Chapter_3_Statistical_Summary.pdf

# Chapter_3_Statistical_Summary.pdf - SQQS1033 Data...

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SQQS1033 Data Exploratory and Generalisation lyf Sept’1 4 Page 1 Chapter 3 Statistical Summary Introduction When we look at a distribution of data, we should consider three characteristics: Shape (chapter 2 and 4) Center / Location (central tendency measurement) Spread (dispersion measurement) With these characteristics, we can numerically describe the main features of a data set. we may describe about the behaviour of the data in much simpler form. Figure 3.1: Distribution of Data Spread Centre/location Shape

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SQQS1033 Data Exploratory and Generalisation lyf Sept’1 4 Page 2 Central Tendency Measurement A measure of central tendency gives the center of a histogram or a frequency distribution. To report a typical value that is representative of the data. Three common measures of central tendency: Mean (Arithmetic mean) Median Mode Other measures of central tendency: Trimmed mean Harmonic mean Geometric mean Table 3.1: The Permissible Central of Tendency for Different Measurement Scale Scale type Permissible central of tendency Nominal Mode Ordinal Median Interval Mean, Mode*, Median* Ratio All statistics are permitted including geometric mean, harmonic mean, trimmed mean, and other robust means. Ungrouped Data Measurement Mean (Arithmetic Mean) The most frequently used measure of central tendency. The mean of a data set is the sum of the observation divided by the number of observation. Population Data Sample Data ̅ where is the sum of all values N is the population size n is the sample size is the population mean ̅ is the sample mean
SQQS1033 Data Exploratory and Generalisation lyf Sept’1 4 Page 3 Median The median is the value of the middle term in a data set that has been ranked in increasing order. Steps: 1) Rank the data in increasing order. 2) Determine the depth (position) of the median. 3) Determine the value of the median. Mode The mode of the data set is its most frequently occurring values. Not unique. 1) No mode a data set with each value occurring only once. 2) Unimodal a data set with only one value occurring with the highest frequency. 3) Bimodal a data set with two values that occur with same (highest) frequency. 4) Multimodal more than two values in a data set occur with the same (highest) frequency. depth of median 𝑛 + 1 2

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SQQS1033 Data Exploratory and Generalisation lyf Sept’1 4 Page 4 Table 3.2: Comparison among mean, median and mode Mean Median Mode Advantages Unique Consider all data set during the mean calculation Unique Resistant to outlier Can be used to calculate qualitative and quantitative data Disadvantages Sensitive to outlier It is difficulty to handle theoretically Not unique Some of the data set doesn’t have mode value Interpretation Center of gravity Divides the bottom 50% of the data from the top 50% Most frequent observation When to use When the data are quantitative and the frequency distribution is roughly symmetric When the frequency
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