100 surnames were randomly picked up from a local telephone directory - the frequency distribution of the number of letters in the English alphabets in the surname was obtained as follows- beginarray - WhineNumber of letters -1-4-4-7-7-10-10-13-13-16-16-19Whline Number of surnames -6-30-40-16-4-4Whline end array Determine the median number of letters in the surnames-

The correct option is A 8.05[ C.I amp;Frequency amp;C.F; 1 4 amp;6 amp;6; 4 7 amp;30 amp;36; ...

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Byju's Answer

Standard X

Mathematics

Median for Grouped Data

100 surnames ...

Question

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

$\begin{matrix} Number of letters & 1 - 4 & 4 - 7 & 7 - 10 & 10 - 13 & 13 - 16 & 16 - 19 Number of surnames & 6 & 30 & 40 & 16 & 4 & 4 \end{matrix}$
Determine the median number of letters in the surnames.

8.05

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Solution

The correct option is A 8.05
$\begin{matrix} C.I & Frequency & C.F 1 - 4 & 6 & 6 4 - 7 & 30 & 36 7 - 10 & 40 & 76 10 - 13 & 16 & 92 13 - 16 & 4 & 96 16 - 19 & 4 & 100 \end{matrix}$

Here $n = 100$ & $\frac{n}{2} = 50$ hence median class = 7-10

Now, We see the 50th Observation on the graph by extending it to the ogive.

The value for median seen from the Graph is 8.05.

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Similar questions

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

$\begin{matrix} Number of letters & 1 - 4 & 4 - 7 & 7 - 10 & 10 - 13 & 13 - 16 & 16 - 19 Number of surnames & 6 & 30 & 40 & 16 & 4 & 4 \end{matrix}$
Determine the median number of letters in the surnames.

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:

Number of letters	$1 - 4$	$4 - 7$	$7 - 10$	$10 - 13$	$13 - 16$	$16 - 19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

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.

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

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.

100

surnames were randomly picked up from a local telephone directry and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows

No. of letters	$1 - 4$	$4 - 7$	$7 - 10$	$10 - 13$	$13 - 16$	$16 - 19$
No. of surnames	$6$	$30$	$40$	$16$	$4$	$4$

Find the median and mean number of letters in the surnames.

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The correct option is A 8.05C.IFrequencyC.F1−4664−730367−10407610−13169213−1649616−194100 Here n=100 & n2=50 hence median class = 7-10 Now, We see the 50th Observation on the graph by extending it to the ogive. The value for median seen from the Graph is 8.05.