ma-250 probability and statistics nazar khan pucit lecture 4
DESCRIPTION
The Normal CurveTRANSCRIPT
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MA-250 Probability and Statistics
Nazar KhanPUCIT
Lecture 4
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The Normal Curve
• An approximation to data distribution that is normally quite accurate– Normally data follows such a distribution
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The Normal Curve
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Standard Units
• Express the data in terms of standard deviation
• Converting a value X to standard units– (X-average)/SD
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The Normal Approximation to Data
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The Normal Approximation to Data
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Finding Areas under Normal Curve
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• Find the area between 0 and 2 under the normal curve.
• Find the area between -2 and 1 under the normal curve.
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• Find the area to the right of 1 under the normal curve.
• Find the area to the left of 2 under the normal curve.
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• Find the area between 1 and 2 under the normal curve
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Key point:Notice how the
original data and its histogram can
now be discarded. This is the
advantage of the normal
approximation!
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Normal approximation is not always accurate
Verify this.
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Percentiles
• Some histograms can not be accurately summarised by the normal curve.
• Can they be summarised some other way?– Yes, using percentiles.
• If 10% of the data lies below x, then x is the 10th percentile.
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Percentiles
• If 10% of the data lies below x, then x is the 10th percentile.
• If k% of the data lies below x, then x is the kth percentile.
• A percentile is not a percentage!• It is a number that lies on the horizontal axis.
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•The 50th percentile is ….•Is there a technical term for the 50th percentile?• Think about what the 50th percentile represents.
Percentiles
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Percentiles
• How can we summarize spread of a histogram using percentiles?– Subtract the 25th percentile from the 75th
percentile.• This is called the interquartile range.– Is the interquartile range a percentage?
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Percentiles
• Percentiles can summarize any histogram, whether it follows the normal curve or not.
• Question:– Assuming that a set of exam scores follows the
normal curve with mean 63 and SD 10, what is the 95th percentile?
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A note on reading Normal Tables• The table in the book is not a standard table.
– Gives area under the normal curve from –z to z• Standard tables give area from –inf to z
• So always note what a normal table represents before using area values from it.
• Is there a relationship between this z-score and percentiles?
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Summary