Question

5. The age (in years) of 360 patients treated in a hospital on a

particular day are given below:

Age in years Number of patients

10 – 20 90

20 – 30 40

30 – 40 60

40 – 50 20

50 – 60 120

60 – 70 30



Draw a histogram and frequency polygon on the same graph to

represent the above data. ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

CONCEPT TO BE IMPLEMENTED

HISTOGRAM :

Histogram is a common device to give a diagrammatic representation of a groupoid frequency distribution.

Histogram is a common device to give a diagrammatic representation of a groupoid frequency distribution. It can be constructed for equal as well as unequal class intervals

Method of construction of a Histogram :

STEP : 1

In a grouped frequency table, the class limits are changed into class boundaries to make it a continuous series and class boundaries are plotted along a horizontal axis ( x axis ) choosing suitable units of measurement

STEP : 2

Upon each class boundaries a rectangle is drawn whose height is proportional to frequency density

STEP : 3

Thus we get a series of adjacent rectangles

FREQUENCY POLYGON :

Frequency polygon is another type of diagrammatic representation of ungrouped or grouped discrete data

Method of construction of a Frequency Polygon :

This process to draw frequency polygon using Histogram

STEP : 1

First draw a Histogram

STEP : 2

We select a point just vertically above mid value at a height equal to the frequency of that class measured in a suitable unit

STEP : 3

Join the points by a straight line to get frequency polygon

CALCULATION

$\sf{Age \: in \: \: \: \: \: \: \: \: Number \: of \: \: \: \: \: \: \: Mid \: value}$

$\sf{years \: \: \: \: \: \: \: \: \: \: \: patients \: \: \: \: \: }$

$\sf{10 \: - \: 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 90 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 15 }$

$\sf{20 \: - \: 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 25 }$

$\sf{30 \: - \: 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 35 }$

$\sf{40 \: - \: 50 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 45 }$

$\sf{50 \: - \: 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 120 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 55 }$

$\sf{60 \: - \: 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 65 }$

GRAPH :

The Histogram and Frequency Polygon of the above data on the same graph is given in the attachment

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LEARN MORE FROM BRAINLY

In a binomial distribution

p=1/2,q=1/2, n =6. Then Find p(x=2)

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