ca_deveaux4.3.1.57-T.tdxex

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</array><array name="Country">
<data expr="&#39;Australia&#39;"/>
<data expr="&#39;Austria&#39;"/>
<data expr="&#39;Belgium&#39;"/>
<data expr="&#39;Canada&#39;"/>
<data expr="&#39;Chile&#39;"/>
<data expr="&#39;Czech Republic&#39;"/>
<data expr="&#39;Denmark&#39;"/>
<data expr="&#39;Estonia&#39;"/>
<data expr="&#39;Finland&#39;"/>
<data expr="&#39;France&#39;"/>
<data expr="&#39;Germany&#39;"/>
<data expr="&#39;Greece&#39;"/>
<data expr="&#39;Hungary&#39;"/>
<data expr="&#39;Iceland&#39;"/>
<data expr="&#39;Ireland&#39;"/>
<data expr="&#39;Israel&#39;"/>
<data expr="&#39;Italy&#39;"/>
<data expr="&#39;Japan&#39;"/>
<data expr="&#39;Korea&#39;"/>
<data expr="&#39;Latvia&#39;"/>
<data expr="&#39;Luxembourg&#39;"/>
<data expr="&#39;Mexico&#39;"/>
<data expr="&#39;Netherlands&#39;"/>
<data expr="&#39;New Zealand&#39;"/>
<data expr="&#39;Norway&#39;"/>
<data expr="&#39;Poland&#39;"/>
<data expr="&#39;Portugal&#39;"/>
<data expr="&#39;Slovak Republic&#39;"/>
<data expr="&#39;Slovenia&#39;"/>
<data expr="&#39;Spain&#39;"/>
<data expr="&#39;Sweden&#39;"/>
<data expr="&#39;Switzerland&#39;"/>
<data expr="&#39;Turkey&#39;"/>
<data expr="&#39;United Kingdom&#39;"/>
<data expr="&#39;United States&#39;"/>
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    <var name="genStart" common="1" type="int">
      <constraint>
        <limits>
          <limit type="ge">1</limit>
          <limit type="le">33</limit>
        </limits>
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<initvalues>
<expr>1</expr>
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    </var>
    <var name="genStep" comments="exclusions ensure: (~mean &#60; ~median)" common="1" type="int">
      <constraint>
<rprime>33</rprime>
        <limits>
          <limit type="ge">1</limit>
          <limit type="le">32</limit>
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        <excl>
          <expr>25</expr>
          <expr>29</expr>
          <expr>5</expr>
          <expr>31</expr>
          <expr>2</expr>
        </excl>
      </constraint>
<initvalues>
<expr>1</expr>
</initvalues>
    </var>
<array name="iGen">
<data expr="mod(fillarray(~n-2,~genStart-1,~genStep),33)+1"/>
</array><array name="i18">
<data expr="ceil((~iGen-16)/100)"/>
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<data expr="ceil((~iGen-19)/100)"/>
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<data expr="$orderA(~iGen+~i4+~i18+~i22+~i25,4,18,22,25)"/>
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    <var name="n" comments="static 25, # of data values" common="1" type="int">
      <constraint>
        <incl>
          <expr>25</expr>
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<array name="iCountry">
<data expr="~country.~index.01"/>
<data expr="~country.~index.02"/>
<data expr="~country.~index.03"/>
<data expr="~country.~index.04"/>
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<data expr="~country.~index.07"/>
<data expr="~country.~index.08"/>
<data expr="~country.~index.09"/>
<data expr="~country.~index.10"/>
<data expr="~country.~index.11"/>
<data expr="~country.~index.12"/>
<data expr="~country.~index.13"/>
<data expr="~country.~index.14"/>
<data expr="~country.~index.15"/>
<data expr="~country.~index.16"/>
<data expr="~country.~index.17"/>
<data expr="~country.~index.18"/>
<data expr="~country.~index.19"/>
<data expr="~country.~index.20"/>
<data expr="~country.~index.21"/>
<data expr="~country.~index.22"/>
<data expr="~country.~index.23"/>
<data expr="~country.~index.24"/>
<data expr="~country.~index.25"/>
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<data expr="~data.~index.01"/>
<data expr="~data.~index.02"/>
<data expr="~data.~index.03"/>
<data expr="~data.~index.04"/>
<data expr="~data.~index.05"/>
<data expr="~data.~index.06"/>
<data expr="~data.~index.07"/>
<data expr="~data.~index.08"/>
<data expr="~data.~index.09"/>
<data expr="~data.~index.10"/>
<data expr="~data.~index.11"/>
<data expr="~data.~index.12"/>
<data expr="~data.~index.13"/>
<data expr="~data.~index.14"/>
<data expr="~data.~index.15"/>
<data expr="~data.~index.16"/>
<data expr="~data.~index.17"/>
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<data expr="~data.~index.19"/>
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<data expr="~data.~index.23"/>
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</message></popupstep><array name="i4" comments="shifts data to insert 4">
<data expr="ceil((~iGen-3)/100)"/>
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    <var name="min" common="1" type="int">
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        <incl>
          <expr>~iDataSort.1</expr>
        </incl>
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    <var name="max" common="1" type="int">
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        <incl>
          <expr>~iDataSort.~n</expr>
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      <constraint>
        <incl>
          <expr>$MEDIAN(~iData)</expr>
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      </constraint>
    </var>
    <var name="mean" common="1" type="real" format="-.##">
      <constraint>
        <incl>
          <expr>$mean(~iData)</expr>
        </incl>
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<data expr="$orderA(~iData)"/>
</array><array name="IQR">
<data expr="~aq3-~aq1"/>
</array><array name="AQ1" comments="First quartiles as calculated by:&#10;1. median of bottom half - w/o median&#10;2. excel&#10;3. minitab&#10;4. median of bottom half - w/ median&#10;5. using rounded index if not half or whole">
<data expr="$MEDIAN(SUBARRAY(~AdataA,1,FLOOR(~AdataA.length/2)))"/>
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<data expr="SUBARRAY(~AdataA,FLOOR(0.25*(~AdataA.length+1)),1)+(0.25*(~AdataA.length+1)-FLOOR(0.25*(~AdataA.length+1)))*(SUBARRAY(~AdataA,CEIL(0.25*(~AdataA.length+1)),1)-SUBARRAY(~AdataA,FLOOR(0.25*(~AdataA.length+1)),1))"/>
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<data expr="$MEDIAN(SUBARRAY(~AdataA,CEIL(~AdataA.length/2)+1,FLOOR(~AdataA.length/2)))"/>
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<data expr="~iDataSort"/>
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        <incl>
          <expr>$StdDev(~iData)</expr>
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        <expr>~min</expr>
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        <expr>~AQ1.1</expr>
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      <solution>
        <expr>~AQ1.2</expr>
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      <solution>
        <expr>~AQ1.3</expr>
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        <expr>~AQ1.4</expr>
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        <expr>~AQ1.5</expr>
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      <solution>
        <expr>~AQ3.2</expr>
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      <solution>
        <expr>~AQ3.3</expr>
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      <solution>
        <expr>~AQ3.4</expr>
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      <solution>
        <expr>~AQ3.5</expr>
      </solution>
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      <solution>
        <expr>~max</expr>
      </solution>
    </field>
    <field name="S1" format=".#" tol=".1" enforceformatting="1" rule="numeric">
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        <expr>~iqr.1</expr>
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      <solution>
        <expr>~iqr.2</expr>
      </solution>
      <solution>
        <expr>~iqr.3</expr>
      </solution>
      <solution>
        <expr>~iqr.4</expr>
      </solution>
      <solution>
        <expr>~iqr.5</expr>
      </solution>
      <defmsgwrong cw="70" ch="0">
        <display step="msg2"/>
      </defmsgwrong>
    </field>
    <field name="S2" format="" tol=".01" enforceformatting="1" rule="numeric">
      <solution>
        <expr>~mean</expr>
      </solution>
      <defmsgwrong cw="70" ch="0">
        <display step="msg3"/>
      </defmsgwrong>
    </field>
    <field name="S3" format="" tol=".01" enforceformatting="1" rule="numeric">
      <solution>
        <expr>~std</expr>
      </solution>
      <defmsgwrong cw="70" ch="0">
        <display step="msg4"/>
      </defmsgwrong>
    </field>
<datatable name="DT1" tooltiptext="" firstrowisheader="1">
<columns>
<column>
<item value="Country"/>
<item value="=~iCountry"/>
</column>
</columns>
<columns>
<column>
<item value="Score"/>
<item value="=~iData"/>
</column>
</columns>
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<data expr="~Zmean+~Zstd*1"/>
<data expr="~Zmean+~Zstd*2"/>
<data expr="~Zmean+~Zstd*3"/>
</array>
    <var name="Zstd" common="1" type="int">
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        <limits>
          <limit type="ge">81</limit>
          <limit type="le">94</limit>
        </limits>
      </constraint>
<initvalues>
<expr>88</expr>
</initvalues>
    </var>
<array name="i25">
<data expr="ceil((~iGen-21)/100)"/>
</array><array name="zNeg">
<data expr="~Zmean-~Zstd*1"/>
<data expr="~Zmean-~Zstd*2"/>
<data expr="~Zmean-~Zstd*3"/>
</array>
    <fillin name="FL1" maxtries="3" correct="0" shuffle="1">
      <choice value="left-skewed."/>
      <choice value="right-skewed."/>
    </fillin>
    <fillin name="FL2" correct="0" shuffle="1" align="Center">
      <choice value="left"/>
      <choice value="right"/>
    </fillin>
    <fillin name="FL3" correct="0" shuffle="1" align="Center">
      <choice value="mean down toward the smaller values, whereas the median"/>
      <choice value="median up toward the larger values, whereas the mean"/>
    </fillin>
    <fillin name="FL4" correct="0" shuffle="1" align="Center">
      <choice value="mean toward it, whereas the median"/>
      <choice value="median toward it, whereas the mean"/>
    </fillin>
    <fillin name="FL5" correct="0" shuffle="1" align="Center">
      <choice value="5-number summary is"/>
      <choice value="mean and standard deviation are"/>
    </fillin>
    <fillin name="FL6" maxtries="3" correct="0" shuffle="1">
      <choice value="the outliers are resisted."/>
      <choice value="there are no outliers."/>
      <choice value="outliers improve the accuracy."/>
    </fillin>
    <var name="Xindex" common="1" type="int">
      <constraint>
        <limits>
          <limit type="ge">1</limit>
          <limit type="le">25</limit>
        </limits>
        <excl>
          <expr>4</expr>
        </excl>
      </constraint>
<initvalues>
<expr>1</expr>
</initvalues>
    </var>
    <var name="Xcountry" common="1" type="text">
      <constraint>
        <incl>
          <expr>~iCountry.~Xindex</expr>
        </incl>
      </constraint>
    </var>
    <var name="Xcomp" comments="TF: Canada &#62; ~Xdata" common="1" type="text">
      <constraint>
        <incl>
          <expr>~iData.4&#60;~iData.~Xindex</expr>
        </incl>
      </constraint>
    </var>
    <var name="Xdata" common="1" type="int">
      <constraint>
        <incl>
          <expr>~iData.~Xindex</expr>
        </incl>
      </constraint>
    </var>
<array name="the">
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;the &#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;the &#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;&#39;"/>
<data expr="&#39;the &#39;"/>
<data expr="&#39;the &#39;"/>
</array><array name="iThe">
<data expr="~the.~index.01"/>
<data expr="~the.~index.02"/>
<data expr="~the.~index.03"/>
<data expr="~the.~index.04"/>
<data expr="~the.~index.05"/>
<data expr="~the.~index.06"/>
<data expr="~the.~index.07"/>
<data expr="~the.~index.08"/>
<data expr="~the.~index.09"/>
<data expr="~the.~index.10"/>
<data expr="~the.~index.11"/>
<data expr="~the.~index.12"/>
<data expr="~the.~index.13"/>
<data expr="~the.~index.14"/>
<data expr="~the.~index.15"/>
<data expr="~the.~index.16"/>
<data expr="~the.~index.17"/>
<data expr="~the.~index.18"/>
<data expr="~the.~index.19"/>
<data expr="~the.~index.20"/>
<data expr="~the.~index.21"/>
<data expr="~the.~index.22"/>
<data expr="~the.~index.23"/>
<data expr="~the.~index.24"/>
<data expr="~the.~index.25"/>
</array>
    <fillin name="FL7" correct="0" shuffle="1" align="Center">
      <choice value="twenty-five"/>
      <choice value="twenty"/>
      <choice value="fifteen"/>
      <choice value="ten"/>
      <choice value="thirty"/>
    </fillin>
    <field name="S4" format=".#" rule="numeric">
      <solution>
        <expr>~max</expr>
      </solution>
    </field>
    <field name="S5" format=".#" rule="numeric">
      <solution>
        <expr>~min</expr>
      </solution>
    </field>
    <field name="S6" format=".#" rule="numeric">
      <solution>
        <expr>~median</expr>
      </solution>
    </field>
    <field name="S7" format=".#" tol=".1" enforceformatting="1" rule="numeric">
      <solution>
        <expr>~iqr.1</expr>
      </solution>
      <solution>
        <expr>~iqr.2</expr>
      </solution>
      <solution>
        <expr>~iqr.3</expr>
      </solution>
      <solution>
        <expr>~iqr.4</expr>
      </solution>
      <solution>
        <expr>~iqr.5</expr>
      </solution>
    </field>
    <field name="S8" format=".#" tol=".1" enforceformatting="1" rule="numeric">
      <solution>
        <expr>~AQ1.1</expr>
      </solution>
      <solution>
        <expr>~AQ1.2</expr>
      </solution>
      <solution>
        <expr>~AQ1.3</expr>
      </solution>
      <solution>
        <expr>~AQ1.4</expr>
      </solution>
      <solution>
        <expr>~AQ1.5</expr>
      </solution>
    </field>
    <field name="S9" format=".#" tol=".1" enforceformatting="1" rule="numeric">
      <solution>
        <expr>~AQ3.1</expr>
      </solution>
      <solution>
        <expr>~AQ3.2</expr>
      </solution>
      <solution>
        <expr>~AQ3.3</expr>
      </solution>
      <solution>
        <expr>~AQ3.4</expr>
      </solution>
      <solution>
        <expr>~AQ3.5</expr>
      </solution>
    </field>
    <field name="S10" format=".#" rule="numeric">
      <solution>
        <expr>~data.4</expr>
      </solution>
    </field>
    <fillin name="FL8" correct="0" shuffle="1" align="Center">
      <choice value="top 25%"/>
      <choice value="bottom 25%"/>
      <choice value="middle 50%"/>
    </fillin>
    <field name="S11" format="" rule="numeric">
      <solution>
        <expr>~zNeg.1</expr>
      </solution>
    </field>
    <field name="S12" format="" rule="numeric">
      <solution>
        <expr>~zVal.1</expr>
      </solution>
    </field>
    <var name="Zmean" common="1" type="int">
      <constraint>
        <incl>
          <expr>~data.4</expr>
        </incl>
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<text>The Programme for International Student Assessment (PISA) reported 2015 average mathematics performance scores for 15-year-olds in </text>
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<text br="0"> Organisation for Economic Co-operation and Development (OECD) nations. </text>
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<text br="0"> led the group, with an average score of </text>
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<text br="0">. (Non-OECD Singapore topped everyone, with a 564 average.) The average scores for each nation are given.</text>
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<text br="0"> Click the icon to view the OECD mathematics scores.</text>
<text></text>
<text>Complete parts a through d.</text>
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<text>a) Find the 5-number summary and IQR, the mean, and the standard deviation of these national averages. Can you explain why the mean is a bit smaller than the median? </text>
<text></text>
<text>Find the 5-number summary.</text>
<text></text>
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<text parastyle="Center">Min.</text>
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<text parastyle="Center">1st Qu.</text>
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<text>Find the IQR of these national averages.</text>
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<text>Find the mean of these national averages.</text>
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<text>Find the standard deviation of these national averages.</text>
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<text>Can you explain why the mean is a bit smaller than the median? </text>
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<text>The distribution of average scores is </text>
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<text br="0"> The long </text>
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<text>b) Which summary of the data would you report? Why?</text>
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<text>c) Write a brief summary of the performance of 15-year-olds in OECD countries. Be sure to comment on the performance of Canada and </text>
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<text>Data was collected from </text>
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<text br="0"> countries that participated in the program. The highest national average is </text>
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<text>d) In Canada, the standard deviation of the individual students&#39; scores was </text>
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<text br="0"> and an upper bound of </text>
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<text br="0"> or more than </text>
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<text br="0">. Only a real math genius could have scored above </text>
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<text br="0">.</text>
<text textstyle="Instructions">(Round to the nearest integer as needed.) </text>
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<text>At least one of your answers is incorrect. Technology can be used to quickly and accurately find the 5-number summary. A 5-number summary consists of minimum, Q1, median, Q3, and maximum. The median is the middle value; half the values are above and half are below the median. To find the median of a batch of n numbers, order the values first. If n is odd, the median is the middle value. This value is in the </text>
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<text br="0"> position. When n is even, there are two middle values. Then, the median is the average of the two values in positions </text>
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<text br="0"> and </text>
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<tdxsym br="0">+</tdxsym>
<text br="0">1. To find the quartiles of an ordered batch of n numbers, start by splitting the batch into two halves at the median. The lower quartile is the median of the lower half, and the upper quartile is the median of the upper half.</text>
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<text>Technology can be used to quickly and accurately find the interquartile range (IQR). The IQR is the difference between the first and third quartiles. The lower quartile is the median of the lower half, and the upper quartile is the median of the upper half.</text>
<text></text>
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<text>Technology can be used to quickly and accurately find the mean of a data set. The mean, </text>
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<text>Technology can be used to quickly and accurately find the standard deviation of a data set. Standard deviation, s, is the square root of the variance.</text>
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<text>At least one of your answers is incorrect. To choose between sample mean and median, start by looking at the data. Use technology to construct a histogram of the data. If the histogram of the data is symmetric and there are no outliers, choose the sample mean. However, if the histogram is skewed or has outliers, choose the median. A distribution is skewed if it&#39;s not symmetric and one tail stretches out farther than the other. Distributions are said to be skewed left (or negatively) when the longer tail stretches to the left (in the negative direction), and skewed right (or positively) when it goes to the right (in the positive direction). A calculated summary measure is said to be resistant if it is affected only a limited amount by any small bunch of cases, such as outliers.</text>
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<text>At least one of your answers is incorrect. A calculated summary measure is said to be resistant if it is affected only a limited amount by any small bunch of cases, such as outliers.</text>
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<text>At least one of your answers is incorrect. Review the calculated statistics.</text>
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<text>At least one of your answers is incorrect. Technology can be used to quickly and accurately find a data value that is a certain number of standard deviations from the mean. The Empirical Rule states:</text>
<text parastyle="Normal.1">i. About 68% of the data will lie within 1 standard deviation of the mean.</text>
<text parastyle="Normal.1">ii. About 95% of the data will lie within 2 standard deviations of the mean.</text>
<text parastyle="Normal.1">iii. Virtually all of the data will lie within 3 standard deviations of the mean.</text>
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<control parastyle="Center" vshiftabs="1" spacing="1" textstyle="Normal" data="">iData.24</control>
</cell>
<cell></cell>
</row>
<row>
<cell width="75">
<control vshiftabs="1" spacing="1" textstyle="Normal" data="">iCountry.25</control>
</cell>
<cell width="75">
<control parastyle="Center" vshiftabs="1" spacing="1" textstyle="Normal" data="">iData.25</control>
</cell>
<cell></cell>
</row>
</table>
</document>
</rvxml>
      </step>
    </window>
  </windows>

  <layout type="topbottom">
    <frame window="top"/>
    <frame window="bottom"/>
  </layout>

  <controller>
    <display step="step1"/>
    <display step="step2"/>
    <display step="step4"/>
    <display step="step5"/>
    <display step="step6"/>
    <display step="step7"/>
    <display step="step8"/>
    <display step="step9"/>
    <display step="step10"/>
  </controller>

</tdx>