The manager at a water park constructed the following frequency distribution to
ID: 3360338 • Letter: T
Question
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August.
Construct the corresponding relative frequency, cumulative frequency, and cumulative relative frequency distributions. (Round "Relative Frequency" and "Cumulative Relative Frequency" answers to 3 decimal places.)
What is the most likely attendance range? (Round percentage answer to the nearest whole number.)
What percentage of the time was attendance at least 1,250 but less than 1,500 people? (Round your answer to 1 decimal place.)
What percentage of the time was attendance less than 1,500 people? (Round your answer to the nearest whole percent.)
What percentage of the time was attendance 1,500 or more? (Round your answer to the nearest whole percent.)
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August.
Explanation / Answer
Let for the ith class, i =1 to 6,
Li and Ui be the lower and upper limits,
fi be the frequency,
Fi be the cumulative frequency,
ri be the relative frequency,
Ri be the cumulative relative frequency and
n = total frequency.
Back-up Theory
F1= f1, Fi = Fi – 1 + fi for i = 2 to 6, ri = fi/n, R1 = r1, Ri = Ri – 1 + ri for i = 2 to 6
Part (a)
i
Class
fi
ri
Fi
Ri
1
1000 - 1250
7
0.156
7
0.156
2
1250 - 1500
5
0.111
12
0.267
3
1500 - 1750
11
0.244
23
0.511
4
1750 - 2000
8
0.178
31
0.689
5
2000 - 2250
10
0.222
41
0.911
6
2250 - 2500
4
0.089
45
1.000
Total
-
45
1.000
-
-
DONE
Part (b.1)
Since maximum frequency is 11, the most likely attendance range is (1500 - 1750) ANSWER
Part (b.2)
Number of times attendance was less than 1750 = 7 + 5 + 11 = 23 ANSWER
Part (c.1)
Percentage of times attendance was at least 1250 but less than 1500 = 100 x (5/45) = 11.1% ANSWER
Part (c.2)
Percentage of times attendance was less than 1500 = 100 x (12/45) = 27 % ANSWER
Part (c.3)
Percentage of times attendance was 1500 or more = 100 – answer for c.2 = 73 ANSWER
Part (d.1)
Histogram B depicts the relative frequency correctly. ANSWER
[Relative frequency for first class is 0.156. A shows it as close to 0.2 and C shows it less than 0.15.]
i
Class
fi
ri
Fi
Ri
1
1000 - 1250
7
0.156
7
0.156
2
1250 - 1500
5
0.111
12
0.267
3
1500 - 1750
11
0.244
23
0.511
4
1750 - 2000
8
0.178
31
0.689
5
2000 - 2250
10
0.222
41
0.911
6
2250 - 2500
4
0.089
45
1.000
Total
-
45
1.000
-
-
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