Business Statistics (BQT 173) ІМ ќ INSTITUT MATEMATIK K E J U R U T E R A A N U N I M A P Descriptive Statistics: Numerical Measures (Statistic)

Lecture 2Abdull Halim Abdul2 What is statistic? Literally it is the number that describe something. Statistically statistic is a number that describe the sample.

Lecture 2Abdull Halim Abdul3 Statistic Studied 1. Measure Of Central Tendency 1. Mean 2. Median 3. Mod 2. Measure Of Dispersion 1. Mean Deviation 2. Standard Deviation

Lecture 2Abdull Halim Abdul4 Measure Of Central Tendency - Mean 1. Ungrouped data 2. Grouped data

Lecture 2Abdull Halim Abdul5 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

Lecture 2Abdull Halim Abdul6 Mean of Grouped Data Example

Lecture 2Abdull Halim Abdul7 Measure Of Central Tendency - Median The median is the middle value of a set of numbers arranged in order of magnitude

Lecture 2Abdull Halim Abdul8 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

Lecture 2Abdull Halim Abdul9 Median of Grouped Data

Lecture 2Abdull Halim Abdul10 Measure Of Central Tendency - Mode The mode of a set of numbers is the value which occurs most often

Lecture 2Abdull Halim Abdul11 Mode of Ungrouped Data The mode of a set of numbers is the value which occurs most often

Lecture 2Abdull Halim Abdul12 Mode of Grouped Data

Lecture 2Abdull Halim Abdul13 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.

Lecture 2Abdull Halim Abdul14 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

Lecture 2Abdull Halim Abdul15 Variance (Ungrouped Data) Variance for population Variance for sample

Lecture 2Abdull Halim Abdul16 Variance (Grouped Data)

Lecture 2Abdull Halim Abdul17 Tchebyshev Theorem At least (1-1/k 2 ) 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.

Lecture 2Abdull Halim Abdul18 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