3-statistical-description-of-data.ppt - 3 STATISTICAL DESCRIPTION OF DATA Frequency Distributions Grouped Data Percentiles Deciles Quartiles Graphical

3-statistical-description-of-data.ppt - 3 STATISTICAL...

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3 . Frequency Distributions Grouped Data Percentiles, Deciles & Quartiles Graphical Representations Symmetry and Skewness STATISTICAL DESCRIPTION OF DATA
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Statistical data collected should be arranged in such a manner that will allow a reader to distinguish their essential features. Depending on the type and the objectives of the person presenting the information, data may be presented using one or a combination of three forms.
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Three Forms of Presenting Data Textual Form – data is presented in paragraph form especially when they are purely qualitative or when very few numbers are involved.
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Tabular Form - data is presented in rows and columns Graphical Form - data is presented in visual form 0 500 1000 1500 2000 2500 3000 3500 4000 1991 1992 1993 1994 1995
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When that data include a large number of observations, it is convenient to group the values into mutually exclusive classes and show the number of observations occurring in each class in a tabular form.
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Frequency Distribution A frequency distribution is the arrangement of data that shows the frequency of occurrence of values falling within arbitrarily defined ranges of the variable known as class intervals . The smallest and largest values that fall in a given interval are called class limits .
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Class Frequency and Class Mark Class frequency refers to the number of observations falling in a particular class while the midpoint between the upper and lower class limits is called class mark/midpoint .
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Steps in Making a Frequency Distribution Find the range. Determine the interval size by dividing the range by the desired number of classes which is normally not less than 10 and not more than 20. Determine the class limits of the class intervals. Tabulation is facilitated if the lower class limits of the class intervals are multiples of the class size. The bottom interval must include the lowest score.
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List the intervals, beginning at the bottom. Tally the frequencies. Summarize these under a column labeled f. Total this column and record the number at the bottom.
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Proble m: Construct a frequency distribution of the given scores on a test. 56 28 42 56 47 39 62 60 54 47 78 82 55 56 41 44 54 42 62 48 79 38 57 55 50 47 42 56 68 53 37 72 65 66 52 52 48 48 42 68
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Solutio n: Computing for the range: R = 82 – 28 = 54 Computing for the class interval: Therefore, class interval may be 5 or 6. 4 . 5 10 54 i
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We choose 5 because it is the odd number. If i = 5 , lowest limit should be We choose 25 because it is the smallest multiple of the chosen interval which is smaller than the smallest value in the set. If lowest limit is 25 , the bottom interval should be 25. 29 – 25. The interval 29 - 25 contains the lowest score ( 28 ).
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Classes 29 - 25 34 - 30 39 - 35 44 - 40 49 - 45 54 - 50 59 - 55 64 - 60 69 - 65 74 - 70 79 - 75 84 - 80 Tally f 40 f N 1 1 1 4 4 7 6 6 6 3 0 1 / / / //// //// /////// ////// ////// ////// /// /
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For Grouped Data ( > 30 values) Methods : 1. Midpoint Method 2. Short Method MEASURES OF CENTRAL TENDENCY MEA N
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Midpoint Method After the f column, make another column and enter the midpoint ( X m ) of each class.
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  • Fall '17
  • Antonino Magallen

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