100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Draw a histogram to depict the given information.

Write the class interval in which the maximum number of surnames lie.

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Solution

(i) Here, the data has class interval of varying width

So, we calculate adjusted frequency

$A d j u s t e d f r e q u e n c y = \frac{f r e q u e n c y \times r e q u i r e d s i z e o f i n t e r v a l}{c u r r e n t s i z e o f i n t e r v a l}$

$R e q u i r e d s i z e o f i n t e r v a l = M i n i m u m s i z e o f i n t e r v a l = 7 - 5 = 2.$

So, frequency distribution table of the given data is:

So, the required table is :

By taking no. of letters on x-axis and the number adjustment frequency on y-axis, the histogram of the given information can be drawn as follows.

(ii) Maximum number of name lies is 7 - 9 as it has 25 surnames in it.

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Similar questions

100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{matrix} Number of letters & 1 - 4 & 4 - 6 & 6 - 8 & 8 - 12 & 12 - 20 Number of surnames & 6 & 30 & 44 & 16 & 4 \end{matrix}$
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.

Q. 100 surnames were randomly picked up from a local telephone directory. A frequency distribution of the number of letters in the English alphabets in the surnames was found as follows.

Name of letters	Number of surnames
2 $-$ 4 4 $-$ 6 6 $-$ 8 8 $-$ 10 10 $-$ 12 12 $-$ 14	9 22 38 19 8 4

Draw a frequency polygon.

Question 9 (i)
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
$\begin{matrix} Number of letters & Number of surnames 1 - 4 & 6 4 - 6 & 30 6 - 8 & 44 8 - 12 & 16 12 - 20 & 4 \end{matrix}$
(i) Draw a histogram to depict the given information.

Question 9 (ii)
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{matrix} Number of letters & Number of surnames 1 - 4 & 6 4 - 6 & 30 6 - 8 & 44 8 - 12 & 16 12 - 20 & 4 \end{matrix}$
(ii) Write the class interval in which the maximum number of surname lie.

Q. 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

\begin{matrix} N u m b e r o f l e t t e r s & N u m b e r o f s u r n a m e s 1 - 4 & 6 4 - 7 & 30 7 - 10 & 40 10 - 13 & 16 13 - 16 & 4 16 - 19 & 4 \end{matrix}

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

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