1 / 23

Descriptive Statistics

Descriptive Statistics. Descriptive Statistics. Measures of Central Tendency Measures of Location Measures of Dispersion Measures of Symmetry Measures of Peakdness. JOIN KHALID AZIZ. ICMAP STAGE 1 FUNDAMENTALS OF FINANCIAL ACCOUNTING & ECONOMICS. STAGE 2 FUNDAMENTALS OF COST ACCOUNTING

ide
Download Presentation

Descriptive Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Descriptive Statistics

  2. Descriptive Statistics Measures of Central Tendency Measures of Location Measures of Dispersion Measures of Symmetry Measures of Peakdness

  3. JOIN KHALID AZIZ ICMAP STAGE 1 FUNDAMENTALS OF FINANCIAL ACCOUNTING & ECONOMICS. STAGE 2 FUNDAMENTALS OF COST ACCOUNTING STAGE 3 FINANCIAL ACCOUNTING & COST ACCOUNTING APPRAISAL 0322-3385752 R-1173, ALNOOR SOCIETY, BLOCK 19, F.B.AREA, KARACHI.

  4. Measures of Central Tendency • The central tendency is measured by averages. These describe the point about which the various observed values cluster. • In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set.

  5. Measures of Central Tendency • Arithmetic Mean • Geometric Mean • Weighted Mean • Harmonic Mean • Median • Mode

  6. Arithmetic Mean • The arithmetic mean is the sum of a set of observations, positive, negative or zero, divided by the number of observations. If we have “n” real numbers their arithmetic mean, denoted by , can be expressed as:

  7. Arithmetic Mean of Group Data • if are the mid-values and are the corresponding frequencies, where the subscript ‘k’ stands for the number of classes, then the mean is

  8. Geometric Mean • Geometric mean is defined as the positive root of the product of observations. Symbolically, • It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment. • Find geometric mean of rate of growth: 34, 27, 45, 55, 22, 34

  9. Geometric mean of Group data • If the “n” non-zero and positive variate-values occur times, respectively, then the geometric mean of the set of observations is defined by: Where

  10. Geometric Mean (Revised Eqn.) Ungroup Data Group Data

  11. Harmonic Mean • Harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. • Typically, it is appropriate for situations when the average of rates is desired. The harmonic mean is the number of variables divided by the sum of the reciprocals of the variables. Useful for ratios such as speed (=distance/time) etc.

  12. Harmonic Mean Group Data • The harmonic mean H of the positive real numbers x1,x2, ..., xn is defined to be Ungroup Data Group Data

  13. Exercise-1: Find the Arithmetic , Geometric and Harmonic Mean

  14. Weighted Mean • The Weighted mean of the positive real numbers x1,x2, ..., xn with their weight w1,w2, ..., wn is defined to be

  15. Median • The implication of this definition is that a median is the middle value of the observations such that the number of observations above it is equal to the number of observations below it. If “n” is Even If “n” is odd

  16. Median of Group Data • L0 = Lower class boundary of the median class • h = Width of the median class • f0 = Frequency of the median class • F = Cumulative frequency of the pre- median class

  17. Steps to find Median of group data • Compute the less than type cumulative frequencies. • Determine N/2 , one-half of the total number of cases. • Locate the median class for which the cumulative frequency is more than N/2 . • Determine the lower limit of the median class. This is L0. • Sum the frequencies of all classes prior to the median class. This is F. • Determine the frequency of the median class. This is f0. • Determine the class width of the median class. This is h.

  18. Example-3:Find Median

  19. Mode • Mode is the value of a distribution for which the frequency is maximum. In other words, mode is the value of a variable, which occurs with the highest frequency. • So the mode of the list (1, 2, 2, 3, 3, 3, 4) is 3. The mode is not necessarily well defined. The list (1, 2, 2, 3, 3, 5) has the two modes 2 and 3.

  20. Example-2: Find Mean, Median and Mode of Ungroup Data The weekly pocket money for 9 first year pupils was found to be: 3 , 12 , 4 , 6 , 1 , 4 , 2 , 5 , 8 Mean 5 Median 4 Mode 4

  21. Mode of Group Data • L1 = Lower boundary of modal class • Δ1 = difference of frequency between modal class and class before it • Δ2 = difference of frequency between modal class and class after • H = class interval

  22. Steps of Finding Mode • Find the modal class which has highest frequency • L0 = Lower class boundary of modal class • h = Interval of modal class • Δ1 = difference of frequency of modal class and class before modal class • Δ2 = difference of frequency of modal class and class after modal class

  23. Example -4: Find Mode

More Related