Measures of variation (dispersion) [مقاييس التشتت]

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Presentation transcript:

Measures of variation (dispersion) [مقاييس التشتت]

Inter Quartile Range (IQR)=Q3-Q1

Dot plots A dot plot consists of a graph in which each data value is plotted as a point or dot a long scale of values, dots representing equal values are stacked. Example: two samples of seedlings were planted in a green house, one containing seedlings treated with nitrogen and the other containing seedlings with no nitrogen. The stem weights in grams were recorded after 140 days, the data are given in the table below:

Dot plots No NitrogenNitrogen Min = 0.26 Max = 0.86

Dot plots Minimum value is 0.26, maximum value is 0.86 then we represent the dot plot as :

Stem and leaf plots A stem and leaf plot represents data by separating each value into two parts: the stem (such as the leftmost digit) and leaf (such as the rightmost digit). Example 1: The data below specifies the life of 40 batteries recorded to the nearest tenth of year. To plot stem and leaf we split each observation into two parts consisting of a stem and a leaf. In our data the stem represents the digit preceding the decimal and the leaf corresponds to the decimal part of the number.

Stem and leaf plots

Minimum value is 1.6 and maximum value is 4.7 We can plot stem and leaf of battery life as:

Stem and leaf plots Example 2: We have a set of data as : (145, 210, 99, 80, 115, 127, 215, 176 and 170), how to plot stem and leaf for the data set? Minimum value =80 Maximum value = 215 Then stem and leaf plot as:

Stem and leaf plots Then stem and leaf plot as: StemLeafFrequency Total8

Geometric mean: الوسط الهندسي The geometric mean is defined as the nth root of the product of n numbers. Geometric mean is defined as:

Geometric mean: الوسط الهندسي The geometric mean answers the question, if all the quantities had the same value, what would that value has to be in order to achieve the same product. Geometric mean is useful when we want to compare things with different properties.

Geometric mean: الوسط الهندسي Example 1: You want to buy a new camera: One camera has a zoom of 200 and gets an 8 in reviews. The other has a zoom of 250 and gets 6 in reviews. Which is the better?

Geometric mean: الوسط الهندسي 1. Calculate arithmetic mean If we compare between them respected to the arithmetic mean the second is the best.

Geometric mean: الوسط الهندسي 2. Calculate geometric mean While in second camera the zoom is 50 bigger but user rating of 6 is still important to user so he preferred 8 rates than 6 rates.

Geometric mean: الوسط الهندسي Example 2: calculate the geometric mean for (2, 8, 4) Solution: