Compute the first quartile and third deciles from the following data :
`{:("Weekly Income (in Rs.)",58,59,60,61,62,63,64,65,66),("No. of workers",2,3,6,15,10,5,4,3,1):}`

Options

A. `Q_(1)`
B. `Q_(2)`
C. `Q_(3)`
D. none of these

Answer

D

Explanation

The cumulative frequency table is as given below :

Lower Quartile: We have, `(N)/(4)=(49)/(4)= 12.25`
The cumulative frequency just greater than `(N)/(4)` is 26 and the corresponding value of the variable is 61.
` therefore Q_(1) = Rs. 61`
Middle Quartile (Median): We have , ` (N)/(2) =(49)/(2) = 24.5`
The cumulative frequency just greater than `N//2` is 26 and hte corresponding value of the variable is 61.
`therefore Q_(2) ` = Middle Quartile = Median = Rs. 61.
Upper Quartile : We have, `(3N)/(4) = 36.75`
The cumulative frequency just greater than `(3N)/(4)` is 41 and the corresponding value of variable is 63.
`therefore Q_(3) ` = Upper Quartile = Rs. 63
`(Q)(1)+(Q_(3))/(2)= (61+63)/(2) = 62`