Question

Find semi-inter quartile range of the following data:
`{:("X",3,6,7,9,10,11,13),("f",2,9,13,17,10,14,15):}`

Answer 1

`{:(X,"Frequency(f)","Cumulative Frequency"),(3," "2," "2),(6," "9," "11),(7," "13," "24),(9," "17," "41),(10," "10," "51),(11," "14," "65),(13," "15," "80),(," "N = 80,):}`
Here, N = 80
`therefore Q_(1) = ((N)/(4))`th observation = 20th observation
`therefore Q_(1) = 7` (as 20th items lies in the class having 24 as cumulative frequency)
`therefore Q_(3) = 3((N)/(4))`th observation = 60th observation
`therefore Q-(3) = 11` (as 60th item lies in the class having 65 as cumulative frequency)
Semi-inter quartile range, `(QD) = (Q_(3)-Q_(1))/(2) = (11 - 7)/(2) = 2`.