MSC III_Research Methodology and Statistics_Descriptive statistics.pdf
- 1. Research Methodology and Statistics Dr. Suchita Rawat MPhil, NET, PhD
- 2. This Photo by Unknown Author is licensed under CC BY-SA-NC Statistics deals with the collection, presentation, analysis and interpretation of quantitative/qualitative information.
- 4. This Photo by Unknown Author is licensed under CC BY
- 5. The facts, observations and all the relevant information that have been collected from research and investigations is known as data This Photo by Unknown Author is licensed under CC BY-SA
- 7. Graphs They are the visual representation of a data for easy understanding and to save time. They present frequency distributions to see the shape of the distribution easily.
- 8. Bar Graphs are a graphical representation of data based on statistics and numerical figures. A bar graph uses the two axes – x-axis and y-axis to plot rectangular bars. Types of Bar Graph •Horizontal bar graph •Vertical bar graph •Double bar graph (Grouped bar graph) •Multiple bar graph (Grouped bar graph) •Stacked bar graph •Bar line graph
- 9. Horizontal bar graph When the Y-axis represents the observation to be compared, and the x-axis represents the magnitude of the observations, then the bars run horizontally along the x-axis up to the point of value proportional to the observation.
- 10. Vertical Bar Graph Vertical bar graphs are just the opposite of horizontal bar graphs. Vertical bar graphs are preferred more than horizontal bar graphs. When the X-axis represents the observation to be compared, and the y-axis represents the magnitude of the observations
- 11. Grouped Bar Graph Double Bar Graph make a comparison among various observations or categories using two parameters. However, those two parameters should be measured in similar quantities, which means that they should be of the same unit.
- 12. Multiple Bar Graph make a comparison among various observations on the basis of multiple parameters. You can include as many parameters as you wish, however, each parameter should have the same unit of measurement.
- 13. Stacked Bar Graph A stacked bar graph also represents various parameters in a single graph. The difference is that in a stacked bar graph all the parameters are represented in a single bar. So you can say that there are segments of a total in a single bar.
- 14. Pie chart type of graph that uses a circular graph to view data. The graph's pieces are equal to the percentage of the total in each group. In other words, the size of each slice of the pie is proportional to the size of the group as a whole. The entire "pie" represents 100% of a total, while the "slices" represent parts of the whole.
- 15. Histogram X axis represents variables and frequencies depending on it are represented on Y axis which constitutes the height of its rectangle
- 16. Boxplot It is a graphical representation of dispersions and extreme scores. This graph represents minimum, maximum and quartile scores in the form of a box with whiskers. The box includes the range of scores falling into the middle 50% of the distribution (Inter Quartile Range = 75th percentile - 25th percentile) and the whiskers are lines extended to the minimum and maximum scores in the distribution.
- 17. Scatterplot Scatterplots are also known as scattergrams and scatter charts. •X-axis representing values of a continuous variable. By custom, this is the independent/ Exposure variable •Y-axis representing values of a continuous variable. Traditionally, this is the dependent/ Outcome variable •Symbols plotted at the (X, Y) coordinates of your data.
- 18. Arithmetic Mean The arithmetic mean or average as referred in common Arithmetic Mean of Grouped Data: Suppose we have data in form of X1, X2…….…….Xn observations with corresponding frequencies f1, f2…………………fn. The arithmetic mean will be Example 3:- Calculate the average number of children per family from the following data.
- 19. Median The median is that value of the variable which divides the group into two parts, one part comprising all the values greater and the other, all the values less than the median. In case of ungrouped data, when the number of observations is odd/even, the median is the middle value after the observations have been arranged
- 20. Determine the median for the following data sets 1) 132, 139, 131, 138, 132, 139, 133, 137, 139 2) 25, 10, 16, 25, 12, 22, 20, 23, 13, 10 3) 56, 23, 48, 78, 94, 35, 88, 69, 44, 53, 27
- 21. Mode Mode is the value the occurrence of which is most frequent. It is the value around which the observations are clustered in a given distribution. Determine the mode for the following data sets 1) 132, 139, 131, 138, 132, 139, 133, 137, 139 2) 3, 3, 3, 5, 5, 5, 3, 6, 4, 8, 5, 4, 2, 4, 3, 5 3) 56, 23, 48, 78, 94, 35, 88, 69, 44, 53, 27
- 22. Mode In case of frequency distribution, it is the value of the variable that has the highest frequency. In case of continuous frequency distribution, the value of the mode is computed using interpolation formula: Where, l=lower limit of the modal class, f1=frequency of the modal class, f0=frequency of the class preceding the modal class, f2=frequency of the class succeeding the modal class, h=width of the modal class.
- 23. The modal class is the class corresponding to the maximum frequency.
- 26. When to use Mean, Median & Mode?
- 27. Dispersion in Statistics Dispersion in statistics is a way of describing how to spread out a set of data is. Measures of Dispersion •Absolute Measures of Dispersion (one data set) •Relative Measures of Dispersion (two or more datasets) The measures of dispersion contain almost the same unit as the quantity being measured. There are many Measures of Dispersion : 1.Range 2.Variance 3.Standard Deviation 4.IQR
- 28. Range: Range is the measure of the difference between the largest and smallest value of the data variability. The range is the simplest form of Measures of Dispersion. Example: 1,2,3,4,5,6,7 Range = Highest value – Lowest value
- 29. Variance (σ2) simple terms, the variance can be calculated by obtaining the sum of the squared distance of each term in the distribution from the Mean, and then dividing this by the total number of the terms in the distribution. (σ2) = ∑ ( X − μ)2 / N X=observation x, x=1….n N=No. Of observation μ= Mean
- 30. Standard Deviation Standard Deviation can be represented as the square root of Variance. To find the standard deviation of any data, you need to find the variance first. Standard Deviation is considered the best measure of dispersion. Formula: Standard Deviation = √σ
- 31. Quartile Deviation Quartile Deviation is the measure of the difference between the upper and lower quartile. This measure of deviation is also known as the interquartile range. Formula: Interquartile Range: Q3 – Q1.
- 32. Relative Measures of Dispersion Relative Measure of Dispersion in Statistics are the values without units. A relative measure of dispersion is used to compare the distribution of two or more datasets.
- 33. Co-efficient of Range: it is calculated as the ratio of the difference between the largest and smallest terms of the distribution, to the sum of the largest and smallest terms of the distribution. Formula: L – S / L + S where L = largest value S= smallest value
- 34. Co-efficient of Variation: The coefficient of variation is used to compare the 2 data with respect to homogeneity or consistency. Formula: C.V = (σ / X) 100 X = standard deviation σ = mean
- 35. Co-efficient of Standard Deviation: The co-efficient of Standard Deviation is the ratio of standard deviation with the mean of the distribution of terms. Formula: σ = ( √( X – X1)) / (N - 1) Deviation = ( X – X1) σ = standard deviation N= total number
- 36. Co-efficient of Quartile Deviation: The co-efficient of Quartile Deviation is the ratio of the difference between the upper quartile and the lower quartile to the sum of the upper quartile and lower quartile. Formula: ( Q3 – Q1) / ( Q3 + Q1) Q3 = Upper Quartile Q1 = Lower Quartile
- 37. Measuring Asymmetry with Skewness
- 38. Skewness is a measure of asymmetry or distortion of symmetric distribution. It measures the deviation of the given distribution of a random variable from a symmetric distribution, such as normal distribution. Types of Skewness 1. Positive Skewness (right skewed) 2. Negative Skewness (left skewed)
- 39. Skewness can be measured using several methods; however, Pearson mode skewness and Pearson median skewness are the two frequently used methods. The formula for Pearson mode skewness: The formula for Person median skewness: Where: X = Mean value Mo = Mode value Md = Median value s = Standard deviation of the sample data