Frequency Distribution & Graghs

8/2/2019 Frequency Distribution & Graghs

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Frequency Distributions andGraphs


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Descriptive Statistics

The goal of descriptive statistics is tosummarize a collection of data in a clear and

understandable way. What is the pattern of scores over the range of

possible values?

Where, on the scale of possible scores, is a point

that best represents the set of scores? Do the scores cluster about their central point or

do they spread out around it?


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Bases of classification

Geographical

Chronological

Qualitative

Quantitative


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Classification of Data

Condenses the data

Facilitates comparison

Relationship study

Analysis of data


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Tabulation

Systematic representation of theinformation collected in the data in rows

or columns according to certaincharacteristics


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Example

In a sample study about coffee habits in twotowns the following information is given :

Town A : Females were 40, total coffeedrinkers were 45% and male non coffeedrinkers were 20%.

Town B : Males were 55%, male non coffee

drinkers were 30% and female coffeedrinkers were 15%. Present the data intabular form


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Example-2

In 2002 out of total of 4000 workers in afactory 3300 were members of a trade union.

The number of women workers was 500 outof which 400 did not belong to the union. In2001 the number of workers in the union was3450 of which 3200 were men. The number

of workers not belonging to the union was760 of which 330 are women. Tabulate thedata


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Frequency Distribution

Frequency distributions organize raw data orobservations that have been collected.

Ungrouped Data

Listing all possible scores that occur in a distributionand then indicating how often each score occurs.

Grouped Data

Combining all possible scores into classes and then

indicating how often each score occurs within eachclass.

Easier to see patterns in the data, but loseinformation about individual scores.


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An Example: GroupedFrequency Distribution

Find the lowest and highest score(order scores from lowest to highest).

Number of Observation N=30

2540 is highest score.

2365 is lowest score.

K=1+3.222log N (5)

Find the rangeby subtracting the lowest score from the highestscore.

2540-2365 = 175

Divide range by Number of classes (k). 175/5 = 35

Round off to the nearest convenient width.

35

Take home salary ratesHotel Rates

2482 2392 2499 2412 2440 2444

2446 2540 2394 2365 2412 2458

2482 2394 2450 2444 2440 2494

2460 2425 2500 2390 2414 23652390 2460 2422 2500 2470 2428


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An Example:Grouped Frequency Distribution

Record the limits of all classintervals, placing the intervalcontaining the score

Count up the number ofscores in each interval.

Class Interval Frequency

2365-2400 6

2400-2435 7

2435-2470 10

2470-2505 6

2505-2540 1

30

Take home salary ratesHotel Rates

2482 2392 2499 2412 2440 2444

2446 2540 2394 2365 2412 2458

2482 2394 2450 2444 2440 2494

2460 2425 2500 2390 2414 2365

2390 2460 2422 2500 2470 2428


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Frequency Table GuidelinesIntervals should not overlap, sono score can belong to morethan one interval.

Make all intervals the samewidth.

Make the intervals continuousthroughout the distribution(even if an interval is empty).

Choose a convenient intervalwidth.

Class Interval Frequency

2365-2400 6

2400-2435 72435-2470 10

2470-2505 6

2505-2540 1

30


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Proportion (RelativeFrequency)

Divide frequency of eachclass by total frequency.

Class Interval Frequency Proportion

2365-2400 6 0.20

2400-2435 7 0.23

2435-2470 10 0.33

2470-2505 6 0.20

2505-2540 1 0.03

30 1


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Proportion (Relative Frequency)

Used when you want to compare the frequencies of onedistribution with another when the total number of data

points is different.

Occupations, 1992 (in hundreds)

Method Males FemalesEngineers 163 24

Doctors 32 22Lawyers 37 9Other 15 6

247 61


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Percentage

Proportion *100

Class Interval Frequency Proportion Percentage

2365-2400 6 0.20 20.00

2400-2435 7 0.23 23.33

2435-2470 10 0.33 33.33

2470-2505 6 0.20 20.00

2505-2540 1 0.03 3.33

30 1 100


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Cumulative Frequency

Shows total number ofobservations in each

class and all lowerclasses.

Class Interval Frequency Proportion Percentage Cumalative

frequency

2365-2400 6 0.20 20.00 6.00

2400-2435 70.23 23.33 13.00

2435-2470 10 0.33 33.33 23.00

2470-2505 6 0.20 20.00 29.00

2505-2540 1 0.03 3.33 30.00

30 1 100


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Cumulative Proportion (Cumulative RelativeFrequency):

Divide Cumulative Frequency by Total Frequency

Percentile Rank Cumulative Proportion * 100

Class Interval Frequency Proportion Percentage Cumalative

frequency

Cumulative

Proportion

Percentile

2365-2400 6 0.20 20.00 6.00 0.20 20.002400-2435 7 0.23 23.33 13.00 0.43 43.33

2435-2470 10 0.33 33.33 23.00 0.77 76.67

2470-2505 6 0.20 20.00 29.00 0.97 96.67

2505-2540 1 0.03 3.33 30.00 1.00 100.00

30 1 100


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Summarize these stock prices inthe form of frequency distribution

Convert the distribution into percentagefrequency and cumulative frequencydistribution

67 34 36 48 49 31 61 34

43 45 38 32 27 61 29 47

36 50 46 30 40 32 30 33

45 49 48 41 53 36 37 4747 30 50 28 35 35 38 36

46 43 34 62 69 50 28 44

43 60 39


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What is the pattern of scores?

Graphs often make it easier to see certaincharacteristics and trends in a set of data.

Graphs for quantitative data. Histogram

Frequency Polygon

Stem and Leaf Display

Graphs for qualitative data.

Bar Chart

Pie Chart


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Histogram

Mumbai Hotel Rates

0

1

2

3

4

5

6

7

8

9

0-99

100-199

200-299

300-399

400-499

500-599

600-699

700-799

800-899

Rates

Frequency

hotel rates


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Histogram

Consists of a number of bars placedside by side.

The width of each bar indicates the intervalsize.

The height of each bar indicates thefrequency of the interval.

There are no gaps between adjacent bars.

Continuous nature of quantitative data.


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Graph Guidelines

Include a descriptive title for the graph.

Label each axis.

The independent variable is on the X axis.

The dependent variable (or frequency) ison the Y axis.

The numbers along the Y axis indicate themeasurement increments.


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Histogram

Temperature and Aggression


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Shapes of Histograms


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Skewed Distributions

Often occur when what is beingmeasured has some upper or lower

limit. Negatively skewed (skewed to the left).

May reflect a ceiling effect(you cant score anyhigher).

Positively skewed (skewed to the right).May reflect a floor effect (you cant score any

lower).


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Bar Graph

A graphical representation of qualitativedata.

Unlike in a histogram, the bars do nottouch.

Discontinuous nature of qualitative data.


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Bar Graph


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What makes a good graph?

Complex ideas communicated with clarity,precision, and efficiency.

Gives the most information in the shortesttime using the least amount of ink and space.

Physical differences measured on the graphare proportional to the numerical differencesin the data.

Clear, detailed, and thorough labeling.

The scale is consistent.


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Housing Complex

The welfare committee of a large housing complex wants tounderstand the possibility of appointing private security guardsat the entrance gate of the complex for 24-hour duty. There are810 flats in the housing complex. And the owners were asked to

vote for or against the proposal. The following data wascollected.

Should the guards be appointed

Yes 194

No 121Not Sure 73

No Response 422

Convert the data to percentages and construct a bar chart.

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Frequency Distribution & Graghs