Descriptive Statistics: Measures of Central Tendency - Measures of Dispersion - DAY 3 - B-Ed - 8614 - AIOU
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Descriptive Statistics - Measures of Central Tendency (Mean - Median - Mode) - Measures of Dispersion ( Normal Curve - Co-efficient of Variation )
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Descriptive Statistics: Measures of Central Tendency - Measures of Dispersion - DAY 3 - B-Ed - 8614 - AIOU
- 1. Unit–5: Descriptive Statistics: Measures of Central Tendency & Unit–4: Descriptive Statistics: Measures of Dispersion Course code 8614
- 2. An average is a single value, which represents the set of data as whole. Since the average tends to lie in the center of distribution they are also called measure of central tendency. There are three methods of measuring the center of any data. Arithmetic mean The Median The Mode
- 3. It is defined as the sum of all the observations divided by the number of observations. It is denoted by X. When to use Arithmetic Mean: We use arithmetic mean, when we are required to study social, economic and commercial problems like production, price, export and import. It helps in getting average income, average price, average production etc.
- 4. 5, 10, 12, 16, 8, 42, 25, 15, 10, 7 Solution: 5+10+12+16+8+42+25+15+10+7=150/10 Mean = 15
- 5. Median is the middle most value of a set of data when the data is arranged in order of magnitude. If the number of observations is in odd form, then median is the mid value and if the number of observations is even form, then median is the average of two middle values. When we Apply Median: We apply median to the situations, when the direct measurements of variables are not possible like poverty, beauty and intelligence etc.
- 6. Example: 12,15, 10, 20, 18, 25, 45, 30, 26 We need to make order of the data 10, 12, 15, 18, 20, 25, 26, 30, 45 So Mean = 20
- 7. The most frequent value that occurs in the set of data is called mode. A set of data may have more than one mode or no mode. When it has one mode it is called uni-modal. When it has two or three modes it is called bi-modal or tri- modal respectively. Example: 12, 24, 15, 18, 30, 48, 20, 24 So Mode = 24
- 8. Measures of central tendency estimate normal or central value of a data set, while measures of dispersion are important for describing the spread of the data, or its variation around a central value.
- 9. A measure of dispersion indicates the scattering of data. In other words, dispersion is the extent to which values in a distribution differ from the average of the distribution. It gives us an idea about the extent to which individual items vary from one another, and from the central value.
- 10. Measure # 1. Range: Measure # 2. Quartile Deviation: Measure # 3. Average Deviation (A.D.) or Mean Deviation (M.D.): Measure # 4. Standard Deviation or S.D. and Variance:
- 11. The range is the simplest measure of spread and is the difference between the highest and lowest scores in a data set. In other words we can say that range is the distance between largest score and the smallest score in the distribution.
- 12. The values that divide the given set of data into four equal parts is called quartiles, and is denoted by Q1, Q2, and Q3.
- 13. MAD= mean average deviation
- 14. Standard deviation is the most commonly used and the most important measure of variation. It determines whether the scores are generally near or far from the mean.
- 23. It cannot be negative. It is only used to measure spread or dispersion around the mean of a data set. For data with almost the same mean, the greater the spread, the greater the standard deviation.
- 24. Variance describes how much a random variable differs from its expected value.
- 28. Mp = middle point
- 29. One way of presenting out how data are distributed is to plot them in a graph. If the data is evenly distributed, our graph will come across a curve. In statistics this curve is called a normal curve.
- 31. Skewness tells us about the amount and direction of the variation of the data set. It is a measure of symmetry (evenness). A distribution or data set is symmetric if it looks the same to the left and right of the central point.
- 32. Kurtosis is a parameter that describes the shape of variation. It is a measurement that tells us how the graph of the set of data is peaked and how high the graph is around the mean. In other words we can say that kurtosis measures the shape of the distribution. The concept of kurtosis is very useful in decision- making.
- 33. Kurtosis has three types, mesokurtic, platykurtic, and leptokurtic. If the distribution has kurtosis of zero, then the graph is nearly normal. This nearly normal distribution is called mesokurtic. If the distribution has negative kurtosis, it is called platykurtic. If the distribution has positive kurtosis, it is called leptokurtic.
- 35. The coefficient of variation is another useful statistics for measuring dispersion of a data set.