Question

In Arecent 159 " ARecent issue of Itta engineering conferences 4 Conferences lasted a day 89 engineering co 36 lasted 3 days 18 LASTED 4 days 19 Lastes sdays 4 Lasted bdays 1 Lasted 7days م كم ع the median, ist Quartile Zosted 9DAYS X= the length in dop of mW a) organize data in chart o find the median, istan c Find the 65th percentile I Find the 10th percentile Constvet Abox plot The middle 50% of the conter days to days Calculate the same HEAN of a

Answer 1

X (length in days)	Frequency (no. of conf)	cumulative freq.
2	4	4
3	36	40
4	18	58
5	19	77
6	4	81
7	1	82
8	1	83
9	1	84
total	84

b) Median : mean of (84/2)th and (84/2 +1 )th value

= mean of 42nd and 43rd value

42nd value is 4 and 43rd value is 4

Thus median = 4

Q₁= (84/4) =21st value = 3

c) 65th percentile = 84 * (65/100) =54.6 i.e, 55th value= 4

d) 10th percentile = 84 * (10/100) =8.4 i.e, 9th value= 3

e) Boxplot

Вох plot 2 3 4 6 8 5 7

For the middle 50% of the first and the third quartile as middle 50% of the data lies between first and third quartile

Q₁= 3

Q₃= (3*84)/4 =63rd data= 5

The middle 50% of the conference id from 3 days to 5 days.

Sample mean = = ( 4*2 + 36*3 + 18*4+........ + 1*8 + 1*9)/ 84

fa/n

= 3.94 ~ 4 days