Construct frequency polygon for the following data.
Class interval frequency
$30 - 35$ $12$
$35 - 40$ $20$
$40 - 45$ $16$
$45 - 50$ $8$
$50 - 55$ $14$

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Solution

Class Interval Frequency Mid Points
$30 - 35 35 - 40 40 - 45 45 - 50 50 - 55$ $122016814$ $32.5 37.5 42.5 47.5 52.5$

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Q. Draw the frequency polygon representing the following frequency distribution.

\begin{matrix} C l a s s i n t e r v a l & 30 - 34 & 35 - 39 & 40 - 44 & 45 - 49 & 50 - 54 & 55 - 59 F r e q u e n c y & 12 & 16 & 20 & 8 & 10 & 4 \end{matrix}

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Q. Draw histogram and frequency polygon on the same graph paper for the following frequency distribution.

Class	Frequency
$15 - 20$	$20$
$20 - 25$	$30$
$25 - 30$	$50$
$30 - 35$	$40$
$35 - 40$	$25$
$40 - 45$	$10$

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution.

Class Interval

Frequency

20 – 25

25 – 30

30 – 35

35 – 40

40 – 45

45 – 50

N = 50

Q. Calculate arithmetic mean from the following data by Short-cut Method:

Class Interval	20−25	25−30	30−35	35−40	40−45	45−50	50−55
Frequency	10	12	8	20	11	4	5

Find the mode of the following frequency distribution:
$\begin{matrix} Marks & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Frequency & 12 & 35 & 45 & 25 & 13 \end{matrix}$

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Construct frequency polygon for the following data.Class intervalfrequency30−351235−402040−451645−50850−5514

Class Interval Frequency Mid Points30−3535−4040−4545−5050−55 122016814 32.537.542.547.552.5

Construct frequency polygon for the following data.
Class interval frequency
$30 - 35$ $12$
$35 - 40$ $20$
$40 - 45$ $16$
$45 - 50$ $8$
$50 - 55$ $14$

Class Interval Frequency Mid Points
$30 - 35 35 - 40 40 - 45 45 - 50 50 - 55$ $122016814$ $32.5 37.5 42.5 47.5 52.5$