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		<title>To the Outside Observer</title>
		<link>http://blog.swlug.org/bron</link>
		<description></description>
		<language>en-UK</language>
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			<title>A Set Difference</title>
			<link>http://blog.swlug.org/bron/2006/08/12/a_set_difference</link>
			<pubDate>Sat, 12 Aug 2006 05:36:25 +0000</pubDate>			<dc:creator>Bron</dc:creator>
			<category domain="main">Measurements in Space</category>			<guid isPermaLink="false">41@http://blog.swlug.org/</guid>
						<description>&lt;p&gt;The BBC reports:&lt;/p&gt;

&lt;p&gt;Secondary school pupils placed in low-ability sets often feel stigmatised as &quot;thick&quot;, a study suggests.&lt;br /&gt;
Researchers at London University's Institute of Education said the system had to change to ensure these children did not lose motivation.&lt;br /&gt;
A survey of 5,000 pupils found they largely backed setting, but those in lower groups were more likely to prefer mixed-ability classes.&lt;br /&gt;
The government said &quot;effective&quot; setting raised overall academic standards.&lt;br /&gt;
The researchers found 62% of pupils preferred to be in sets, while 24% wanted mixed-ability classes. &lt;/p&gt;

&lt;p&gt;My feeling is the other 14% didn't understand the question.&lt;/p&gt;&lt;div class=&quot;item_footer&quot;&gt;&lt;p&gt;&lt;small&gt;&lt;a href=&quot;http://blog.swlug.org/bron/2006/08/12/a_set_difference&quot;&gt;Original post&lt;/a&gt; blogged on &lt;a href=&quot;http://b2evolution.net/&quot;&gt;b2evolution&lt;/a&gt;.&lt;/small&gt;&lt;/p&gt;&lt;/div&gt;</description>
			<content:encoded><![CDATA[<p>The BBC reports:</p>

<p>Secondary school pupils placed in low-ability sets often feel stigmatised as "thick", a study suggests.<br />
Researchers at London University's Institute of Education said the system had to change to ensure these children did not lose motivation.<br />
A survey of 5,000 pupils found they largely backed setting, but those in lower groups were more likely to prefer mixed-ability classes.<br />
The government said "effective" setting raised overall academic standards.<br />
The researchers found 62% of pupils preferred to be in sets, while 24% wanted mixed-ability classes. </p>

<p>My feeling is the other 14% didn't understand the question.</p><div class="item_footer"><p><small><a href="http://blog.swlug.org/bron/2006/08/12/a_set_difference">Original post</a> blogged on <a href="http://b2evolution.net/">b2evolution</a>.</small></p></div>]]></content:encoded>
								<comments>http://blog.swlug.org/bron/2006/08/12/a_set_difference#comments</comments>
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				<item>
			<title>Liars, Damn Liars &#38; Statisticians</title>
			<link>http://blog.swlug.org/bron/2006/07/06/liars_damn_liars_aamp_statisticians</link>
			<pubDate>Thu, 06 Jul 2006 09:19:53 +0000</pubDate>			<dc:creator>Bron</dc:creator>
			<category domain="main">Measurements in Space</category>			<guid isPermaLink="false">40@http://blog.swlug.org/</guid>
						<description>&lt;p&gt;In 1999 the government said it wanted to gradually eliminate child poverty. It set itself the goals of reducing child poverty by a quarter by 2005, half by 2010 and altogether by 2020.&lt;/p&gt;

&lt;p&gt;In March, the government announced it had narrowly missed its first target, managing to reduce poverty levels by about a fifth rather than a quarter. &lt;/p&gt;

&lt;p&gt;Yesterday, the Joseph Rowntree Foundation stated the government may miss its child poverty target unless it changes its approach to boosting the incomes of the poor.  &lt;/p&gt;

&lt;p&gt;Well what is poverty? The way the government defines it: 60% of median earnings. &lt;/p&gt;

&lt;p&gt;Now, I'm no Mathematician, but is it not the case that in any given set of numbers, if we order them one will always (by its very definition), have a median with equal distribution either side.?&lt;/p&gt;

&lt;p&gt;Would a more accurate metric of relative poverty be 60% of the mean.?  &lt;/p&gt;

&lt;p&gt;Well, let's start by making the (not unreasonable) assumption that the UK enjoys a standard distribution, so if we have the following arbitrary ordered set:&lt;/p&gt;

&lt;p&gt;10, 10, 15, 18, 25, 45, 150&lt;/p&gt;

&lt;p&gt;The median (midpoint) is 18&lt;br /&gt;
The mode (most occurrences) is 10&lt;br /&gt;
The mean (average) is (10+10+15+18+25+45+150 / 7) is 39&lt;/p&gt;

&lt;p&gt;Yet 39 doesn't appear in our set; averages don't have to, they are calculated with reference to the set members, and that's why they can be DANGEROUS and certainly INVITE COMPARISONS!!&lt;/p&gt;

&lt;p&gt;5/7ths of our set members are less than average (over 71%)&lt;/p&gt;

&lt;p&gt;Assume these figures represent 000's in annual incomes (10,000 15,000 etc)&lt;br /&gt;
The poverty stricken 60% of the median (as our government defines poverty) applies to all those earning less than 10,800 which is the two lowest numbers in our set, 2/7ths of the sample, or over 28%&lt;/p&gt;

&lt;p&gt;Now, if we were to use the mode, the poverty definition would apply to all those earning less than 6,000. We have no 6 in our sample. So in a simple step I have eliminated 'poverty' from my sample.&lt;/p&gt;

&lt;p&gt;What about the mean.? 60% of 39 (our calculated average) is 23.4, so turning this back into our 000's of income; 23,400&lt;/p&gt;

&lt;p&gt;4 members of our sample fall under this, 4/7ths, or just over a whopping 57%&lt;/p&gt;

&lt;p&gt;&lt;em&gt;&quot;That's great, but what's your point.?&quot;&lt;/em&gt;&lt;/p&gt;

&lt;p&gt;By using the same set of numbers, I have been able to manipulate perception by changing my method of calculation:&lt;/p&gt;

&lt;p&gt;Using 60% of the median (as the government): &gt;28% in poverty&lt;br /&gt;
Using 60% of the mode: 0% in poverty&lt;br /&gt;
Using 60% of the mean: &gt;57% in poverty&lt;/p&gt;

&lt;p&gt;I do long for a system of government that supplies its benefactors raw data for analysis as opposed to the fashion for keeping the mathematical illiterati spoon-fed with junk information. It's the salt 'n' sugar packed soylent-yellow foodstuff of the targets game.&lt;/p&gt;

&lt;p&gt;How long before the government announces it's exceeded its target.? How long 'til the next election.?&lt;/p&gt;
&lt;div class=&quot;item_footer&quot;&gt;&lt;p&gt;&lt;small&gt;&lt;a href=&quot;http://blog.swlug.org/bron/2006/07/06/liars_damn_liars_aamp_statisticians&quot;&gt;Original post&lt;/a&gt; blogged on &lt;a href=&quot;http://b2evolution.net/&quot;&gt;b2evolution&lt;/a&gt;.&lt;/small&gt;&lt;/p&gt;&lt;/div&gt;</description>
			<content:encoded><![CDATA[<p>In 1999 the government said it wanted to gradually eliminate child poverty. It set itself the goals of reducing child poverty by a quarter by 2005, half by 2010 and altogether by 2020.</p>

<p>In March, the government announced it had narrowly missed its first target, managing to reduce poverty levels by about a fifth rather than a quarter. </p>

<p>Yesterday, the Joseph Rowntree Foundation stated the government may miss its child poverty target unless it changes its approach to boosting the incomes of the poor.  </p>

<p>Well what is poverty? The way the government defines it: 60% of median earnings. </p>

<p>Now, I'm no Mathematician, but is it not the case that in any given set of numbers, if we order them one will always (by its very definition), have a median with equal distribution either side.?</p>

<p>Would a more accurate metric of relative poverty be 60% of the mean.?  </p>

<p>Well, let's start by making the (not unreasonable) assumption that the UK enjoys a standard distribution, so if we have the following arbitrary ordered set:</p>

<p>10, 10, 15, 18, 25, 45, 150</p>

<p>The median (midpoint) is 18<br />
The mode (most occurrences) is 10<br />
The mean (average) is (10+10+15+18+25+45+150 / 7) is 39</p>

<p>Yet 39 doesn't appear in our set; averages don't have to, they are calculated with reference to the set members, and that's why they can be DANGEROUS and certainly INVITE COMPARISONS!!</p>

<p>5/7ths of our set members are less than average (over 71%)</p>

<p>Assume these figures represent 000's in annual incomes (10,000 15,000 etc)<br />
The poverty stricken 60% of the median (as our government defines poverty) applies to all those earning less than 10,800 which is the two lowest numbers in our set, 2/7ths of the sample, or over 28%</p>

<p>Now, if we were to use the mode, the poverty definition would apply to all those earning less than 6,000. We have no 6 in our sample. So in a simple step I have eliminated 'poverty' from my sample.</p>

<p>What about the mean.? 60% of 39 (our calculated average) is 23.4, so turning this back into our 000's of income; 23,400</p>

<p>4 members of our sample fall under this, 4/7ths, or just over a whopping 57%</p>

<p><em>"That's great, but what's your point.?"</em></p>

<p>By using the same set of numbers, I have been able to manipulate perception by changing my method of calculation:</p>

<p>Using 60% of the median (as the government): >28% in poverty<br />
Using 60% of the mode: 0% in poverty<br />
Using 60% of the mean: >57% in poverty</p>

<p>I do long for a system of government that supplies its benefactors raw data for analysis as opposed to the fashion for keeping the mathematical illiterati spoon-fed with junk information. It's the salt 'n' sugar packed soylent-yellow foodstuff of the targets game.</p>

<p>How long before the government announces it's exceeded its target.? How long 'til the next election.?</p>
<div class="item_footer"><p><small><a href="http://blog.swlug.org/bron/2006/07/06/liars_damn_liars_aamp_statisticians">Original post</a> blogged on <a href="http://b2evolution.net/">b2evolution</a>.</small></p></div>]]></content:encoded>
								<comments>http://blog.swlug.org/bron/2006/07/06/liars_damn_liars_aamp_statisticians#comments</comments>
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