Statistics math

1. Data Management using
Statistics

2. “statistics” has been derived from Latin word “status” or the Italian
word “statista”, which is a “Political State” or a Govt.
Statistics - the science of collecting, analyzing, presenting, and
interpreting data.
Division of Statistics
1. Descriptive Statistics – is a statistical procedure concerned
with describing the characteristics and properties of a group of
persons, places or things that was based on easily verifiable
facts.
2. Inferential Statistics – is a statistical procedure used to draw
inferences for the population on the basis of information
obtained from the sample using the techniques of descriptive
statistics.
Statistics

3. Data Collection and Presentation of
Statistical Data
A. Types of Data
1. Raw Data – data in their original form and structure.
2. Grouped Data – place in tabular form characterized by class
intervals with the corresponding frequency.
3. Primary Data – measured and gathered by the researcher
who published it.
4. Secondary Data – republished by another researcher or
agency.
B. Data Presentation
1. Textual Presentation – in sentences or paragraph.
2. Tabular Presentation – makes use of rows and columns.
3. Graphical Presentation – using pictorial representation.

4. C. Data Gathering Techniques
1. Direct or Interview Method – person to person exchange of
data from interviewer to interviewee.
2. Indirect or Questionnaire Method – responses are written
and given more time to answer.
3. Registration Method – respondents provide information in
compliance with certain laws, policies, rules, decrees,
regulations or standard practices.
4. Experimental Method – the researcher wants to control the
factors affecting the variable being studied to find out cause
and effect relationship.
5. Observation Method – utilized to gather data regarding
attitudes, behavior or values and cultural pattern of the
samples under investigation.
Data Collection and Presentation of
Statistical Data

5. - is the numerical descriptive measures which indicate or
locate the center of distribution of a set of data.
1. Mean (Arithmetic) - is equal to the sum of all the values in
the data set divided by the number of values in the data set.
2. Median - is the middle score for a set of data that has been
arranged in order of magnitude.
3. Mode - is the most frequent score in our data set.
4. Weighted Mean – is an average in which each quantity to be
averaged is a assigned a weight.
Measures of Central Tendency

6. Ex. 1. Find the mean, median and mode in the given data.
63, 55, 89, 56, 35,14, 58, 55, 87,45, 92
Solution:
n = 11
a. mean = (63+55+89+56+35+14+58+55+87+45+92)/11
= 59
b. median – arranging the data from lowest to highest data
14 35 45 55 55 56 58 63 87 89 92
Median location is on the sixth position: median = 56
c. mode = 55
Measures of Central Tendency

7. Ex. 2. Find the median in the given data.
65 55 89 56 35 14 56 55 87 45
Solution: arranging the data
14 35 45 55 55 56 56 65 87 89
Median location is on the 5th and 6th position:
median = (55 + 56)/2 = 55.5
Note: If the number of observed values (N) is odd, the median
position is equal to (n+1)/2, and the value in the (n+1)/2 th is taken
as the median. If N is even, the mean of the two middle values is
the median.
Measures of Central Tendency

8. Ex. 3. Given the data below, determine if Roy passed the
subject.
Solution: Grade = (0.25)(75) + (0.15)(92) + (0.20)(88) + (0.10)(68)
+ (0.30(72)
Grade = 78.55 (passed)
Measures of Central Tendency
Grading
Criteria
Weighted
Percentage
Roy’s Score
Quizzes 25% 75
Recitation 15% 92
Assignment 20% 88
Seatwork 10% 68
Term
Examination
30% 72

9. - indicate the extent to which individual items in a series are
scattered about an average. It is used to determine the
extent of the scatter so that steps may be taken to control
the existing variation. It is also used as a measure of
reliability of the average value.
A. Measures of absolute Dispersion
- expressed in the units of the original observations.
1. Range – can be determined by finding the difference
between the largest and smallest values.
Range (R) = maximum value - minimum value
Ex. 4. The test results of five students are 90, 98, 76, 85
and 92. Find the range.
Solution: R = 98 – 76 = 22
Measures of Dispersion

10. 2. Variance – describes how the data is spread out. It is the average
of the squared deviations about the mean for a set of numbers
Measures of Dispersion

11. 3. Standard Deviation – is the most reliable measure of
dispersion. Standard Deviation is a measure of how much
the data is dispersed from its mean. A high standard deviation
implies that the data values are more spread out from the
mean. The population standard deviation is denoted by σ.
Measures of Dispersion

12. Measures of Dispersion
Ex. 5. A sample of five households showed the following
number of household members: 3, 8, 5, 4 and 4. Find the
variance (σ2) and the standard deviation(σ).
Solution:

13. B. Measures of Relative Dispersion
- are unit less and are used when one wishes to compare
the scatterings of one distribution with another distribution.
The coefficient of variation (CV) is the ratio of the
standard deviation to the mean and is usually expressed
in percentage.
Measures of Dispersion

14. Ex. 6. A company analyst studied recent measurements made
with two different instruments. The first measure obtained a
mean of 4.96 mm with a standard deviation of 0.022 mm. The
second measure obtained a mean of 6.48 mm with a standard
deviation of 0.032. Which of the two instruments was relatively
more precise?
Solution:
instrument #1: CV = (0.022/4.96) (100%) = 0.44%
instrument #2: CV = (0.032/6.48) (100%) = 0.49%
instrument #1 was relatively more precise than
instrument#2
Measures of Relative Dispersion

15. C. Measures of Relative Position or Fractiles
Fractiles – is the division of an array into equivalent
subgroups. It identifies the position of a value in an array.
An array divided into hundred equal parts is Percentile.
In Quartile, array is divided into four equal parts and Decile
dividers an array into 10 equal parts.
Measures of Dispersion

16. Fractiles
Ex. 7. The following were the scores of 12 students in 20-item
quiz, find the : a) 80th percentile b) 6th decile c) 1st quartile.
4 3 6 12 11 6 18 5 6 6 17 13
Solution: arranging the data from lowest to highest,
a) P80th: i = 80, n = 12 and F = 100 (percentile)
P80 = i(n+1)/F = (80)(12+1)/100 = 10.4th or 11th position
P80 = 17 – which means that 80% of the scores are below 17.
b) D6th: I = 6, n = 12 and F = 10 (decile)
D6 = i(n+1)/F = (6)(12+1)/10 = 7.8th or 8th position
D6 = 11 – which means that 60% of the scores are below 11.
Number 3 4 5 6 6 6 6 11 12 13 17 18
Position 1 2 3 4 5 6 7 8 9 10 11 12

17. Fractiles
c) Q1st: I = 1, n = 12 and F = 4 (quartile)
Q1 = i(n+1)/F = (1)(12+1)/4 = 3.25 or 4th position
Q1 = 6 – which means that 25% of the scores are below 6.
Number 3 4 5 6 6 6 6 11 12 13 17 18
Position 1 2 3 4 5 6 7 8 9 10 11 12

18. Exercises A:
Find the mean, median and mode(s)
1. 4, 3, 12, 5, 13, 3
2. -3, 0, 5, -2, 5, -3, 0
3. 120, 123, 123, 120, 112, 134, 128, 126, 162
Exercises B:
The scores of 10 students in a Math Test are given as: 9, 10, 16,
15, 18, 25, 20, 32, 30, 35. Find: a) P70 b) D8 c) Q3