Description

A bar diagram can be utilized to delineate any of the levels of estimation ... Pie Chart. A pie outline is valuable for showing a relative recurrence dissemination. A circle is separated ...

Transcripts

Dr. Ka-fu Wong ECON1003 Analysis of Economic Data

Chapter Two Describing Data: Frequency Distributions and Graphic Presentation GOALS Organize information into a recurrence circulation. Depict a recurrence dissemination in a histogram, recurrence polygon, and total recurrence polygon. Build up a stem-and-leaf show. Present information utilizing such realistic strategies as line graphs, bar diagrams, and pie outlines.

Frequency Distribution A Frequency appropriation is a gathering of information into fundamentally unrelated classifications demonstrating the quantity of perceptions in every class.

Construction of a Frequency Distribution Question to be tended to. Gather information (crude information). Compose information. Recurrence circulation Present information. Reach determination.

Terms Related to Frequency Distribution In developing a recurrence circulation, information are separated into comprehensive and fundamentally unrelated classes. Mid-point: A point that partitions a class into two a balance of. This is the normal of the upper and lower class limits. Class recurrence: The quantity of perceptions in every class. Class interim: The class interim is gotten by subtracting the lower furthest reaches of a class from the lower furthest reaches of the following class.

Four stages to build recurrence conveyance Decide on the quantity of classes. Decide the class interim or width. Set the individual class limits. Count the information into the classes and include the quantity of things each. For outline, it is advantageous to convey a case with us – case 1 .

EXAMPLE 1 Dr. Tillman is Dean of the School of Business Socastee University. He wishes to set up a report demonstrating the quantity of hours every week understudies spend concentrating on. He chooses an irregular specimen of 30 understudies and decides the quantity of hours every understudy concentrated a week ago. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Sort out the information into a recurrence dissemination.

Step 1: Decide on the quantity of classes. The objective is to utilize simply enough groupings or classes to uncover the state of the dissemination. " sufficiently just " Recipe –" 2 to the k principle " Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n).

Sample size (n) = 80 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … The principle propose 7 classes. Test size (n) = 1000 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; 2 8 =256; 2 9 =512; 2 10 =1024 … The standard recommend 10 classes. 2 to the k guideline Select the littlest number (k) for the quantity of classes such that 2 k is more noteworthy than the quantity of perceptions (n).

Sample size (n)=10000 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … ,2 13 =8192; 2 14 = 16384 The standard propose 14. Test size (n)=100000 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … 2 to the k standard Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n).

2 to the k guideline Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n). We need to discover littlest k such that 2 k > n . Littlest k such that k log 2 > log n Smallest k such that k > (log n)/(log 2) Example: If n=10000, (log n)/(log 2) = 13.28. Subsequently the formula propose 14 classes. Note: Same result for base 10 log and normal log .

Step 1: Decide on the quantity of classes. 2 to the k principle Select the littlest number (k) for the quantity of classes such that 2 k is more noteworthy than the quantity of perceptions (n). Case 1 (proceeded with): Sample size (n) = 30 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … The tenet propose 5 classes . Elective, by figuring (Log 30/log 2) = 4.91, we get the same proposal of 5 classes.

Step 2: Determine the class interim or width. By and large the class interim or width ought to be the same for all classes . The classes all taken together should cover in any event the separation from the most minimal quality in the crude information to the most astounding worth. The classes must be totally unrelated and thorough . Class interim ≥ (Highest quality – most reduced worth)/number of classes. Generally we will picked some helpful number as class interim that fulfill the disparity.

Step 2: Determine the class interim or width. Class interim ≥ (Highest quality – most minimal worth)/number of classes. Case 1 (proceeded with): Highest quality = 33.8 hours Lowest esteem = 10.3 hours k=5 . Subsequently, class interim ≥ (33.8-10.3)/5 = 4.7 We pick class interim to be 5 , some helpful number.

Step 3: Set the individual class confines as far as possible must be set so that the classes are fundamentally unrelated and thorough . Round up so some helpful numbers.

Step 3: Set the individual class limits Example 1 (proceed with): Highest quality = 33.8 hours. Least esteem = 10.3 hours. Range = most noteworthy – least = 23.5. K=5 ; Interval = 5. With k=5 and interim = 5, the classes will cover a scope of 25. Let " s split the surplus in the lower and upper tail similarly. (25-23.5)/2 = 0.75. Consequently, the lower furthest reaches of the top notch ought to be around (10.3 – 0.75)=9.55 and maximum farthest point of the last class ought to be (33.8 + 0.75)=34.55. 9.55 and 34.55 look odd. Some advantageous and close numbers would be 10 and 35.

Step 3: Set the individual class limits Example 1 (proceed with): We have decided K=5; Interval = 5. The lower furthest reaches of the top of the line = 10 and The maximum furthest reaches of the last class = 35. "10 up to 15" implies the interim from 10 to 15 that incorporates 10 however not 15.

Step 4: Tally the information into the classes and include the quantity of things each 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Hours studying 7 10 up to 15 12 15 up to 20 up to 25 7 25 up to 30 3 30 up to 35 1

EXAMPLE 1 ( proceeded with )

EXAMPLE 1 ( proceeded with ) A relative recurrence appropriation demonstrates the percent of perceptions in every class.

Stem-and-leaf Displays Stem-and-leaf show: A factual strategy for showing an arrangement of information. Each numerical quality is isolated into two sections: the main digits turn into the stem and the trailing digits the leaf. Note : preference of the stem-and-leaf show over a recurrence dissemination is we don\'t lose the personality of every perception. An impediment is that it is bad for extensive information sets.

EXAMPLE 2 Colin accomplished the accompanying scores on his twelve bookkeeping tests this semester: 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Develop a stem-and-leaf diagram.

EXAMPLE 2 (proceeded) 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Stem Leaf 6 9 8 9 7 8 6 4 8 3 2 5 9 2 6 1

EXAMPLE 2 (proceeded) 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Stem Leaf 6 9 8 7 4 2 3 8 5 6 8 9 1 6 2

Graphic Presentation of a Frequency Distribution The three regularly utilized realistic structures are histograms , recurrence polygons , and a total recurrence dispersion . A Histogram is a diagram in which the classes are set apart on the even pivot and the class frequencies on the vertical hub. The class frequencies are spoken to by the statures of the bars and the bars are attracted nearby each other.

Graphic Presentation of a Frequency Distribution A recurrence polygon comprises of line portions interfacing the focuses framed by the class midpoint and the class recurrence. An aggregate recurrence conveyance is utilized to decide what number of or what extent of the information qualities are underneath or over a specific worth.

Histogram for quite a long time Spent Studying Example 1 (proceeded with): A Histogram is a chart in which the classes are set apart on the level hub and the class frequencies on the vertical pivot.

Frequency Polygon for quite a long time Spent Studying Example 1 (proceeded with): A recurrence polygon comprises of line fragments interfacing the focuses shaped by the class midpoint and the class recurrence.

Cumulative Frequency Distribution For Hours Studying Example 1 (proceeded with): An aggregate recurrence circulation is utilized to decide what number of or what extent of the information qualities are underneath or over a specific worth.

Bar Chart A bar diagram can be utilized to delineate any of the levels of estimation (ostensible, ordinal, interim, or proportion).

Example 3 Construct a bar outline for the quantity of unemployed per 100,000 populace for chose urban communities amid 2001

Bar Chart for the Unemployment Data Example 3 (proceeded):

Pie Chart A pie graph is valuable for showing a relative recurrence circulation. A circle is partitioned relatively to the relative recurrence and bits of the circle are allotted for the diverse gatherings.

EXAMPLE 4 A specimen of 200 runners were solicited to demonstrate their most loved sort from running shoe. Draw a pie outline in light of the accompanying data.

EXAMPLE 4 ( proceeded with ) Compute the rate and degree every sort possess out of 360 o . Degree possessed around = rate x 360

Pie Chart for Running Shoes Example 4 (proceeded):

Chapter Two Describing Data: Frequency Distributions and Graphic Presentation - END -