Six hundred adult Americans were asked, \"What do you think constitutes a middle
ID: 3040697 • Letter: S
Question
Six hundred adult Americans were asked, "What do you think constitutes a middle-class income?" The results are in the following table. Also, include left endpoint in the frequency, but not the right endpoint.
Salary ($)
Relative Frequency
< 20,000
0.02
20,000–25,000
0.09
25,000–30,000
0.19
30,000–40,000
0.26
40,000–50,000
0.18
50,000–75,000
0.17
75,000–99,999
0.02
What percentage of the survey answered "not sure"?
What percentage think that middle-class is from $25,000 to $50,000?
Construct a histogram of the data.
How do you think the <20,000 and the 100,000+ intervals be handled? Why?
Find the 40th and 80th percentiles
Construct a bar graph of the data
PLEASE SHOW DETAIL ON EACH QUESTIONS!! THANK YOU
Salary ($)
Relative Frequency
< 20,000
0.02
20,000–25,000
0.09
25,000–30,000
0.19
30,000–40,000
0.26
40,000–50,000
0.18
50,000–75,000
0.17
75,000–99,999
0.02
Explanation / Answer
Part (a)
Percentage of the survey answered "not sure" cannot be determined because the given relative frequency totals 0.93 leaving 0.07 unaddressed. This gap of 0.07 could include more than 100000 as well as "not sure". ANSWER
Part (b)
Percentage thinking that middle-class is from $25,000 to $50,000 =
100 x 0.63 = 63% ANSWER [as detailed below]
25,000–30,000
0.19
30,000–40,000
0.26
40,000–50,000
0.18
Part (c)
Handling precisely open end class will be required only for determining mean and standard deviation. In such cases, the rule is not universal.
One possibility is to treat 20000 and 100000 as the representative of the respective open end classes. ANSWER
Part (d)
40 percentile = 30000 + {(0.4 – 0.3)(10000/0.26)
= 30000 + 3846.15
= 33846.15 ANSWER 1
80 percentile = 50000 + {(0.8 – 0.74)(15000/0.17)
= 50000 + 5294.12
= 55294.12 ANSWER 2
25,000–30,000
0.19
30,000–40,000
0.26
40,000–50,000
0.18
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