Question

The following frequency table summarizes the number of hours worked by a sample of 120 students in the same week. Hours worked by students Class (hours) Frequency (0, 10] 10 (10, 20] 60 (20, 30] 40 30 or more 10 Total 120 Show/hide advanced buttonsParagraph stylesBoldItalicUnordered listOrdered listLinkUnlinkInsert or edit imageInsert or edit an audio/video fileRecord audioRecord videoManage files

A) How many students worked more than 10 hours but less than or equal to 30 hours?

B) What is the relative frequency of students who worked more than 10 hours but less than or equal to 20 hours?

C) What is the cumulative frequency of students who worked less than or equal to 30 hours?

D) What are the units of measure for this sample of data?

Answer 1

Solution-

According to question the frequency table that summarizes the number of hours worked by a sample of 120 students in the same week.

HOURS OF WORK BY STUDENTS CLASS (in hours)	FREQUENCY
(0, 10]	10
(10, 20]	60
(20, 30]	40
30 or more	10
TOTAL	120

(A)

Number students who worked more than 10 hours but less than or equal to 30 hours is

=Number of students worked for (10, 20], (20, 30] hours

=60 +40 =100

Hence, 100 students worked for more than 10 hours but less than or equal to 30 hours.

(B)

The relative frequency of students who worked more than 10 hours but less than or equal to 20 hours is

={ frequency of interval (10, 20] } ÷{ Total students)

= 60÷120 = 1 ÷ 2 = 0.5

Hence, the relative frequency of students who worked more than 10 hours but less than or equal to 20 hours is 0.5 .

(C)

The cumulative frequency of students who worked less than or equal to 30 hours

={ Frequency of interval (0, 10] } + { frequency of interval (10, 20] }+ { frequency of interval (20, 30] }

=10 + 60 + 40 = 110

Hence, cumulative frequency of students who worked less than or equal to 30 hours is 110

(D)

Here, we are measuring number of students who worked for different intervals

So, the units of measurement for this sample of data are number of students work for the the particular range of hota in a week.

For example:-

10 students of worked between (0, 10] hours of work in a week

60 students worked between (10, 20] hours of work in a week. etc