Question

Calculate all the quartiles for the following frequency distribution:

No. of E-transactions per day	0	1	2	3	4	5	6	7
No. of days	10	35	45	95	64	32	10	9

Answer 1

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

No. of E-transaction per day	No. of days	Less than cumulative frequency (c.f.)
0	10	10
1	35	45
2	45	90 ← Q1
3	95	185 ← Q2
4	64	249 ← Q3
5	32	281
6	10	291
7	9	300
Total	300

Here, n = 300

Q1 = value of `(("n" + 1)/4)^"th"`observation

= value of `((300 + 1)/4)^"th"`observation

= value of (75.25)^th observation

Cumulative frequency which is just greater than (or equal to) 75.25 is 90.
∴ Q₁ = 2

Q₂ = value of 2`(("n" + 1)/4)^"th"`observation

= value of 2`((300 + 1)/4)^"th"`observation

= value of (2 × 75.25)^th observation

= value of (150.50)^th observation

Cumulative frequency which is just greater than (or equal to) 150.50 is 185.
∴ Q₂ = 3

Q₃ = value of 3`(("n" + 1)/4)^"th"` observation

= value of 3`((300 + 1)/4)^"th"` observation

= value of (3 × 75.25)^th observation

= value of (225.75)^th observation

Cumulative frequency which is just greater than (or equal to) 225.75 is 249.
∴ Q₃ = 4