AP Statistics Curriculum 2007 EDA Var - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T17:35:45Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

IvoDinov: /* Coefficient of Variation */

2011-11-16T22:25:22Z

‎Coefficient of Variation

IvoDinov: /* Coefficient of Variation */

2011-01-11T16:51:27Z

‎Coefficient of Variation

IvoDinov: /* General Advance-Placement (AP) Statistics Curriculum - Measures of Variation */ added CV section

2011-01-11T16:50:11Z

‎General Advance-Placement (AP) Statistics Curriculum - Measures of Variation: added CV section

Jenny: /* Quartiles and IQR */

2010-06-28T18:59:04Z

‎Quartiles and IQR

Jenny: /* Measures of Variation and Dispersion */

2010-06-28T18:58:44Z

‎Measures of Variation and Dispersion

ChiccoChou: /* Quartiles and IQR */

2010-05-14T00:00:02Z

‎Quartiles and IQR

ChiccoChou: /* Quartiles and IQR */

2010-05-13T23:58:12Z

‎Quartiles and IQR

IvoDinov: added Five-number summary

2010-04-02T15:47:58Z

added Five-number summary

IvoDinov: added a link to the Problems set

2009-10-26T04:45:53Z

added a link to the Problems set

← Older revision		Revision as of 17:35, 3 March 2020
Line 87:		Line 87:
	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=AP_Statistics_Curriculum_2007_EDA_Var}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_EDA_Var}}

← Older revision		Revision as of 22:25, 16 November 2011
Line 29:		Line 29:

	Obviously, the CV is well-defined for processes with well-defined first two moments (mean and variance), but also requires a ''non-trivial'' mean (<math>\mu \not= 0</math>). If the CV is expressed as percentage, than this ratio is multiplied by 100. The sample coefficient of variation is computed mostly for data measured on a ratio scale. For instance, if a set of distances are measured, the standard deviation does not depend on whether the distances were measured in kilometers (metric) or miles. This is because changes in the particle/object's distances by 1 kilometer also changes its distance by 1 mile. However the mean distance of the data would differ in each measurement scale (as [http://en.wikipedia.org/wiki/Mile 1 mile is approximately 1.7 kilometers]) and thus the coefficient of variation would differ. In general, the CV may not have any meaning for data on an interval scale.		Obviously, the CV is well-defined for processes with well-defined first two moments (mean and variance), but also requires a ''non-trivial'' mean (<math>\mu \not= 0</math>). If the CV is expressed as percentage, than this ratio is multiplied by 100. The sample coefficient of variation is computed mostly for data measured on a ratio scale. For instance, if a set of distances are measured, the standard deviation does not depend on whether the distances were measured in kilometers (metric) or miles. This is because changes in the particle/object's distances by 1 kilometer also changes its distance by 1 mile. However the mean distance of the data would differ in each measurement scale (as [http://en.wikipedia.org/wiki/Mile 1 mile is approximately 1.7 kilometers]) and thus the coefficient of variation would differ. In general, the CV may not have any meaning for data on an interval scale.
		+
		+	The sample-coefficient of variation is computed by plugin the sample-driven estimates of the standard deviation (sample-standard deviation, <math>s</math>, and the sample-average, <math>\bar{x}</math>). In image processing, the reciprocal of the coefficient of variation is μ/σ is called ''signal-to-noise-ratio'' (SNR).

	===Five-number summary===		===Five-number summary===

@@ Line 28: / Line 28: @@
 :<math>CV = \frac{\sigma}{\mu}.</math>
-Obviously, the CV is well-defined for processes with well-defined first two moments (mean and variance), but also requires a ''non-trivial'' mean (<math>\mu \not= 0</math>). If the CV is expressed as percentage, than this ratio is  multiplied by 100. The sample coefficient of variation is computed mostly for data measured on a ratio scale. For instance, if a set of distances are measured, the standard deviation does not depend on whether the distances were measured in kilometers (metric) or miles. This is because changes in the particle/object's distances by 1 kilometer also changes its distance by 1 mile. However the mean distance of the data would differ in each measurement scale (as 1 mile is approximately 1.7 kilometers) and thus the coefficient of variation would differ. In general, the CV may not have any meaning for data on an interval scale.
+Obviously, the CV is well-defined for processes with well-defined first two moments (mean and variance), but also requires a ''non-trivial'' mean (<math>\mu \not= 0</math>). If the CV is expressed as percentage, than this ratio is  multiplied by 100. The sample coefficient of variation is computed mostly for data measured on a ratio scale. For instance, if a set of distances are measured, the standard deviation does not depend on whether the distances were measured in kilometers (metric) or miles. This is because changes in the particle/object's distances by 1 kilometer also changes its distance by 1 mile. However the mean distance of the data would differ in each measurement scale (as [http://en.wikipedia.org/wiki/Mile 1 mile is approximately 1.7 kilometers]) and thus the coefficient of variation would differ. In general, the CV may not have any meaning for data on an interval scale.
 ===Five-number summary===

← Older revision		Revision as of 16:50, 11 January 2011
Line 23:		Line 23:

	For example, <math>Q_1=(64+68)/2=66</math>, <math>Q_3=(78+80)/2=79</math> and <math>IQR=Q_3-Q_1=13</math>, for the Long-Jump data shown above. Thus we expect the middle half of all long jumps (for that population) to be between 66 and 79 inches.		For example, <math>Q_1=(64+68)/2=66</math>, <math>Q_3=(78+80)/2=79</math> and <math>IQR=Q_3-Q_1=13</math>, for the Long-Jump data shown above. Thus we expect the middle half of all long jumps (for that population) to be between 66 and 79 inches.
		+
		+	===Coefficient of Variation===
		+	For a given process, the coefficient of variation (CV) is defined as the ratio of the standard deviation (<math>\sigma </math>) to the mean (<math>\mu </math>):
		+	:<math>CV = \frac{\sigma}{\mu}.</math>
		+
		+	Obviously, the CV is well-defined for processes with well-defined first two moments (mean and variance), but also requires a ''non-trivial'' mean (<math>\mu \not= 0</math>). If the CV is expressed as percentage, than this ratio is multiplied by 100. The sample coefficient of variation is computed mostly for data measured on a ratio scale. For instance, if a set of distances are measured, the standard deviation does not depend on whether the distances were measured in kilometers (metric) or miles. This is because changes in the particle/object's distances by 1 kilometer also changes its distance by 1 mile. However the mean distance of the data would differ in each measurement scale (as 1 mile is approximately 1.7 kilometers) and thus the coefficient of variation would differ. In general, the CV may not have any meaning for data on an interval scale.

	===Five-number summary===		===Five-number summary===

@@ Line 20: / Line 20: @@
 ===Quartiles and IQR===
-The first quartile (<math>Q_1</math>) and the third quartile (<math>Q_3</math>) are defined values that split the dataset into ''bottom-25% vs. top-75%'' and ''bottom-75% vs. top-25%'', respectively. Thus the inter-quartile range (IQR), which is the difference <math>Q_3 - Q_1</math>, represents the central 50% for the data and can be considered as a measure of data dispersion or variation. The wider the IQR, the more variant the data.
+The first quartile (<math>Q_1</math>) and the third quartile (<math>Q_3</math>) are defined values that split the dataset into ''bottom-25% vs. top-75%'' and ''bottom-75% vs. top-25%'', respectively. Thus the inter-quartile range (IQR), which is the difference <math>Q_3 - Q_1</math>, represents the central 50% of the data and can be considered as a measure of data dispersion or variation. The wider the IQR, the more variant the data.
 For example, <math>Q_1=(64+68)/2=66</math>,  <math>Q_3=(78+80)/2=79</math> and <math>IQR=Q_3-Q_1=13</math>, for the Long-Jump data shown above. Thus we expect the middle half of all long jumps (for that population) to be between 66 and 79 inches.

@@ Line 4: / Line 4: @@
 There are many measures of (population or sample) variation, e.g., the range, the variance, the standard deviation, mean absolute deviation, etc. These are used to assess the dispersion or spread of the population.
-Suppose we are interested in the long-jump performance of some students. We can carry an experiment by randomly selecting 8 male statistics students and ask them to perform the standing long jump.  In reality every student participated, but for the ease of calculations below we will focus on these eight students.  The long jumps were as follows:
+Suppose we are interested in the long-jump performance of some students. We can carry an experiment by randomly selecting eight male statistics students and ask them to perform the standing long jump.  In reality every student participated, but for the ease of calculations below we will focus on these eight students.  The long jumps were as follows:
 <center>
 {| class="wikitable" style="text-align:center; width:75%" border="1"

← Older revision		Revision as of 15:47, 2 April 2010
Line 23:		Line 23:

	For example, <math>Q_1=(64+68)/2=66</math>, <math>Q_3=(78+80)/2=79</math> and <math>IQR=Q_3-Q_1=13</math>, for the Long-Jump data shown above. Thus we expect the middle half of all long jumps (for that population) to be between 66 and 79 inches.		For example, <math>Q_1=(64+68)/2=66</math>, <math>Q_3=(78+80)/2=79</math> and <math>IQR=Q_3-Q_1=13</math>, for the Long-Jump data shown above. Thus we expect the middle half of all long jumps (for that population) to be between 66 and 79 inches.
		+
		+	===Five-number summary===
		+	The five-number summary for a dataset is the 5-tuple <math>\{min, Q_1, Q_2, Q_3, max\}</math>, containing the sample minimum, first-quartile, second-quartile (median), third-quartile, and maximum.

	===Variance and Standard Deviation===		===Variance and Standard Deviation===

← Older revision		Revision as of 04:45, 26 October 2009
Line 65:		Line 65:

	*Most of the [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] compute the variance or standard deviation for the sample. You can see these examples of [[SOCR_EduMaterials_ChartsActivities \| Charts Activities]] and [[SOCR_EduMaterials_AnalysesActivities \| Analyses Activities]] and you can test these using [[SOCR_012708_ID_Data_HotDogs \| hotdogs dataset]].		*Most of the [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] compute the variance or standard deviation for the sample. You can see these examples of [[SOCR_EduMaterials_ChartsActivities \| Charts Activities]] and [[SOCR_EduMaterials_AnalysesActivities \| Analyses Activities]] and you can test these using [[SOCR_012708_ID_Data_HotDogs \| hotdogs dataset]].
		+
		+	===[[EBook_Problems_EDA_Var \| Problems]]===

	<hr>		<hr>