STATISTIC : ORGANIZING DATA

Raw Data

Information obtained by observing values of variable.

Frequency distribution

List all categories and the number of elements that belong to each categories

Relative frequency

Obtained by dividing the frequency for a category by the sum of all the frequenciesThe sum of the relative frequencies will always equal one

Percentage

Obtained by multiplying the relative frequency for that category by 100

See Table 2.0

STATISTIC : ORGANIZING DATA

CATEGORY FREQUENCY RELATIVE

FREQUENCY

PERCENTAGE

Rape 2 2/25=0.8 0.8 x 100 = 8%

Robbery 3 3/25=0.12 0.12 x 100 = 12%

Burglary 3 3/25=0.12 0.12 x 100 = 12%

Arson 3 3/25=0.12 0.12 x 100 = 12%

Murder 3 3/25=0.12 0.12 x 100 = 12%

Theft 8 8/25=0.32 0.12 x 100 = 12%

Manslaughter 3 3/25=0.12 0.12 x 100 = 12%

Total 25 1.00 100%

Table 2.0

STATISTIC : ORGANIZING DATA

Bar graph

Graphs composed of bars whose height are the frequencies of different categories

Figure 2.0

Pie Chart

Used to graphically display qualitative data. A circle divided into portions thatrepresent relative frequency or percentages belonging to each categories.

Figure 2.1

Histograms

Graph that displays the classes on the horizontal axis and the frequencies of classes on the vertical axis (x, y). Although is similar to bar graph a histogramutilizes classes or intervals and frequencies while bar graph utilizes categories and frequencies.

Figure 2.2

STATISTIC : ORGANIZING DATA

Class limits, Class Boundaries, Class Marks, And Class Width

Frequency Distributions

When forming a frequency distribution, these general guidelines shouldBe followed

(i) The number of classes should be between 5 and 15 (ii) Each data value must belong to one, and only one, class (iii) When possible all classes must be in equal width

See Table 2.1

STATISTIC : ORGANIZING DATA

Frequency Distributions

Score/ Class Limits

Frequency Lower Limit

Upper Limit

Class Boundaries Class Width Class Marks

80-94 8 80 94 79.5-94.5 15 87.0

95-109 14 95 109 94.5-109.5 15 102.0

110-124 24 110 124 109.5-124.5 15 117.0

125-139 16 125 139 124.5-139.5 15 132.0

140-154 13 140 154 139.5-154.5 15 147.0

Boundaries

If the lower class limit for second class, 95, is added to the upper class limitfor the first class 94, and the sum divided by 2 the upper boundary and lowerboundary for the second class is determined.

Class Marks

If the lower class limit is added to the upper class limit for any class and the sum dividedby 2, the class mark is obtained.

Table 2.1

Camping 29%

Swimming 32%

Horse Riding 39%

Figure 2.1

A B C

Figure 2.0

10

20

30

40

50 Number of students for each grade in a Class

Types of Most Favored Hobbies and the percentages

STATISTIC : ORGANIZING DATA

Frequency Distributions

Figure 2.2

1

2

3

4

5 Price for 1 liter mineral water in several outlets

2.55 2.752.65 2.85

Price

Frequency

CATEGORY FREQUENCY RELATIVE

FREQUENCY

PERCENTAGE

India 2

China 5

Japan 10

Malaysia 10

Australia 4

Indonesia 4

Total

Exercise 1 : Fill the empty spaces with the required details

Create a pie chart using the details you’ve got from the table above

Exercise 2 : Fill the empty spaces with the required details

Cholesterol Cholesterol valuevalue

FrequencyFrequency Lower Lower limitlimit

Upper Upper LimitLimit

Lower Lower boundaryboundary

Upper Upper boundaryboundary

Class markClass mark

170-189170-189 33

190-209190-209 1010

210-229210-229 1717

230-249230-249 1313

250-269250-269 22

Create a Histogram with the answers you get from the filled table above