Question

The following table shows the funds collected by 50 students for flood affected people. Find the mean of the funds.

Fund (Rupees)	0 – 1000	1000 – 1500	1500 – 2000	2000 – 3000
No. of students	6	24	18	2

Solution: Let A = 1250, examining all d_i,g = 250.

Class Fund (₹)	Class mark xi	di = xi – A = xi – 1250	`u_i = d_i/g`	Frequency fi	fiui
0 – 1000	500	`square`	–3	6	–18
1000 – 1500	1250 → A	0	0	24	0
1500 – 2000	1750	500	2	18	`square`
2000 – 3000	2500	1250	`square`	2	10
Total				Σfi = 50	Σfiui = 28

`baru = (sumf_iu_i)/(sumf_i) = 28/50 = square`

`barug = square xx 250 = square`

`barx = A + gbaru = 1250 + 140 = 1390`

∴ The average of the funds is ₹ 1390.

Answer 1

Let A = 1250, examining all d_i,g = 250.

Class Fund (₹)	Class mark xi	di = xi – A = xi – 1250	`u_i = d_i/g`	Frequency fi	fiui
0 – 1000	500	\[\boxed{-750}\]	–3	6	–18
1000 – 1500	1250 → A	0	0	24	0
1500 – 2000	1750	500	2	18	\[\boxed{36}\]
2000 – 3000	2500	1250	\[\boxed{5}\]	2	10
Total				Σfi = 50	Σfiui = 28

`baru = (sumf_iu_i)/(sumf_i) = 28/50` = \[\boxed{0.56}\]

`barug` = \[\boxed{0.56}\] × 250 = \[\boxed{140}\]

`barx = A + gbaru = 1250 + 140 = 1390`

∴ The average of the funds is ₹ 1390.