using a graph sheet draw a frequency polygon data
class: 25-35 , 35-45,45-55,55-65,65-75,75-85
frequency 5,8,12,9,6,4
Share
using a graph sheet draw a frequency polygon data
class: 25-35 , 35-45,45-55,55-65,65-75,75-85
frequency 5,8,12,9,6,4
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Given :
[tex]\boxed{\begin{array}{c|c|c}\bf \: Class \: Interval&\bf \: Mid-value \: of \: class(x) \: &\bf \: Frequency(f)\\\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad}{}\\\sf25 - 35&\sf 30&\sf5\\\sf35 - 45&\sf40&\sf8\\\sf45 - 55&\sf50&\sf12\\\sf55 - 65&\sf60&\sf9\\\sf65 - 75 &\sf70&\sf6\\\sf75 - 85 &\sf80&\sf4\end{array}}[/tex]
To Find :
Frequency Polygon.
Solution :
For drawing a frequency polygon we need to find the
[tex]\\ :\boxed{\bf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}}[/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 25-35:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 25-35=\dfrac{35+25}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 25-35=\dfrac{60}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 25-35=\cancel{\dfrac{60}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 25-35=30.} \\ \\ [/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 35-45:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 35-45=\dfrac{45+35}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 35-45=\dfrac{80}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 35-45=\cancel{\dfrac{80}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 35-45=40.} \\ \\ [/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 45-55:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 45-55=\dfrac{45+55}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 45-55=\dfrac{100}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 45-55=\cancel{\dfrac{100}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 45-55=50.} \\ \\ [/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 55-65:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 55-65=\dfrac{65+55}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 55-65=\dfrac{120}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 55-65=\cancel{\dfrac{120}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 55-65=60.} \\ \\ [/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 65-75:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 65-75=\dfrac{75+65}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 65-75=\dfrac{140}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 65-75=\cancel{\dfrac{140}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 65-75=70.} \\ \\ [/tex]
[tex]\bf\bullet{\underline{\underline{Mid\ Value\ of\ 75-85:-}}}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ Class=\dfrac{Upper\ limit+Lower\ limit}{2}[/tex]
where,
[tex]\\ :\implies\sf Mid\ Value\ of\ 75-85=\dfrac{85+75}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 75-85=\dfrac{160}{2}[/tex]
[tex]\\ :\implies\sf Mid\ Value\ of\ 75-85=\cancel{\dfrac{160}{2}}[/tex]
[tex]\\ \therefore\boxed{\bf Mid\ Value\ of\ 75-85=80.} \\ \\ [/tex]
We got all the mid values.
Now, plotting the points (30, 5), (40, 8), (50, 8), (60, 9), (70, 6), (80, 4). Join the plotted points by line segments. The end points (30, 5) and (80, 4) are joined to the mid points (15 – 25) and (85 – 95) respectively with frequency zero.
At the very beginning of the x-axis we have to add a kink because the frequency starts from (25 – 35).
Hence,
The frequency polygon for the above data is given in the attachment.
Answer:
using a graph sheet draw a frequency polygon data
class: 25-35 , 35-45,45-55,55-65,65-75,75-85
frequency 5,8,12,9,6,4