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# Descriptive Statistics

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# Descriptive Statistics

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Descriptive statistics

Descriptive statistics

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### Descriptive Statistics

1. 1. GROUP NO: 04 Descriptive Analysis
2. 2. • Descriptive statistics used in censuses taken by the Babylonians and Egyptians between 4500 and 3000 B.C. • In addition, the Roman Emperor Augustus (27 B.C.—A.D. 17) conducted surveys on births and deaths of the citizens of the empire, as well as the number of livestock each owned and the crops each citizen harvested yearly.
3. 3.  Data: the information that has been collected from an experiment, a survey, a historical record, etc.  A variable is a characteristic or attribute that can assume different values.  A statistic is a characteristic or measure obtained by using the data values from a sample.  A parameter is a characteristic or measure obtained by using all the data values from a  specific population
4. 4.  consists of the Collection Organization Summarization Presentation of data.
5. 5.  Summarize,describe and characterize the sample being studied  Determine if the sample is normally distributed (bell curve) most statistical tests require the sample to have normal distribution  Determine if the sample can be compared to the larger population  Are displayed as tables, charts, percentages, frequency, distributions and reported as measures of central tendency
6. 6.  Central tendancy- the sample mean, mode, median  Measures of Position  Measures of variability- range,varience and standard deviation  Exploratory Data Analysis
7. 7.  The Mean  The Mode  The Median  The Midrange
8. 8.  The mean is the sum of the values, divided by the total number of values.  Sample Mean The symbol represents the sample mean.
9. 9. =Sum of all data value = number of data in sample =number of data items in population The mean is sensitive to extreme scores (outliers) in the sample For a population, the Greek letter (mu) is used for the mean.  Population Mean
10. 10.  The median is the midpoint of the data array. The symbol for the median is MD  the middle value or 50th procentile (the value of the observation, that divides the sorted data in almost equal parts). • The median is not sensitive to extreme scores 2 1n Mode Median Mean
11. 11. • When n odd: median is the middle observation • When n even: median is the average of values of two middle observations
12. 12. The value that occurs most often in data set is called the mode. The mode=10
13. 13.  The midrange is defined as the sum of the lowest and highest values in the data set, divided by 2. The symbol MR is used for the midrange.
14. 14.  Min and max  Range  Standard deviation
15. 15.  The range is the highest value minus the lowest value. The symbol R is used for the range. 
16. 16. The variance is the average of the squares of the distance each value is from the mean. The symbol for the population variance is The standard deviation is the square root of the variance. The symbol for the
17. 17. The formula for the sample variance, denoted by , is The standard deviation of a sample (denoted by s) is
18. 18. Applications of the Variance and Standard Deviation 1. To determine the spread of the data 2. To determine the consistency of a variable ex: in the manufacture of fittings, such as nuts and bolts, the variation in the diameters must be small, or the parts will not fit together. 3. To determine the number of data values thatfall within a specified interval in a distribution
19. 19.  68% of the population in a normal distribution is within 1 standard deviation of the mean
20. 20.  The coefficient of variation, denoted by CVar, is the standard deviation divided by the mean. The result is expressed as a percentage.
21. 21.  A z score or standard score  Percentiles  Quartiles and Deciles  Outliers
22. 22.  A z score or standard score for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation. The symbol for a standard score is z. The formula is
23. 23.  The z score represents the number of standard deviations that a data value falls above or below the mean.
24. 24.  Percentiles divide the data set into 100 equal groups.
25. 25.  Quartiles divide the distribution into four groups, separated by Q1, Q2, Q3
26. 26.  An outlier is an extremely high or an extremely low data value when compared with the rest of the data values  An outlier can strongly affect the mean and standard deviation of a variable
27. 27.  M.M.B.S.SILVA UWU/EAG/13/0035

### Editor's Notes

• Descriptive statistics consists of the collection, organization, summarization, and
presentation of data.
• A data set that has only one value that occurs with the greatest frequency is said to
be unimodal.
If a data set has two values that occur with the same greatest frequency, both values
are considered to be the mode and the data set is said to be bimodal. If a data set has more
than two values that occur with the same greatest frequency, each value is used as the
mode, and the data set is said to be multimodal. When no data value occurs more than
once, the data set is said to have no mode. A data set can have more than one mode or no
mode at all. These situations will be shown in some of the examples that follow.