Bsic Statistics Presentation

							INTRODUCTION TO
   STATISTICS

Md. Mortuza Ahmmed
Applications of Statistics

            Agriculture
       Business and economics
         Marketing Research
             Education
             Medicine
              Variable
              Qualitative
               Variable

Independe                    Dependent
nt variable                   variable



 Discrete                    Continuous
 variable                     variable

              Quantitative
               Variable
Scales of Measurement



    Nominal   Ordinal
     scale     Scale


     Ratio    Interval
     scale      scale
          FREQUENCY TABLE
Rating of                            Relative
            Tally marks Frequency
 Drink                              Frequency

   P            IIII        05      05 / 25 = 0.20


   G         IIII IIII II   12      12 / 25 = 0.48


   E           IIII III     08      08 / 25 = 0.32


  Total                     25               1.00
      SIMPLE BAR DIAGRAM
160
        150
140

120
               100
100

80

60                       56

40
                                     25
20

 0
      Muslim    Hindu   Christians   Others
      COMPONENT BAR DIAGRAM


300

250

200
                              Section D
                              Section C
150
                              Section B
100                           Section A


50

  0
      Male   Female
      MULTIPLE BAR DIAGRAM

100
90
80
70
60                       Section A
50                       Section B
40                       Section C
                         Section D
30
20
10
 0
      Male   Female
         PIE CHART

   Religion of students
Muslim    Hindu     Christians   Others


               8%

         15%
                        46%


         31%
                  LINE GRAPH

                 Share price of BEXIMCO
7000
                                  6400
6000

                      5600
5000
          5000                                          4500
4000

3000
                                           3000
2000

1000

   0
       July       August     September   October   November
     HISTOGRAM

20
18
16
14
12
10
8
6
4
2
0
  BAR DIAGRAM VS. HISTOGRAM

    Histogram            Bar diagram


Area gives frequency Height gives frequency

Bars are adjacent to Bars are not adjacent
    each others          to each others

  Constructed for       Constructed for
 quantitative data     qualitative data
STEM AND LEAF PLOT

   Stem    Leaf
     1    1479
     2    13479
     3    1379
     4    1347
     5    1349
     6    1347
                   SCATTER DIAGRAM

         300

         250

         200
Supply




         150

         100

          50

           0
               0    5   10    15     20   25   30
                             Price
  COMPARISON AMONG THE GRAPHS

  Graph            Advantages               Disadvantages
                 Shows percent of total     Use only discrete data
  Pie chart
                    for each category
                 Can compare to normal     Use only continuous data
 Histogram
                         curve
                Compare 2 or 3 data sets    Use only discrete data
Bar diagram
                         easily
                Compare 2 or 3 data sets Use only continuous data
 Line graph
                         easily
                Shows a trend in the data Use only continuous data
 Scatter plot
                      relationship

Stem and Leaf    Handle extremely large     Not visually appealing

    Plot                data sets
MEASURES OF CENTRAL TENDENCY

A measure of central tendency is a single
 value that attempts to describe a set of data
 by identifying the central position within
 that set of data.


          Arithmeticmean (AM)
          Geometric mean (GM)

          Harmonic mean (HM)

                Median

                 Mode
          ARITHMETIC MEAN

It is equal to the sum of all the values in the
  data set divided by the number of values in
  the data set.
                   PROBLEMS
   Find the average of the values 5, 9, 12, 4, 5, 14,
    19, 16, 3, 5, 7.

   The mean weight of three dogs is 38
    pounds.   One of the dogs weighs 46
    pounds.  The other two dogs, Eddie and
    Tommy, have the same weight. Find Tommy’s
    weight.

   On her first 5 math tests, Zany received
    scores 72, 86, 92, 63, and 77. What test score
    she must earn on her sixth test so that her
    average for all 6 tests will be 80?
  AFFECT OF EXTREME VALUES ON AM




Staff   1   2 3 4   5   6   7   8   9 10



Salary 15 18 16 14 15 15 12 17 90 95
CALCULATION OF AM FOR GROUPED DATA


    x              f       f.x
    0             05       00
    1             10       10
    2             05       10
    3             10       30
    4             05       20
   10             02       20
  Total        N = 37      90
 AM     =   90 / 37   =    2.43
        MEDIAN

1   3   2
                   MEDIAN = 2

1   2   3


1   4   3   2
                MEDIAN = (2 + 3) / 2
                              = 2.5
1   2   3   4
MODE
WHEN TO USE THE MEAN, MEDIAN
         AND MODE

                          Best measure of central
   Type of Variable
                                tendency
       Nominal                    Mode

       Ordinal                    Median

  Interval/Ratio (not
                                   Mean
       skewed)

Interval/Ratio (skewed)           Median
  WHEN WE ADD OR MULTIPLY EACH
           VALUE BY SAME AMOUNT


                   Data             Mean Mode Median
Original     6, 7, 8, 10, 12, 14,   12.2   14   13
data Set       14, 15, 16, 20

Add 3 to     9, 10, 11, 13, 15,     15.2   17   16
  each       17, 17, 18, 19, 23
  value
Multiply 2   12, 14, 16, 20, 24,    24.4   28   26
 to each     28, 28, 30, 32, 40
  value
MEAN, MEDIAN AND MODE FOR
       SERIES DATA


   For a series 1, 2, 3 ….n,
   mean = median = mode
        = (n + 1) / 2

  So, for a series 1, 2, 3 ….100,
     mean = median = mode
       = (100 + 1) / 2 = 50.5
GEOMETRIC MEAN
HARMONIC MEAN
          AM X HM = (GM) 2

For any 2 numbers              AM X HM
     a and b,
                           = (a + b) / 2 . 2ab /
AM = (a + b) / 2                        (a + b)

GM = (ab) ^ ½              = ab

                           = (GM) 2
HM = 2 / (1 / a + 1 / b)
     = 2ab / (a + b)
                   EXAMPLE
For any two numbers, AM = 10 and
  GM = 8. Find out the numbers.

(ab)^ ½ = 08               (a - b)2 = (a + b)2 – 4ab

ab = 64                            = (20)2 – 4 .64
                                    = 144
(a + b) / 2 = 10
a + b = 20 . . . . .(1)     => a - b = 12 . . . .(2)

      Solving (1) and (2) (a, b) = (16, 4)
                     EXAMPLE

 For any two numbers, GM = 4√3 and HM = 6.
       Find out AM and the numbers.
   AM           √ab = 4√3    (a - b)2
= (GM)2/   HM       =>ab = 48       = (a + b)2 – 4ab
= (4√3) 2 / 6                       = (16)2 – 4 . 48
=8              (a + b) / 2 = 8
                                    = 64

                => a + b = 16 …(1) a - b = 8 ...(2)

      Solving (1) & (2) (a, b) = (12, 4)
CRITERIA FOR GOOD MEASURES OF CENTRAL
              TENDENCY


              Clearly defined

         Readily comprehensible

        Based on all observations

            Easily calculated

       Less affected by extreme values

        Capable of further algebraic
                treatment
             AM ≥ GM ≥ HM
For any two numbers a & b (√a - √b) 2 ≥ 0

AM = (a + b) / 2          a + b – 2(ab)^1/2 ≥ 0

GM = (ab)^1/2             a + b    ≥ 2(ab)^1/2
HM = 2 / (1 / a + 1 / b) (a + b) / 2 ≥ (ab)^1/2
    = 2ab / (a + b)       => AM    ≥ GM

 Multiplying both sides by 2(ab)^1/2 / (a + b)
              (ab)^1/2 ≥ 2ab / (a + b)
                   GM ≥ HM

           So, AM ≥ GM ≥ HM