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Unformatted text preview: EC 41 UCLA  — Sample Problems #1; RE Ch 1 material
These problems will NOT be collected or graded, but they will be useful for studying for exams. I) Let x be the income (in thousands ofS) for households in a US. neighborhood Suppose 10 households are sampled and the
values forx are: 15, 35, 45, IO, 40, 35, IO, 15, I5, 50 a) Write :1 stemplot ofthis data: b) Write two histograms below with either counts or percent on the vertical axis. i) To the left make a histogram such that OlO includes 10 but not 0, 1020 includes 20 but not 10... (Excel will construct such a
histogrzun if“hin entries“ are 10,20,30,40,50) ii) To the right make a histogram such that 0IO includes 0 but not I0, l020 includes 10 but not 20... Which way does 0111' text use for drawing histograms.)
//'; 0 IO 20 30 40 SO 60 Income 0 10 20 30 40 50 Income \ Htﬁt’ftlbld’n 0C) 2) Let x be the income (in Yen) for households in a Japanese neighborhood. Suppose 9 households are sampled and the values
for x are: 2000, 3500. 4000, 2500. 4000, 3500, 1500, 2500, 4:300 ft? ’20 :33: ‘21: 3c 7, s” W W L/S‘ us. Suppose one US. $ —~ I00 Yen. Convert Japanese earnings 8' S' Q" 0 l  I;
and make a backtoback stem plot using data from #1 and #2. ._ _ — — ——  —— "H ‘
2 0 4: S
b) What is the average (—' arithmetic mean) income ofthe a __
Japanese households in Yen and in S"? _ ,2) I I try‘3" 3 5 5 Kimmie  — ' H c) Compare the lQR for Japanese and U.S. household incomes. .. ._.. —
(measure both in S) 5. Us; TEXT r1121 rift“3. 3) Consider the ten household incomes from #1: IS, 35, 45, IO, 40, 35, IO, 15, 15,50. / y,
Z I a) What is the average (arithmetic mean) income (in thousands) for the 10 observations? _ m d 2 / ‘— X
b) What is the standard deviation ofthese l0 values? l ‘5. ST . . /V
c) What is the variance ofthese 10 values? ” 0
Follow the text and use “sample” not “population” values for standard deviation and variance unless instructed to do otherwise. d) Use the data from question #1 to perform a “ﬁve number summary," )3)» )ﬂ / P {g 2. q. 3. S.“ :57 5\ [/ﬂ (a... (\0 Minimum Value: /0 . ._ First Quartile, Q]: If?) ‘3 U .w
,s mt 36‘ z 1
Median: ’2 (e. : l ' "t P H0
Third Quartile, Q3. 1H) ’5 6"
J 2 8—
, ' . h‘ ‘6 Maximum Value. 0 _ I 0 ,_ I”; e) To the right make a boxplot with “whiskers” extending, to max and min values What is the inter uartile ranoe'.’ .‘~ \ "
0 q t? L Griz — 4) Consider the data on luck and children’s scores (from  to 10) for problem 1.60 on page 49. . . . « 5' 7 l
b) What IS the (sample) standard devralten? x“ f l ‘ I
. . . it 2 ‘ 9  ' . c) What IS the variance? _ 1:2 ‘ ~ ‘.  a; .. _. t
 realize we follow the text and use “sample” standard deviation, not “population” ‘I I " ' _ h I. ,
 you may use a your calculator or Excel to answer questiOn 4 and 5. ' 1 n
5) Use the data from question #4 to perform a “ﬁve number summary”
and write a boxplot as described on pages 37 & 38
i k'l T»— '
Minimle Value: \ '
First Quartile, Q.: l ‘
. t  /
Median: {9. l
‘ ' '"S
  .9" t r
Third Quartile. Q3 1“] a t
.. I
1 F
Maximum Value. JU '
What is one aspect ofthe data that the boxplot and sumnun'y statisties can not show? . l". .
{ft ...
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 Spring '07
 Guggenberger
 Standard Deviation, 20 30 40, ﬁve number summary

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