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Homework 1 Material Type: Notes; Professor: Kim; Class: Business Statistics; Subject: Business Administration; University: Dalton State College; Term: Summer 2011;
Typology: Study notes
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College Board If you are interested in SAT scores across states and whether they are related to student-teacher ratios, the charts at http://flowingdata.com/2009/11/10/do-we- need-more-teachers/sat-scores/ are quite revealing.
College Board If you are interested in SAT scores across states and whether they are related to student-teacher ratios, the charts at http://flowingdata.com/2009/11/10/do-we- need-more-teachers/sat-scores/ are quite revealing.
Combined 1658 (^15281534) (^17001511) (^16981534) (^14771378) (^14751460) (^14501601) (^17751483) (^18131734) (^17071676) (^13901497) (^15471762) (^17821680) (^17791602) (^17531485) (^15561505) (^16331465) (^14861749) (^16061703) (^15471477) (^14881452) 1758
Histogram Bin Min Bin Max Bin MidpointMath / Data Set #1 Freq. Rel. Freq. Prb. Density Bin #1 Bin #2 451.00474.43^ 474.43497.86^ 462.71486.14^23 0.03920.0588^ 0.00170. Bin #3 Bin #4 497.86521.29^ 521.29544.71^ 509.57533.00^186 0.35290.1176^ 0.01510. Bin #5 Bin #6 544.71568.14^ 568.14591.57^ 556.43579.86^85 0.15690.0980^ 0.00670. Bin #7 591.57^ 615.00^ 603.29^9 0.1765^ 0.
Histogram Bin Min Bin Max Bin Midpoint^ Writing / Data Set #1 Freq. Rel. Freq. Prb. Density Bin #1 Bin #2 455.00474.00^ 474.00493.00^ 464.50483.50^104 0.07840.1961^ 0.00410. Bin #3 Bin #4 493.00512.00^ 512.00531.00^ 502.50521.50^133 0.25490.0588^ 0.01340. Bin #5 531.00^ 550.00^ 540.50^4 0.0784^ 0.
476.29 496.86 517.43 538.00 558.57 579.14 599.
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Frequency
462.71 486.14 509.57 533.00 556.43 579.86 603.
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46
(^108) 1214
1618
20^ Histogram of Math / Data Set #
Frequency
Bin #6 Bin #7 550.00569.00^ 569.00588.00^ 559.50578.50^107 0.19610.1373^ 0.01030.
Histogram Bin Min Bin Max Bin Midpoint^ Combined / Data Set #1 Freq. Rel. Freq. Prb. Density Bin #1 Bin #2 1378.001440.14^ 1440.141502.29^ 1409.071471.21^132 0.03920.2549^ 0.00060. Bin #3 Bin #4 1502.291564.43^ 1564.431626.57^ 1533.361595.50^123 0.23530.0588^ 0.00380. Bin #5 Bin #6 1626.571688.71^ 1688.711750.86^ 1657.641719.79^67 0.11760.1373^ 0.00190. Bin #7 1750.86^ 1813.00^ 1781.93^8 0.1569^ 0.
464.50 483.50 502.50 521.50 540.50 559.50 578.
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14^ Histogram of Writing / Data Set #
Frequency
1409.07 1471.21 1533.36 1595.50 1657.64 1719.79 1781.
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14^ Histogram of Combined / Data Set #
Frequency
fficult to characterize them as symmetric or skewed.t a. All histograms are irregularly shaped, so it's swers.^ ow are rough interpretations, not the absolute correct tical reading: symmetric and bimodal^ cent taking: skewed iting: bimodal^ th: N/A mbined: N/A
fficult to characterize them as symmetric or skewed.rt a. All histograms are irregularly shaped, so it's low are rough interpretations, not the absolute correct swers. rcent taking: skewed tical reading: symmetric and bimodal ath: N/A riting: bimodal mbined: N/A
Part b. The distributions of verbal scores (i.e., writing and reading) are bimodal (see part a.). The distribution of Math is hard to define.
Part b. The distributions of verbal scores (i.e., writing and reading) are bimodal (see part a.). The distribution of Math is hard to define.
Performed By: Date: (^) Friday, May 07, 2010Chris Albright Updating: Live One Variable Summary^ Percent TakingData Set #1 Critical ReadingData Set #1 MathData Set #1^ WritingData Set #1^ CombinedData Set # Mean Std. Dev. 0.37180.3049^ 534.4540.75 538.7641.26 521.3739.44 1594.59120. Median Mode 0.26000.0500 523.00486.00 525.00502.00 510.00480.00 1556.001477. Minimum Maximum 0.03000.9000^ 466.00610.00^ 451.00615.00^ 455.00588.00^ 1378.001813. Count 1st Quartile^51 0.0600^51 497.00^51 505.00^51 484.00^51 1486. 3rd Quartile 0.6700^ 572.00^ 572.00^ 559.00^ 1701. Parts c, d: For the "score" variables except Math, neither the mean or median could represent the "typical" value well since the distributions look like bimodal. For the Math score, either mean or median could be quoted. Probably the median would be preferred because it isn't affected by extremes. For the % taking, the mean clearly overstates the "typical" value, which is apparent from the histograms. Again, the median might be preferred. The mode is 5% because more states (6 of them) have this value than any other value. Still, it's not a very "stable" measure. Part e: The mean of a sum (combined score) is always the sum of the means (see cell H9). Medians don't combine this way, although it's pretty close in this example (see cell H11).
Parts c, d: For the "score" variables except Math, neither the mean or median could represent the "typical" value well since the distributions look like bimodal. For the Math score, either mean or median could be quoted. Probably the median would be preferred because it isn't affected by extremes. For the % taking, the mean clearly overstates the "typical" value, which is apparent from the histograms. Again, the median might be preferred. The mode is 5% because more states (6 of them) have this value than any other value. Still, it's not a very "stable" measure. Part e: The mean of a sum (combined score) is always the sum of the means (see cell H9). Medians don't combine this way, although it's pretty close in this example (see cell H11).
