Question 6
Refer to Q.5. Draw the less than type and more than type ogive for the data and use them to find the median weight.

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Solution

Here, we observe that, the weight of all 70 packets is more than or equal to 200. Since, 13 packets lie in the interval 200-201. So, the weight of 70-13=57 packets is more than or equal to 201. Continuing in this manner we will get remaining more than or equal to 202, 203,204,205 and 206.
$\begin{matrix} W e i g h t (i n g) & N u m b e r o f p a c k e t s & N u m b e r o f p a c k e t s & N u m b e r o f s t u d e n t s L e s s t h a n 200 & 0 & M o r e t h a n o r e q u a l t o 200 & 70 L e s s t h a n 201 & 13 & M o r e t h a n o r e q u a l t o 201 & 70 - 13 = 57 L e s s t h a n 202 & 40 & M o r e t h a n o r e q u a l t o 202 & 57 - 27 = 30 L e s s t h a n 203 & 58 & M o r e t h a n o r e q u a l t o 203 & 30 - 18 = 12 L e s s t h a n 204 & 68 & M o r e t h a n o r e q u a l t o 204 & 12 - 10 = 2 L e s s t h a n 205 & 69 & M o r e t h a n o r e q u a l t o 205 & 2 - 1 = 1 L e s s t h a n 206 & 70 & M o r e t h a n o r e q u a l t o 206 & 1 - 1 = 0 \end{matrix}$
To draw the less than type ogive, we plot the points (200,0),(201,13),(202,40),(203,58),(204,68),(205,69),(206,70) on the paper and join them by free hand.
To draw the more than type ogive plot the points (200,70),(201,57),(202,30),(203,12),(204,2),(205,1),(206,0) on the graph paper and join them by free hand.

The abscissa(x-coordinate) where the two graphs meet is median =201.8 g

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Similar questions

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

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

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

For determining median from ogive curves ,

S1 : one can use less than type curve.

S2 : one can use more than type curve.

If the 'less than type' ogive and 'more than type' ogive intersect each other at (20.5,15.5) then the median of the given data is

(a) 5.5 (b) 15.5 (c) 20.5 (d) 36.0

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