Question 11 Size of agricultural holdings in a survey of 200 families is given in the following table begin array - - Whe Imathbf Size - of - agricultural - holdingsin hec - mathbf Number - of families Whline 0-5 - 10 5-10 - 15 115-20 - 80 - 20-25 - - 40 -25-30 - 20 - 30-35 - 55 Whlinelendarray 1 Compute median and size of the holdings-

[ 𝐒𝐢𝐳𝐞 𝐨𝐟 𝐚𝐠𝐫𝐢𝐜𝐮𝐥𝐭𝐮𝐫𝐚𝐥 𝐡𝐨𝐥𝐝𝐢𝐧𝐠𝐬(𝐢𝐧 𝐡𝐞𝐜) amp; 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐟𝐚𝐦𝐢𝐥𝐢𝐞𝐬 (𝐟_𝐢) amp; 𝐂𝐮𝐦𝐮𝐥𝐚𝐭𝐢𝐯𝐞 𝐟𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲; ...

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Standard X

Mathematics

Median for Grouped Data

Question 11 S...

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Question 11
Size of agricultural holdings in a survey of 200 families is given in the following table
$\begin{matrix} S i z e o f a g r i c u l t u r a l h o l d i n g s (i n h e c) & N u m b e r o f f a m i l i e s 0 - 5 & 10 5 - 10 & 15 10 - 15 & 30 15 - 20 & 80 20 - 25 & 40 25 - 30 & 20 30 - 35 & 5 \end{matrix}$
Compute median and size of the holdings.

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Solution

$\begin{matrix} S i z e o f a g r i c u l t u r a l h o l d i n g s (i n h e c) & N u m b e r o f f a m i l i e s (f_{i}) & C u m u l a t i v e f r e q u e n c y 0 - 5 & 10 & 10 5 - 10 & 15 & 25 10 - 15 & 30 & 55 15 - 20 & 80 & 135 20 - 25 & 40 & 175 25 - 30 & 20 & 195 30 - 35 & 5 & 200 \end{matrix}$
(i) Here, N=200
Now, $\frac{N}{2} = \frac{200}{2} = 100,$ which lies in the interval 15-20.
Lower limit, l=15, h=5, f=80 and cf=55
$∴ M e d i a n = l + (\frac{\frac{N}{2} - c f}{f}) \times h = 15 + (\frac{100 - 55}{80}) \times 5 = 15 + (\frac{45}{16}) = 15 + 2.81 = 17.81 h e c$
(ii) In a given table 80 is the highest frequency.
So, the modal class is 15-20.
Here , l=15, $f_{m} = 80, f_{1} = 30, f_{2} = 40 a n d h = 5$
$∴ M o d e = l + (\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}) \times h = 15 + (\frac{80 - 30}{2 \times 80 - 30 - 40}) \times 5 = 15 + (\frac{50}{160 - 70}) \times 5 = 15 + (\frac{50}{90}) \times 5 = 15 \times \frac{25}{9} = 15 + 2.77 = 17.77 h e c$

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Q. Question 11
Size of agricultural holdings in a survey of 200 families is given in the following table

\begin{matrix} S i z e o f a g r i c u l t u r a l h o l d i n g s (i n h e c) & N u m b e r o f f a m i l i e s 0 - 5 & 10 5 - 10 & 15 10 - 15 & 30 15 - 20 & 80 20 - 25 & 40 25 - 30 & 20 30 - 35 & 5 \end{matrix}

Compute median and size of the holdings.

Q. Size of the agriculture holding in a survey of 200 families is given in the following table:

Size of Agriculture	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Number of family	10	15	30	80	40	20	5

Complete median and mode size of the holdings.

Q. The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares): 1-3 3-5 5-7 7-9 9-11 11-13

Number of families: 20 45 80 55 40 12

Find the modal agricultural holdings of the village .

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.

$\begin{matrix} Size of Land Holdings in(acres) & Less than 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 and above Number of Families & 40 & 89 & 148 & 64 & 39 \end{matrix}$

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.

Size of Land Holdings (in acres)	Less than 100	100 – 200	200 – 300	300 – 400	400 and above
Number of families	40	89	148	64	39

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Question 11 Size of agricultural holdings in a survey of 200 families is given in the following table Size of agricultural holdings(in hec)Number of families0−5 105−10 1510−15 3015−20 8020−25 4025−30 2030−35 5 Compute median and size of the holdings.