Basic Statistics Presentation

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Introduction to Statistics

• Md. Mortuza Ahmmed

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Frequency table
Rating of Drink Tally marks Frequency Relative 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
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simple bar diagram
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Component bar Diagram
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Multiple bar Diagram
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Pie Chart
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Line graph
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Histogram
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Bar diagram vs. histogram
Histogram Bar diagram
Area gives frequency Height gives frequency
Bars are adjacent to each others Bars are not adjacent to each others
Constructed for quantitative data Constructed for qualitative data
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Stem and leaf plot
Stem Leaf
1 1 4 7 9
2 1 3 4 7 9
3 1 3 7 9
4 1 3 4 7
5 1 3 4 9
6 1 3 4 7
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Scatter diagram
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Comparison among the graphs
Graph Advantages Disadvantages
Pie chart Shows percent of total for each category Use only discrete data
Histogram Can compare to normal curve Use only continuous data
Bar diagram Compare 2 or 3 data sets easily Use only discrete data
Line graph Compare 2 or 3 data sets easily Use only continuous data
Scatter plot Shows a trend in the data relationship Use only continuous data
Stem and Leaf Plot  Handle extremely large data sets Not visually appealing
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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.
• Arithmetic mean (AM)
• Geometric mean (GM)
• Harmonic mean (HM)
• Median
• Mode

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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.

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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 Tommys 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? 

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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
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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
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Median
1 3 2
MEDIAN 2 MEDIAN 2 MEDIAN 2 MEDIAN 2 MEDIAN 2
1 2 3

1 4 3 2
MEDIAN (2 3) / 2 2.5 MEDIAN (2 3) / 2 2.5 MEDIAN (2 3) / 2 2.5 MEDIAN (2 3) / 2 2.5 MEDIAN (2 3) / 2 2.5
1 2 3 4
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Mode
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when to use the mean, median and mode
Type of Variable Best measure of central tendency
Nominal Mode
Ordinal Median
Interval/Ratio (not skewed) Mean
Interval/Ratio (skewed) Median
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when we add or multiply each value by same amount
Data Mean Mode Median
Original data Set 6, 7, 8, 10, 12, 14, 14, 15, 16, 20 12.2 14 13
Add 3 to each value 9, 10, 11, 13, 15, 17, 17, 18, 19, 23 15.2 17 16
Multiply 2 to each value 12, 14, 16, 20, 24, 28, 28, 30, 32, 40 24.4 28 26
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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

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Geometric mean
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Harmonic mean
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AM X HM (GM) 2
For any 2 numbers a and b, AM (a b) / 2 GM (ab) ½ HM 2 / (1 / a 1 / b) 2ab / (a b) AM X HM (a b) / 2 . 2ab / (a b) ab (GM) 2
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Example
For any two numbers, AM 10 and GM 8. Find out the numbers. For any two numbers, AM 10 and GM 8. Find out the numbers.
(ab) ½ 08 ab 64 (a b) / 2 10 a b 20 . . . . .(1) (a - b)2 (a b)2 4ab (20)2 4 .64 144 gt a - b 12 . . . .(2)
Solving (1) and (2) (a, b) (16, 4) Solving (1) and (2) (a, b) (16, 4)
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Example
For any two numbers, GM 4v3 and HM 6. Find out AM and the numbers. For any two numbers, GM 4v3 and HM 6. Find out AM and the numbers. For any two numbers, GM 4v3 and HM 6. Find out AM and the numbers.
AM (GM)2/ HM (4v3) 2 / 6 8 vab 4v3 gtab 48 (a b) / 2 8 gt a b 16 (1) (a - b)2 (a b)2 4ab (16)2 4 . 48 64 a - b 8 ...(2)
Solving (1) (2) (a, b) (12, 4) Solving (1) (2) (a, b) (12, 4) Solving (1) (2) (a, b) (12, 4)
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Criteria for good measures of central tendency
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AM GM HM
For any two numbers a b AM (a b) / 2 GM (ab)1/2 HM 2 / (1 / a 1 / b) 2ab / (a b) (va - vb) 2 0 a b 2(ab)1/2 0 a b 2(ab)1/2 (a b) / 2 (ab)1/2 gt AM GM
Multiplying both sides by 2(ab)1/2 / (a b) (ab)1/2 2ab / (a b) GM HM Multiplying both sides by 2(ab)1/2 / (a b) (ab)1/2 2ab / (a b) GM HM
So, AM GM HM So, AM GM HM