The More We Get Together         The more we get together,            Together, together,         The more we get together...
GraphicalRepresentation          &                Shapes of              Distribution
A graph adds life and beauty toone’s work, but more than this, it helps facilitate comparison and   interpretation without...
Kinds of Graphs     Bar Chart     Histogram     Frequency Polygon     Pie Chart     Ogive
Bar Chart of the Grouped Frequency Distribution                    for the Entrance Examination Scores of 60            18...
The Histogram of the Grouped Frequency                 Distribution for the Entrance Examination Scores            18     ...
The Frequency Polygon of the Grouped Frequency                 Distribution for the Entrance Examination Scores of 60     ...
The Pie Chart of the Grouped FrequencyDistribution for the Entrance Examination          Scores of 60 Students            ...
A pie chart is drawn by dividing the circle according tothe number of classes. The size of each piece dependson the relati...
The relative frequency of each class is obtained bydividing the class frequency by the total frequency.Relative Frequency ...
The Less than and Greater than Ogives for the                     Entrance Examination Scores of 60 Students        70C   ...
Shapes ofDistribution            Symmetrical           Asymmetrical
SYMMETRICAL      DISTRIBUTIONNormal Distribution   Each half or side of the   distribution is a mirror   image of the oth...
ASYMMETRICAL       DISTRIBUTIONNegatively Skewed/Skewedto the Left    In a negative skew the    tail extends far into the...
ASYMMETRICAL        DISTRIBUTIONPositively Skewed/Skewed tothe Right    In a positive skew the tail    on the right side ...
Skewness refers to the degree of symmetry or asymmetry of a distribution. The extent of skewness can be obtained bygetting...
Let us summarize the measurements from the 3 types ofdistribution:                  Normal     Skewed to    Skewed to     ...
Using the formula to find the coefficient of skewness, we have:For normal                           For skewed to the left...
Exercise       Find the coefficient of skewness and indicate if thedistribution is normal, skewed to the left or skewed to...
FIN      Reporters:      Ando, Lilian      Dillo, Charlyn      Lapos, Emilia
The more we get together
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The more we get together

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The more we get together

  1. 1. The More We Get Together The more we get together, Together, together, The more we get together, The happier well be. For your friends are my friends, And my friends are your friends. The more we get together, The happier well be!
  2. 2. GraphicalRepresentation & Shapes of Distribution
  3. 3. A graph adds life and beauty toone’s work, but more than this, it helps facilitate comparison and interpretation without going through the numerical data.
  4. 4. Kinds of Graphs Bar Chart Histogram Frequency Polygon Pie Chart Ogive
  5. 5. Bar Chart of the Grouped Frequency Distribution for the Entrance Examination Scores of 60 18 17Students 16 14 14 12 11frequency 10 8 8 6 6 4 3 2 1 0 0 18-23 24-29 30-35 36-41 42-47 48-53 54-59 60- 65 class interval A bar chart is a graph represented by either vertical or horizontal rectangles whose bases represent the class intervals and whose heights represent the frequencies.
  6. 6. The Histogram of the Grouped Frequency Distribution for the Entrance Examination Scores 18 of 60 Students 16 14Frequency 12 10 8 6 4 2 0 20.5 26.5 32.5 38.5 44.5 50.5 56.5 class mark A histogram is a graph represented by vertical or horizontal rectangles whose bases are the class marks and whose heights are the frequencies.
  7. 7. The Frequency Polygon of the Grouped Frequency Distribution for the Entrance Examination Scores of 60 Students 18 16 14Frequency 12 10 8 6 4 2 0 14.5 20.5 26.5 32.5 38.5 44.5 50.5 56.5 62.5 class mark A frequency polygon is a line graph whose bases are the class marks and whose heights are the frequencies.
  8. 8. The Pie Chart of the Grouped FrequencyDistribution for the Entrance Examination Scores of 60 Students 5.00% 1.67% 10.00% 13.33% 18.33% 23.33% 28.33% A pie chart is a circle graph showing the proportion of each class through either the relative or percentage frequency.
  9. 9. A pie chart is drawn by dividing the circle according tothe number of classes. The size of each piece dependson the relative or percentage frequency distribution. How to compute for the Relative Frequency?
  10. 10. The relative frequency of each class is obtained bydividing the class frequency by the total frequency.Relative Frequency Distribution for the Entrance Examination Scores of 60 Students Class Midpoint Frequency Relative Interval (X) (f) Frequency (ci) (rf) 18 - 23 20.5 6 0.1000 24 - 29 26.5 11 0.1833 30 - 35 32.5 17 0.2833 36 - 41 38.5 14 0.2333 42 - 47 44.5 8 0.1333 48 - 53 50.5 3 0.0500 54 - 59 56.5 1 0.0167 N = 60
  11. 11. The Less than and Greater than Ogives for the Entrance Examination Scores of 60 Students 70C F 60u r 50 Less than ogivem eu q 40l u 30 Greater than ogivea e 20t ni c 10v y 0e 17.5 23.5 29.5 35.5 41.5 47.5 53.5 59.5 Class Boundaries An ogive is a line graph where the bases are the class boundaries and the heights are the <cf for the less than ogive and >cf for the greater than ogive.
  12. 12. Shapes ofDistribution  Symmetrical Asymmetrical
  13. 13. SYMMETRICAL DISTRIBUTIONNormal Distribution Each half or side of the distribution is a mirror image of the other side (bell-shaped appearance) Mean ,median ,and mode coincides (mean = median = mode) Skewness is equal to zero
  14. 14. ASYMMETRICAL DISTRIBUTIONNegatively Skewed/Skewedto the Left In a negative skew the tail extends far into the negative side of the Cartesian graphmean < medianSkewness is less than 0.the mass of the distributionis concentrated on the right ofthe figure
  15. 15. ASYMMETRICAL DISTRIBUTIONPositively Skewed/Skewed tothe Right In a positive skew the tail on the right side of the distribution exdends far into the positive side of the Cartesian graph.mean > medianSkewness is greater than 0.the mass of the distribution isconcentrated on the left of thefigure
  16. 16. Skewness refers to the degree of symmetry or asymmetry of a distribution. The extent of skewness can be obtained bygetting the coefficient of skewness using the formula: SK = 3(Mean – Median) Standard deviation
  17. 17. Let us summarize the measurements from the 3 types ofdistribution: Normal Skewed to Skewed to the left/ the right/ Negatively Positively skewed skewed Mean 4.00 5.58 2.40 Median 4.00 6.00 2.00 Mode 4.00 6.00 2.00 Standard 1.53 1.07 1.07 deviation
  18. 18. Using the formula to find the coefficient of skewness, we have:For normal For skewed to the leftdistribution: distribution: For skewed to the right distribution:SK= 3(Mean – Median) SK= 3(Mean – Median) Standard deviation Standard deviation SK= 3(Mean – Median) = 3(5.6 – 6.0) Standard deviation = 3(4.0 – 4.0) 1.07 = 3(2.4 – 2.0) = - 1.12 1.07 1.53 = 1.12 =0 Notice that if •SK = 0, distribution is normal •SK < 0, distribution is skewed to the left •SK > 0, distribution is skewed to the right
  19. 19. Exercise Find the coefficient of skewness and indicate if thedistribution is normal, skewed to the left or skewed to theright.72, 81, 67, 83, 61, 75, 78, 82, 71, 67 Solution: Find the mean : Mean = 73.7 Find the median: Median = 73.5 Find the SD: SD = 7.38 Find the SK: SK = 3(Mean – Median)/Standard deviation = 3(73.7 – 73.5)/ 7.38 = 0.08 Interpretation: Since SK is positive, then it is skewed to the right. But the value is too small, so we can say that the distribution is almost normal.
  20. 20. FIN Reporters: Ando, Lilian Dillo, Charlyn Lapos, Emilia

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