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Long Questions (Question 5 & 6)

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Question 5:
The table shows the cumulative frequency distribution for the distance travelled by 80 children in a competition.



(a) Based on the table above, copy and complete the table below.


(b) Without drawing an ogive, estimate the interquartile range of this data.


Solution:
(a)


(b)
Interquartile range = Third Quartile – First Quartile

Third Quartile class, Q3 = ¾ × 80 = 60
Therefore third quartile class is the class 60 – 69.

First Quartile class, Q1= ¼ × 80 = 20
Therefore first quartile class is the class 30 – 39.

Interquartile Range = L Q 3 + ( 3 N 4 − F f Q 3 ) c − L Q 1 + ( N 4 − F f Q 1 ) c = 59.5 + ( 3 4 ( 80 ) − 59 10 ) 10 − 29.5 + ( 1 4 ( 80 ) − 7 18 ) 10 = 59.5 + 1 − ( 29.5 + 7.22 ) = 23.78



Question 6:
Table shows the daily salary obtained by 40 workers in a construction site.


Given that the median daily salary is RM35.5, find the value of x and of y.
Hence, state the modal class.


Solution:


Total workers = 40
22 + x + y = 40
x = 18 – y ------(1)

Median daily salary = 35.5
Median class is 30 – 39

m = L + ( N 2 − F f m ) c 35.5 = 29.5 + ( 40 2 − ( 4 + x ) y ) 10 6 = ( 16 − x y ) 10 6 y = 160 − 10 x 3 y = 80 − 5 x − − − − ( 2 )

Substitute (1) into (2):
3y = 80 – 5(18 – y)
3y = 80 – 90 + 5y
–2y = –10
y = 5
Substitute y = 5 into (1)
x = 18 – 5 = 13
Thus x = 13 and y = 5.

The modal class is 20 – 29 daily salary (RM).