A survey was conducted to identify vegetarians in a group of people. Find the mode of the data.
Group $5 - 7$ $7 - 9$ $9 - 11$ $11 - 13$ $13 - 15$ $15 - 17$
Frequency $6$ $7$ $3$ $7$ $12$ $9$

15.25

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12.25

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14.25

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13.25

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Solution

The correct option is B $14.25$

Group

frequency

5-7

6

7-9

7

9-11

3

11-13

7

13-15

12

15-17

9

Maximum frequency $= 12$
Modal class $= 13 - 15$
$l = 3$ , $h = 12$
$f_{I} = 12 {, f}_{0} {= 7, f}_{2} = 9$
Mode $= (\frac{f_{I} - f_{0}}{{2 f}_{I} - f_{0} {- f}_{2}}) \times h$
$= 13 + (\frac{12 - 7}{24 - 7 - 9}) \times 2$
$= 13 + (\frac{5}{8}) \times 2$
$= 13 + (\frac{5}{4})$
$= 13 + 1.25$
$= 14.25$

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Similar questions

Without adding, find the sum:
(i) (1+3+5+7+9+11+13)
(ii) (1+3+5+7+9+11+13+15+17+19)
(iii) (1+3+5+7+9+11+13+15+17+19+21+23)

Q. Without adding, find the sum
(i)

1 + 3 + 5 + 7 + 9

(ii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Without adding find the sum

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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Group	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$	$15 - 17$
Frequency	$6$	$7$	$3$	$7$	$12$	$9$

A survey was conducted to identify vegetarians in a group of people. Find the mode of the data.Group5−77−99−1111−1313−1515−17Frequency6737129

The correct option is B 14.25 Group frequency 5-7 6 7-9 7 9-11 3 11-13 7 13-15 12 15-17 9 Maximum frequency=12Modal class=13−15l=3, h=12fI=12,f0=7,f2=9Mode =(fI−f02fI−f0−f2)×h =13+(12−724−7−9)×2 =13+(58)×2 =13+(54) =13+1.25 =14.25

A survey was conducted to identify vegetarians in a group of people. Find the mode of the data.
Group $5 - 7$ $7 - 9$ $9 - 11$ $11 - 13$ $13 - 15$ $15 - 17$
Frequency $6$ $7$ $3$ $7$ $12$ $9$