Q1. Following dataset shows percentage of population of 65 years old or over of 50 different countries.
11.1, 13.0, 9.9, 13.3, 14.5, 11.0, 10.0, 14.3, 12.6, 13.6 10, 12.6, 11.4, 12.5, 11.4, 12.5, 12.6,
15.2, 13.7, 12.6, 11.4, 13.9, 11.3, 14.2, 12.4, 12.4, 12.3, 13.9, 13.1, 13.9, 11.4, 11.9, 13.7,
10.9, 13.4, 12.5, 14.5, 13.4, 15.9, 15.7, 12.0, 14.4, 13.5, 13.6, 12.5, 10.2, 9.4, 12.0, 11.1,
11.6,
13.3, 15.3.
i)Construct a frequency table of the above data.
II. Find a suitable measure of central tendency and dispersion for the given data
III. Hence draw a histogram and frequency polygon from it.
Answers
Given : dataset shows percentage of population of 65 years old or over of 50 different countries.
To Find : i) Construct a frequency table of the above data.
II. Find a suitable measure of central tendency and dispersion for the given data
III. Hence draw a histogram and frequency polygon from it.
Solution:
frequency table
Class f cf
9 - 10 2 2
10 - 11 4 6
11 - 12 10 16
12 - 13 13 29
13 - 14 14 43
14 - 15 5 48
15 - 16 4 52
Median = 12 + 1 * (26 - 16) /13
= 12 + 0.77
= 12.77
Median from raw data = 12.6
Mean from Raw data = 658.8/52 = 12.67
Mode from Raw data = 11.4 , 12.5 , 12.6 ,
Mode from grouped data = 13 + 1 * ( 14 - 13)/(14 - 13 + 14 - 5)
= 13 + 1/10
= 13.1
Range = 15.9 - 9.4 = 6.5
A frequency polygon is another type of frequency distribution graph. In a frequency polygon, the number of observations is marked with a single point at the midpoint of an interval. A straight line then connects each set of points.
Histogram: a graphical display of data using bars of different heights. It is similar to a Bar Chart, but a histogram groups numbers into ranges
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