Sam collected data on the number of shots required to finish an eighteen holeround in the videogame Golf with Your Friends. They lost some of the data,but recorded what was left in the frequency distribution table below:Score (x)Frequency (f) Cumulative Frequency10

Answered: Sam collected data on the number of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.2: Representing Data

Problem 23PFA

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Sam collected data on the number of shots required to finish an eighteen hole
round in the videogame Golf with Your Friends. They lost some of the data,
but recorded what was left in the frequency distribution table below:
Score (x)
Frequency (f) Cumulative Frequency
10 <x < 20
2
20 < x < 30
15
17
30 <x < 40
b
a
40 < x < 50
25
56
50 <x < 60
30
86
60 <x < 70
12
98
70 < x < 80
2
100
Copy the table and add any required columns for the following questions.
i) Find a and b.
ii) Approximate the mean to two decimal places.
iii) Approximate the standard deviation to three significant figures.
iv) Par score for a single hole is the expected number of shots required for a
player to complete the hole. If the mean par score for each of the eighteen
holes is 3, approximate the percentage of players who scored under par for
the round. That is, approximate the percentage of players who complete
the round in fewer shots than expected.
Hint. Find the par score for the entire round first.
2.

Expert Solution

Step 1

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.

From the given frequency table, the total frequency is 100

$2 + 15 + a + 25 + 30 + 12 + 2 = 100 a + 86 = 100 a = 100 - 86 = 14$

Consider the cumulative frequency for class 30<=x<40 is,

b=17+a

=17+14

=31

Thus, a=14 and b=31.

Step 2

ii)

Mean:

Score(x)	Frequency(f)	m=(lower limit+ upper limit)/2	m*f
10<=x<20	2	15	30
20<=x<30	15	25	375
30<=x<40	14	35	490
40<=x<50	25	45	1125
50<=x<60	30	55	1650
60<=x<70	12	65	780
70<=x<80	2	75	150
			$\sum m * f = 4600$

$M e a n = \frac{\sum m f}{T o t a l f r e q u e n c y} = \frac{4600}{100} = 46$

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