# Chap3.ppt - Chapter III Descriptive Statistics Hayet Ben...

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1 Chapter III: Descriptive Statistics Hayet Ben Hamida

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Objectives of this course 2 Apply various measures of central tendency Apply various measures of variability Describe a data distribution statistically and graphically Use computer packages to compute various measures on a set of data
3 If a business analyst is using data gathered on a group (sample) to describe or reach conclusions about that same group, the statistics are called descriptive statistics

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Outline 3-1 MEASURES OF LOCATION: 3-2 MEASURES OF VARIABILITY 4 3-3 MEASURES OF SHAPE 3-4 DESCRIPTIVE STATISTICS ON THE COMPUTER
3.1 MEASURES OF LOCATION 5

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6 Measures of central tendency: Mean; Median; Mode Measures of non central tendency - Quantiles (Quartiles; Quintiles; Deciles Percentiles) Measures of location indicate where on the number line the data are to be found.
Measures of Central Tendency (Location) Measures of central tendency yield information about the center, or middle part of a group of numbers. Common measures of central tendency are: the Arithmetic Mean , the Median, and the Mode 7

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8 Mode (grouped & ungrouped) The mode is the value of the data that occurs with the greatest frequency. (an ordering of the numbers from smallest to largest helps to locate the mode) Example . 1, 1, 1, 2, 3, 4, 5 Answer . The mode is 1 since it occurs three times. The other values each appear only once in the data set. Example . 5, 5, 5, 6, 8, 10, 10, 10. Answer . The mode is: 5, 10. There are two modes. This is a bi-modal dataset.
The mode may not exist. Data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 Here you have 10 observations and they are all different. The mode may not be unique. Data: 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7 Mode = 1, 2, 3, 4, 5, and 6. There are six modes. bimodal, multimodal 9

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10 The mode for grouped data is the class midpoint of the modal class. The modal class is the class interval with the greatest frequency Example : the 7–under 9 class interval contains the greatest frequency, 19. Thus, the modal class is 7– under 9. The class midpoint of this modal class is 8. Therefore, the mode for the frequency distribution is 8. The modal unemployment rate is 8%. Grouped data
The median is the middle value of the ordered data: 50% of the observations are smaller than the Median and 50% of the observations are larger. To get the median: 11 o we must first rearrange the data into an ordered array (in ascending or descending order). o If n is odd, the median is the middle observation of the ordered array. o If n is even, it is midway between the two central observations. Median (grouped & ungrouped)

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Example : Note: Data has been ordered from lowest to highest. Since n is odd (n=7), the median is the (n+1)/2 ordered observation, or the 4 th observation.
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