Bar charts and Histograms

Frequency distribution Definition: It is a list of values from a sample. Example: Number of children per family Size = {1,2,2,2,4,2,2,1,2,2,2,3,1,2,3,2,2,1,2,1,1,2,3,2,1} Size Absolute Frequency 1 7 2 14 3 4 Total 25

Absolute and relative frequencies, and percentage Size Absolute Frequency Relative Frequency Percentage 1 7 0.28 28 2 14 0.56 56 3 0.12 12 4 0.04 Total 25 100

Bar chart Usually, categorical and nominal data are visualized by using a bar chart. Example: Number of children in a family Size = {1,2,2,2,4,2,2,1,2,2,2,3,1,2,3,2,2,1,2,1,1,2,3,2,1}

Histogram If the x-axis is continuous, then we use an histogram Example: Scores on an empathy scale Score = {60, 38, 41, 45, 40, 75, 31, 35, 45, 46, 55, 61, 40, 15, 58, 71, 46, 53, 65, 54, 41, 56, 45, 65, 69, 50, 54, 41, 57, 44, 75, 30, 44, 30, 63, 44, 58, 34, 33, 66, 49, 42, 58, 70, 28, 49, 47, 47, 58, 38} Since there is too many data, we have to regroup them in bins.

Histogram Size of bins = 1

Histogram Size of bins = 5

Histogram Size of bins= 10

Histogram Size of bins = 20

Frequency distribution: Shapes II III IV V VI VII Modality Kurtosis Skewness - Unimodal : I, IV,V, VI, VII - Mesokurtic : I, II - symetric : I, II, III, V, VI - Bimodal : II - Platykurtic : V - asymetric : IV, VII - Rectangular: III - Leptokurtic : IV,VI,VII