Question

Following is the grouped data for duration of fixed deposits of 100 senior citizens from a certain bank:

Fixed deposit (in days)	0 – 180	180 – 360	360 – 540	540 – 720	720 – 900
No. of senior citizens	15	20	25	30	10

Calculate the limits of fixed deposits of central 50% senior citizens.

Answer 1

We construct the less than cumulative frequency table as given below:

Fixed deposit (in days)	No. of senior citizens (f)	Less than Cumulative frequency (c.f.)
0 – 180	15	15
180 – 360	20	35 ← Q1
360 – 540	25	60
540 – 720	30	90 ← Q3
720 – 900	10	100
Total	100

To find the limits of fixed deposits of central 50% senior citizens, we have to find Q₁ and Q₃.

Here, N = 100

Q₁ class = class containing `(("N")/4)^"th"` observation

∴ `"N"/4=100/4` = 25

Cumulative frequency which is just greater than (or equal to) 25 is 35.

∴ Q₁ lies in the class 180 – 360.
∴  L= 180, f = 20, c.f. = 15, h = 180

∴ Q₁ = `"L"+"h"/"f"("N"/4 - "c.f.")`

= `180 + (180)/(20)(25 - 15)`

= 180 + 9(10)
= 180 + 90
∴ Q₁ = 270

Q₃ class = class containing `(("3N")/4)^"th"` observation

∴ `(3"N")/(4) = (3(100))/(4)` = 75

Cumulative frequency which is just greater than (or equal to) 75 is 90.
∴ Q₃ lies in the class 540 – 720
∴ L= 540, f = 30, c.f. = 60, h = 180

∴ Q₃ = `"L"+"h"/"f"("3N"/4 - "c.f.")`

= `540 + (180)/(30)(75 - 60)`

 = 540 + 6(15)
= 540 + 90
∴ Q₃ = 630
∴ Limits of the duration of fixed deposits of central 50% of senior citizens are from 270 to 630.