Question

For a continuous data distribution, 10-20 with frequency 3, 20-30 with frequency 5, 30-40 with frequency 7and 40-50 with frequency 1, the value of Q_3 is ________.
Select one:
a. 34
b. 30
c. 35.7
d. 32.6

Answer 1

Answer:

35.7

Explanation:

First, we need to build the table with the date provided

Class Freq Cumulative Freq(C.F)

10-20   3                    3

20-30   5                    8

30-40   7                    15

40-50   1                    16

Total          16

Q3 can be calculated as

Q3 = $l+(3N/4-C.F)*h/f$

where

l is the lower limit/value of each class, eg- l=10 for class 10-20 and l=20 for class 20-30

N is the total frequency, obtained by adding up all the frequency values, so here it is 16

C.F or cumulative frequency is obtained by adding the frequency value of a class with the one before it

h is the class width, meaning difference between the lower limit and upper limit eg - for class 10-20, h= 10 as 20-10 =10

f is the frequency value of the respective class

Now 3N/4 = 3*16/4 =12.  This will allow us to identify the Q3 class that we need to use, which will be the 12th value in the C.F rows

Here, we can see that the second row with value of 15 would include the freq value of 12. The corresponding class for the CF =15 is Class 30-40 and freq is 7. So now we have

l = 30

N= 16

C.F = The value above the identified Q3 class value of 15, which is 8

h = 10

f=7

Plugging all this into the equation , we have

Q3 = $l+(3N/4-C.F)*h/f$

= $30+(12-8)*10/7$

= $30+40/7$

=35.7

Answer 2

Answer:

option c is right I will prove it