A random sample of 200 students was chosen from UMUC STAT 200 classes. The frequ
ID: 2927010 • Letter: A
Question
A random sample of 200 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours)
(a) Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places.
(b) What percentage of the study times where at most 15 hours?
(c) In what class interval must the median lie?
Study time (in hours)
Frequency
Relative Frequency
0.0-5.0
6
5.1 – 10.0
24
10.1 – 15.0
50
15.1 – 20.0
0.35
20.1 - 25.0
Total
200
Study time (in hours)
Frequency
Relative Frequency
0.0-5.0
6
5.1 – 10.0
24
10.1 – 15.0
50
15.1 – 20.0
0.35
20.1 - 25.0
Total
200
Explanation / Answer
Study time Frequency Relative frequency
0.0 - 5.0 6 0.03
5.1 - 10.0 24 0.12
10.1 - 15.0 50 0.25
15.1 - 20.0 70 0.35
20.1 - 25.0 50 0.25
--------------------------------------------------------
Total 200 1.00
EXPLANATION:
Relative frequency of each class is obtained by dividing the frequency by total frequency = 200.
Frequency of the 15.1 - 20.0 is obtained by multiplying the relative frequency by 200.
Frequency of the class 20.1 - 25.0 is obtained by subtracting the total of other frequencies from the total frequency of 200.
(b) Percentage of the study time where at most 15 hours = 0.03 + 0.12 + 0.25 = 0.40
(c) Median occurs in the class where cumulative relative frequency = 0.5
Adding the relative frequencies, we note
Study time Cumulative relative frequency
0.0 - 5.0 0.03
5.1 - 10.0 0.15
10.1 - 15.0 0.40
15.1 - 20.0 0.75
20.1 - 25.0 1.00
So, we note that median is in the class 15.1 - 20.0.
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