Statistics I: Collection, Organization & Presentation of Data

Abdullah Al Mahmud

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Data Collection

Types of Data

  • Qualitative
  • Quantitative

Sources of Data

  • Primary: Obtained directly (not collected from someone else)

  • Secondary: Using pre-collected data from someone else/some organization

  • Example

  • A researcher buys data from BMD to build a model of rainfall behavior

  • A researcher runs an experiment to measure speed of light using a novel technique.

  • A researcher makes use of the data generated by the one in example 2

Method of Data Collection

  • Direct personal Inquiry

  • Indirect oral inquiry

  • Mail

  • Telephone etc.

  • Each method has its own advantages and disadvantages;

Sources of Secondary Data

  • Published: Journal, Newspaper etc.
  • Unpublished: BBS, WHO, IMF, FAO, ICDDR,B

DIsadvantages of Secondary Data

  • Purpose might be different
  • Suitability
  • Reliability
  • Unit

Organizing Data

Tabluation

table

Data Classification

  • Geographical
  • Chronological
  • Quantitative
  • Qualitative

Example

Geographical

Country Bangladesh USA
GDP(m) 120 500

Chronological (Time series data)

Year 2015 2016
GDP(m) 120 500

Quantitative Classification

Income level 40,000-50,000 50,000-1,00,000
Frequency 120 34

Frequency Distribution

Three things required

  • Range
  • No. of classes (k) &
  • Class Interval (CI)

Let k or CI & find the other

  • \(CI = \frac{Range}{\text{Number of classes (k)}}\)
  • \(\text{Number of classes, k}= \frac{Range}{\text{CI}}\)
  • Sturges Method: \(k = 1 + 3.322 \space logN\); where N = no. of observations

Frequency Distribution Example

No. of Surviving Plants Frequency Cumulative Frequency Percentage Cumulative Percentage
20–29 3 3 3% 3%
30–39 14 17 14% 17%
40–49 12 29 12% 29%
50–59 8 37 8% 37%
60–69 18 55 18% 55%
70–79 10 65 10% 65%
80–89 23 88 23% 88%
90–99 12 100 12% 100%
Total 100 100%

Insights on the next page

Key Insights

  • In most schools (23), the number of surviving plants is between 80 to 89.
  • Very few schools (3) have surviving plants in the 20–29 range.
  • More than half of the schools (55%) have up to 69 surviving plants.
  • A significant portion of schools (35%) report 70 or more surviving plants, with the 80–89 range alone accounting for 23%.
  • The 50–59 range has relatively few schools (8%), creating a noticeable dip between the lower and higher survival groups.

Weight Distribution

Weight (lb) 110–119 120–129 130–139 140–149 150–159 160–169 170–179 180–189 190–199 200–209 210–219
Frequency 1 4 17 28 25 18 13 6 5 2 1
  1. Peak weight class: The distribution peaks at the 140–149 lb interval, with the highest frequency of 28 individuals.
  2. Central concentration: The majority of the data (70 out of 120, or 58.3%) lies within the 140–169 lb range, indicating a strong central tendency.
  3. Right-skewed tail: The distribution is skewed to the right. The frequencies decrease gradually toward higher weights.
  4. Low-frequency extremes: The extreme ends are very sparse. The lowest (110–119) and highest (210–219) weight classes each contain only 1 individual.
  5. Rapid drop-off: After the peak at 140–149, the frequencies decline steadily (28 → 25 → 18 → 13).

Messages by Teens

Messages Sent Per Day Number of Teens
0–39 13
40–79 44
80–119 34
120–159 9
160–199 0

Total: 100 teenagers

  1. Most teens send 40–79 messages a day.
  2. Very few teens send 120 or more messages.
  3. The middle three groups cover almost everyone.
  4. Light texting is also uncommon.
  5. The distribution leans slightly to the heavier side.

Normal Distribution

Height in cm) 157 - 162 162 - 167 167 - 172 172 - 177 177 - 182 182 - 187 187 - 192
Frequency (\(f_i\)) 20 120 250 320 200 70 20

Graphs

Histogram

  • Inclusive vs exclusive
What does it tell us

Histogram (contd.)

Can these intervals be readily used?

(5-10); (10-15); (15-20)

(5-9); (10-14); (15-20)

If not, what should we do?

Stem and Leaf

  • key in stem and leaf plot
  • How to interpret stem and leaf plot

  The decimal point is 1 digit(s) to the right of the |

  0 | 1
  1 | 0246
  2 | 0567
  3 | 0

How to interpret cf and rf

Class Frequency Cumulative

Frequency (cf)		 Relative

Frequency (rf)		 Cumulative

Relative

Frequency (crf)
30-35 4 4 0.09 0.09
35-40 10 14 0.23 0.32
40-45 20 34 0.45 0.77
45-50 8 42 0.18 0.95
50-55 2 44 0.04 1
n=44 n=44

What Ogives tell us

Bar vs Pie

  • When to use which?
  • How to calculate angles?
  • Can we draw on 180 degrees?

Draw Suitable Chart

Favorite colors of 30 individuals are noted down.

  Brown Red   Pink  Green Green Green Brown Pink  Brown Red   
  
Brown Red   Green Pink  White Red   Brown Green White Brown 

White Brown Pink  Red   White Brown Green Red   Pink  Red

Choose Diagram

year Sales ($)
1996 76
1997 58
1998 95
1999 85

Category Cost(Tk.)
House rent 10,000
Utility Bill 3,000
Telecom 2000

Frequency Polygon vs Frequency Curve

  • Curve: Smoothed corners

Bar Diagram vs Histogram

Example Charts

Bar Chart

Pie Chart

Donut Chart

Rose Plot

Question Bank

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