Business Statistics (BQT 173)

ІМќINSTITUT MATEMATIK K E J U R U T E R A A NU N I M A P

Descriptive Statistics: Numerical Measures (Statistic)

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What is statistic?

Literally it is the number that describe something.

Statistically statistic is a number that describe the sample.

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Statistic Studied

1. Measure Of Central Tendency1. Mean

2. Median

3. Mod

2. Measure Of Dispersion1. Mean Deviation

2. Standard Deviation

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Measure Of Central Tendency- Mean

1. Ungrouped data

2. Grouped data

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Mean of Ungrouped Data

The mean of a set of measurements is the sum of the measurements divided by the number of measurements in the set.

Example

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Mean of Grouped Data

Example

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Measure Of Central Tendency- Median

The median is the middle value of a set of numbers arranged in order of magnitude

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Median of Ungrouped Data

The median depends on the number of observations in the sample.

If it is odd, the median is the X((n+1)/2) and

is even, the median is the [X(n/2)+X(n/2 + 1) ]/2

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Median of Grouped Data

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Measure Of Central Tendency- Mode

The mode of a set of numbers is the value which occurs most often

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Mode of Ungrouped Data

The mode of a set of numbers is the value which occurs most often

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Mode of Grouped Data

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Measure Of Dispersion

The measure of dispersion or spread is the degree to which a set of data tends to spread about an average value.

It shows whether the set of data is concentrated around the average not.

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Variance

The variance of a set of sample measurements is the sum of the squared deviations of the measurements from their mean divided by its degree of freedom (n-1).

The most popular measure of dispersion

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Variance (Ungrouped Data)

Variance for population

Variance for sample

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Variance (Grouped Data)

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Tchebyshev Theorem

At least (1-1/k2) from the measurements in the related data will be in the range of k standard deviation from mean,

which k is the positive number exceed than 1.

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Empirical Theorem

For a data that is mountshaped, the interval Contains approximately 68% of the measurements lie in

one std deviation interval, Contains approximately 95% of the measurements lie in

two std deviation interval, Contains approximately 99.7% of the measurements lie

three std deviation interval

),( sxsx

)2,2( sxsx

)3,3( sxsx