STAT 200 Week 2 Homework Problems

STAT 200 Week 2 Homework Problems 2.2.2 The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #2.2.10 ("Median income of," 2013). Create a frequency distribution, relative frequency distribution, and cumulative frequency distribution using 7 classes.

Table #2.2.10: Data of Median Income for Females

$31,862 $40,550 $36,048 $30,752 $41,817 $40,236 $47,476 $40,500

$60,332 $33,823 $35,438 $37,242 $31,238 $39,150 $34,023 $33,745

$33,269 $32,684 $31,844 $34,599 $48,748 $46,185 $36,931 $40,416

$29,548 $33,865 $31,067 $33,424 $35,484 $41,021 $47,155 $32,316

$42,113 $33,459 $32,462 $35,746 $31,274 $36,027 $37,089 $22,117

$41,412 $31,330 $31,329 $33,184 $35,301 $32,843 $38,177 $40,969

$40,993 $29,688 $35,890 $34,381

Create a frequency distribution

Find the range:

largest value – smallest value = $60,332 - $22,117 = $38,215 using 7 classes

Find the class width:

width=range/7=$38,215/7=$5459.286=$5460

Find the class limits:

$22117 + $5460 = $27577

$27577 + $5460 = $33037

$33037 + $5460 = $38497

$38497 + $5460 = $43957

$43957 + $5460 = $49417

$49417 + $5460 = $54877

$54877 + $5460 = $60337

Find the class boundaries:

$22117 - .5 = $22116.50

$27577 - .5 = $27576.50

$33037 - .5 = $33036.50

$38497 - .5 = $38496.50

$43957 - .5 = $43956.50

$49417 - .5 = $49416.50

$54877 - .5 = $54876.50

Find the class midpoints:

midpoint = (lower limit + upper limit)/2

($22117 + $27577)/2=$24847

($27577 + $33037)/2=$30307

($33037 + $38497)/2=$35767

($38497 + $43957)/2=$41227

($43957 + $49417)/2=$46687

($49417 + $54877)/2=$52147

($54877 + $60337)/2=$57607

Frequency Distribution for median incomes of females by state in US Class limits Class boundaries Class midpoint Tally Frequency

$22117 - $27576 $22,116.50 - $27576.50 $24,847.00 I 1

$27577 - $33036 $27576.50 - $33036.50 $30,307.00 IIIIIIIIIIII

II 14

$33037 - $38496 $33036.50 - $38496.50 $35,767.00 IIIIIIIIIIII

IIIIIIIII

21

$38497 - $43956 $38946.50 - $43956.50 $41,227.00 IIIIIIIIIII 11

$43957 - $49416 $43953.50 - $49416.50 $46,687.00 IIII 4

$49417 - $54876 $49416.50 - $54876.50 $52,147.00 0

$54877 - $60337 $54976.50 - $60337.50 $57,607.00 I 1

Relative Frequency Distribution for median incomes of females by state in US Class limits Class boundaries Class midpoint Frequency Relative Frequency

$22117 - $27576 $22,116.50 - $27576.50 $24,847.00 1 1/52=.02

$27577 - $33036 $27576.50 - $33036.50 $30,307.00 14 14/52=.27

$33037 - $38496 $33036.50 - $38496.50 $35,767.00 21 21/52=.40

$38497 - $43956 $38946.50 - $43956.50 $41,227.00 11 11/52=.21

$43957 - $49416 $43953.50 - $49416.50 $46,687.00 4 4/52=.08

$49417 - $54876 $49416.50 - $54876.50 $52,147.00 0 0/52=.00

$54877 - $60337 $54976.50 - $60337.50 $57,607.00 1 1/52=.02

Total 52 1 Cumulative Distribution for median incomes of females by state in US Class limits Class boundaries Class midpoint Frequency Cumulative Frequency

$22117 - $27576 $22,116.50 - $27576.50 $24,847.00 1 1

$27577 - $33036 $27576.50 - $33036.50 $30,307.00 14 15

$33037 - $38496 $33036.50 - $38496.50 $35,767.00 21 36

$38497 - $43956 $38946.50 - $43956.50 $41,227.00 11 47

$43957 - $49416 $43953.50 - $49416.50 $46,687.00 4 51

$49417 - $54876 $49416.50 - $54876.50 $52,147.00 0 51

$54877 - $60337 $54976.50 - $60337.50 $57,607.00 1 52

2.2.6