The table given below shows the weekly expenditures on food of some households in a locality.

$\begin{matrix} W e e k l y e x p e n d i t u r e (i n R s .) & N u m b e r o f h o u s e h o l d s 100 - 200 & 5 200 - 300 & 6 300 - 400 & 11 400 - 500 & 13 500 - 600 & 5 600 - 700 & 4 700 - 800 & 3 800 - 900 & 2 \end{matrix}$

Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

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Solution

The frequency distribution table of less than type is as follows:

Weekly expenditure ( in Rs)
(Upper class limits)
Cumulative frequency (cf)

Less than 200 5

Less than 300 5+6=11

Less than 400 11+11=22

Less than 500 22+13=35

Less than 600 35+5=40

Less than 700 40+4=44

Less than 800 44+3=47

Less than 900 47+2=49

Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows:

Now,

The frequency distribution table of more than type is as follows:

Weekly expenditure (in Rs) ( lower class limits) Cumulative frequencies (cf)

More than 100 44+5=49

More than 200 38+6=44

More than 300 27+11=38

More than 400 14+13=27

More than 500 9+5=14

More than 600 5+4=9

More than 700 2+3=5

More than 800 2

Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows:

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Similar questions

Q. The table given below shows the weekly expenditures on food of some households in a locality.

Weekly expenditure (in ₹)	Number of households
100−200	5
200−300	6
300−400	11
400−500	13
500−600	5
600−700	4
700−800	3
800−900	2

Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find:

interquartile range
$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 10 - 20 & 2 20 - 30 & 4 30 - 40 & 6 40 - 50 & 8 50 - 60 & 10 \end{matrix}$

Q. Daily expenditure of

25

householders is given in the following table:

Daily expenditure of a household (in rupees)	100-150	150-200	200-250	250-300	300-350
No. of households	$4$	$5$	$12$	$2$	$2$

Draw a "less than type" cumulative frequency Ogive curve for this data.

Q. Draw a " less than type " ogive and "more than type" ogive for the following distribution and hence obtain the median from the graph

C.I.	20 - 30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency	8	12	24	6	10	15	25

Which type of ogive curve would be best suitable to determine the median?

For less than type ogive type L , for more than type ogive type M

$\begin{matrix} T i m e & T o t a l N u m b e r o f Q u e s t i o n s < 10 & 2 < 20 & 5 < 30 & 10 < 40 & 15 < 50 & 17 < 60 & 25 \end{matrix}$

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Weekly expenditure ( in Rs) (Upper class limits)	Cumulative frequency (cf)
Less than 200	5
Less than 300	5+6=11
Less than 400	11+11=22
Less than 500	22+13=35
Less than 600	35+5=40
Less than 700	40+4=44
Less than 800	44+3=47
Less than 900	47+2=49

Weekly expenditure (in Rs) ( lower class limits)	Cumulative frequencies (cf)
More than 100	44+5=49
More than 200	38+6=44
More than 300	27+11=38
More than 400	14+13=27
More than 500	9+5=14
More than 600	5+4=9
More than 700	2+3=5
More than 800	2