STAISTICS – CONTINOUS DATA

8/4/2019 STAISTICS CONTINOUS DATA

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STATISTICS CONTINOUS DATA

Dr Hjh Madihah Khalid


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Discrete and Continuous Data

A set of data is said to be continuous if the values /observations belonging to it may take on any valuewithin a finite or infinite interval. You can count, orderand measure continuous data. For example height,weight, temperature, the amount of sugar in an

orange, the time required to run a mile. A set of data is said to be discrete if the values /

observations belonging to it are distinct and separate,i.e. they can be counted (1,2,3,....). Examples mightinclude the number of kittens in a litter; the number ofpatients in a doctors surgery; the number of flaws inone metre of cloth; gender (male, female); blood group(O, A, B, AB).


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Histogram

A histogram is a special type of graph used to display

continuous data. It is similar to a bar graph but,because of the continuous nature of the variable, anumber line is used for the horizontal axiz and thecolumns are joined together. The rectangles may havedifferent widths but the area is proportional to the

frequency. The histogram is only appropriate for variables whose

values are numerical and measured on an intervalscale. It is generally used when dealing with large data

sets (>100 observations), when stem and leaf plotsbecome tedious to construct. A histogram can also helpdetect any unusual observations (outliers), or any gapsin the data set.


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Box and Whisker Plot (or Boxplot) A box and whisker plot is a wayof summarising a set of data measured on an interval scale. It isoften used in exploratory data analysis. It is a type of graph which isused to show the shape of the distribution, its central value, andvariability. The picture produced consists of the most extreme

values in the data set (maximum and minimum values), the lowerand upper quartiles, and the median.

A box plot (as it is often called) is especially helpful for indicatingwhether a distribution is skewed and whether there are anyunusual observations (outliers) in the data set.

Box and whisker plots are also very useful when large numbers of

observations are involved and when two or more data sets arebeing compared.


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Example

Make a frequency distribution and graph this


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Height (cm) Arm Span (cm)

155-

164

165-

174

175-

184

185-

194

155-

164

165-

174

175-

184

185-

194

195-

204

Female 6 4 1 1 7 4 0 1 0

Male 0 1 6 5 0 1 4 5 2

Total 6 5 7 6 7 5 4 6 2


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0

1

2

3

4

5

6

7

8

155-164 165-174 175-184 185-194 More

Frequency

height bin

Histogram

Frequency


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Steps for constructing a histogram:

Draw and label thex(horizontal) and the y

(vertical) axes.

Represent the frequencies on the yaxis and

the class boundaries on thexaxis.

Using the frequencies as the heights draw

vertical bars for each class.

Note: For the histogram we need the

frequencies and the class boundaries.


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Frequency polygons/Ogives

A frequency polygon is a graph that displays thedata by using lines that connect points plotted forthe frequencies at the midpoints of the classes. Inthe Cartesian system OXYthe midpoints are the

first coordinates of the vertices of the polygonand the frequencies are the second coordinates.

An ogive is a graph that represents thecumulative frequencies for the classes in afrequency distribution. It shows how many ofvalues of the data are below certain boundary.


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Steps for constructing a frequency

polygon

Draw and label thex(horizontal) and the y(vertical)axes.

Represent the frequencies on the yaxis and themidpoints on thexaxis.

Plot the vertices of the polygon.

Connect adjacent points with line segments. Draw aline back to thexaxis at the beginning and the end ofthe graph at the same distance that the previous andthe next midpoints would be located.

Note: For the frequency polygon we need thefrequencies and the midpoints.


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Steps for constructing an ogive

Draw and label thex(horizontal) and the y(vertical)axes.

Represent the cumulative frequencies on the yaxis andthe class boundaries on thexaxis.

Plot the cumulative frequency at each upper classboundary with the height being the correspondingcumulative frequency.

Connect the points with segments. Connect the firstpoint on the left with thexaxis at the level of thelowest lower class boundary.

Note: For the ogive we need the class boundaries andthe cumulative frequencies


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Example

Construct a histogram, frequency polygon and

an ogive for the data below:

Class Limits Class Boundaries Frequency (f) CumulativeFrequency Midpoints (Xm)

100-104 99.5-104.5 2 2 102105-109 104.5-109.5 8 10 107110-114 109.5-114.5 18 28 112115-119 114.5-119.5 13 41 117120-124 119.5-124.5 7 48 122125-129 124.5-129.5 1 49 127130-134 129.5-134.5 1 50 132


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From the data, draw a histogram


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Line graphs

A graph that uses points connected by lines toshow how something changes in value (astime goes by, or as something else happens).


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title The title of the line graph tells us what the graph is about.

labels The horizontal label across the bottom and the vertical label along the

side tells us what kinds of facts are listed.scales The horizontal scale across the bottom and the vertical scale along the

side tell us how much or how many.

points The points or dots on the graph show us the facts.

lines The lines connecting the points give estimates of the values between

the points.

Let's define the various parts of a line graph.


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QUESTION

1. What is the line graph about?

2 What is the busiest time of day at the store?

3. At what time does business start to slow down?

4. How many people are in the store when it opens?

5. About how many people are in the store at 2:30 pm?

6. What was the greatest number of people in the store?

7. What was the least number of people in the store?

The linegraphshows

people in astore atvarioustimes of theday.


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Exercise

Age in years Frequency

0 age < 20 56

20 age < 30 72

30 age < 40 96

40 age < 50 45

50 age < 70 135

70 age < 100 36

Draw the histogram of the data


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City 2000 2005 2010 2015

Cape Town 2715 3063 3316 3401

Durban 2370 2631 2804 2876Gauteng 2732 3254 3574 3674

a. Use the information above and draw a line graph for population in thousands.

b. What is the trend of population?

c. Draw a line graph for the table given below and comment on the trends

South Africa Urban Population

(thousands) 2000 2030

South Africa Rural Population

(thousands) 2000 2030

Year Population Year Population

2000 25948 2000 19662

2005 28119 2005 193132010 29505 2010 18314

2015 30722 2015 17181

2020 32017 2020 16083

2025 33312 2025 14985

2030 34523 2030 13882


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.

From the frequency distribution above, answer the following questions:

a. approximately what percentage of students is above 179 cm tall?

b. If you are 170 cm tall, approximately what percentage of students istaller than you?

c. To be in the top 20% of the class in terms of height, approximately how

tall would you have to be?
http://shex.org/wiki/Image:Height_frequency_distribution.PNGhttp://shex.org/wiki/Image:Height_frequency_distribution.PNGhttp://shex.org/wiki/Image:Height_frequency_distribution.PNG

STAISTICS – CONTINOUS DATA

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