering 240
Total 4000
Bar Graph Uses the height of the bar to display the amount in a
particular category.
Pie Chart Displays how the total quantity is distributed among the
categories.
Program Frequency
Relative
Percent
Architecture 320 0.08 8%
Computer Engineering 440 0.11 11%
Computer Science 720 0.18 18%
Electronics & Communication 1080 0.27 27%
Entrepreneurship 800 0.20 20%
Information Technology 400 0.10 10%
Mechanical Engineering 240 0.06 6%
Total 4000 1.00 100%
When a quantitative variable is recorded over time at equally spaced intervals, the data set forms a time series. Time series data are most effectively presented on a line chart.
Example. Table that shows the daily production of Gardenia Bread
Day 1 2 3 4 5 6 7
Number of Loaves(In Thousands)
200 190 230 170 240 250 245
Line Graph
A stem and leaf plot presents a graphical display of the data using the actual numerical values of each data point.
Steps in constructing:1. Divide each measurement into two parts: stem
and leaf2. List the stem in column, with a vertical line to the
right.3. For each measurement, record the leaf portion in
the same row as its corresponding stem.4. Order the leaves from lowest to highest in each
stem.
Stem and Leaf Plot
Daily sales of desktop computers of JRC Computer Company for 40 days.
Example
34 40 31 33 20 25 51 62
45 30 38 45 61 42 30 28
35 31 28 42 39 40 52 43
36 46 48 51 52 47 42 39
40 31 29 33 47 36 45 21
2 8 9 0 8 1
3 4 5 6 0 1 1 1 8 3 3 9 6 0 9
4 5 0 0 6 8 5 2 7 2 0 7 2 5 3
5 1 2 1 2
6 1 2
Solution
2 0 1 8 8 9
3 0 0 1 1 1 3 3 4 5 6 6 8 9 9
4 0 0 0 2 2 2 3 5 5 5 6 7 7 8
5 1 1 2 2
6 1 2
REORDERING
Steps in Constructing a Frequency Distribution Table
1. Determine the number of classes by using Sturges’ Formula:
K = 1 + 3.322 log n = approximate number of
classes n = number of observations
2. Determine the approximate class size. Whenever possible, all classes should be of the same size. The following steps can be used to determine the class size:* Solve for the range, R = max- min*Compute for C’ = R / K*Round-off C’ to a convenient number(nearest whole number)
Frequency Distribution
Steps in Constructing a Frequency Distribution Table
3. Determine the lowest class limit. The first class must include the smallest value in the data set.
4. Determine all class limits by adding the class size , C, to the limit of the previous class.
5. Tally the frequencies for each class. Sum the frequencies and check against the total number of observations.
Frequency Distribution
Construct a frequency distribution from the final grades of Stat 101 Students given below:
Example
82 82 83 79 72 71 84 59 77 50 87
83 82 63 75 50 85 76 79 68 69 62
79 69 74 53 73 71 50 76 57 81 62
72 88 84 80 68 50 74 84 71 73 68
71 80 72 60 81 89 94 80 84 81 50
84 76 75 82 76 53 91 69 60 89 79
59 62 79 82 72 81 60 84 68 66 94
77 78 87 75 86 82 74 73 72 84 51
50 69 75 70 77 87 86 77 75 96 66
87 73 84 68 85 62 87 92 69 52 65
1. Construct a stem and leaf plot.
Solution
5 0 0 0 0 0 0 1 2 3 3 7 9 9
6 0 0 0 2 2 2 2 3 5 6 6 8 8 8 8 8 9 9 9 9 9
7 0 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5 5 5 5 5 6 6 6 6 7 7 7 7 8 9 9 9 9 9
8 0 0 0 1 1 1 1 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 5 5 6 6 7 7 7 7 7 7 8 9 9
9 1 2 4 4 6
The Complete Frequency Distribution Table
Class Frequency
LCB UCB RF RFP <CF >CF
Graphical Representation of a Frequency Distribution
1. Frequency Histogram – a bar graph that displays the classes on the horizontal axis and frequencies of the classes on the vertical axis; the vertical lines of the bars are erected at the class boundaries and the height of the bars correspond to the class frequency.
2. Relative Frequency Histogram – a graph that displays the classes on the horizontal axis and the relative frequencies on the vertical axis.
Graphical Representation of a Frequency Distribution
3. Frequency Polygon – a line chart that is constructed by plotting the frequencies at the class marks and connecting the plotted points by means of straight lines; the polygon is closed by considering an additional class at each end and the ends of the lines are brought down to the horizontal axis at the midpoints of the additional classes.
4. Ogives – graphs of the cumulative frequency distribution.a. < ogive – the <CF is plotted against the UCBb. > ogive – the >CF is plotted against the LCB
The Categorical frequency distribution is used for data that can be placed in specific categories, such as nominal or ordinal-level data.
Categorical Frequency Distribution
Twenty five students were given the following grades. The data set is:
C A B A DF B A C AC D F B BA B D F CB C C B D
Example
a. Make a table with A, B, C, D, and F as classes.
b. Tally the data and count the tallies.c. Find the percentage of values in each class
by using the formula
d. Find the total frequency and percent .
Solution
%100% 1 xb
b
o
Class Frequency Percent
A 5 20
B 7 28
C 6 24
D 4 16
F 3 12
TOTAL 25 100
Table of frequency and percent