Download Cumulative frequency of more than

Applying
the rules
of
statistics
in problem
solving
􀂊 Mean of statistic and
statistics
􀂊 Mean of population and
sample
􀂊 Data types
􀂊 Table and diagram
􀂊 Mean
unaxepectedly
􀂊 Median
􀂊 Mode
􀂊 Range
􀂊 Average deviation
􀂊 Standard deviation
􀂊 Semiinterquartile range
􀂊 Percentile range
􀂊 Score default( Z-score)
􀂊 Variation coefficient
Solve the
problem
statistics
Statistic is collection of information is organized, managed, and presented in the form
of a table or chart so that illustrate the characteristics of data.
Statistics is a discipline to learn about the collection, analysis, presentation, and
drawing a conclusion from the data.
Based activities, statistics were divided into two things :
1. Descriptive statistics or deductive statistics
is a discipline to learn about the collection, analysis, and presentation of a data.
2 Inference statistics or inductive statistics
is a discipline of study drawing conclusions about the results of data processing.
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Population is a set of objects from the research that has one or more of the
characteristics and the same characteristics.
Sampling is part of the collective population of the right - are correct.
Example :
1. A mother will buy oranges. To find out whether the orange is sweet or
not,
a mother to take one of a number of oranges in the basket for taste.
2. A father to buy a cup of coffee in the coffee shop. To find out if coffee is fit
or not with the tongue of the father, the father took a spoon to taste the
coffee.
3. To find out if all the class XII students already pay fees, the school
principal to request the
administration to check the data for all
students in class XII.
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Conclusion :
 A basket of oranges as a population, while an orange as a sample.
 A cup of coffee as a population, while a coffee spoon as a sample.
 As population and sample is the class XII students
Notes :
When research is done to each member of the population, research is called
the census.
When the research carried out on only part of the population, research is
called sampling.
Method of determining a representative sample learned specifically in the
theory of sampling (sampling theory).
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Mean of data
Datum is information (information) obtained from an observation, may be a
number, symbol, or character.
Collection of data referred to as the datum. Thus, the data is the plural of
datum.
According to the data are divided into two, namely :
a. Qualitative data is data that indicates the nature of an object or
situation.
b. Quantitative data is the data obtained from the measure or
calculate.
 Digital or discrete data
is the data obtained with a tattoo, consider, or the object.

Size or continuous data
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Look at the table below :
No.
Irrigated
Plot
Many Penggarap
(person)
Area (m2)
Rice Gabah Dry
Weight (kg)
Quality Dry Rice
Gabah
1
2
3
4
5
5
7
15
9
8
2.400
2.700
4.500
3.500
3.100
1.800
2.050
3.460
2.740
2.360
middle
well
very good
less
middle
According to how the data is divided into two, namely:
a. Primary data is data that is collected and processed by the
organization that publishes.
b. Secondary data is data collected by someone other than the user.
Data size
Data size is determined by the number of datum in a database.
Data size have represented as "n" or "N" or “fi”.
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To create a frequency distribution table, required several steps :
Step 1 :
Define the scope or range or range, the biggest datum difference with the
smallest.
R = xmaks – xmin
Step 2 :
Specify the number of classes, one using the rules Sturgess
K = 1 + 3,3.logN
Value of K is usually taken at intervals 5  K  15
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Step 3 :
Determine the width or length or interval class with the formula :
R
i 
K
For ease in determining the value of midpoint is usually the length of the
class selected the odd class.
Step 4 :
Define the boundary down the first class where the value is  xmin provided
xmax must be included in the class last.
Step 5 :
Determine the frequency of each class by using the pillar system.
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Example :
Make a table of frequency distribution of the daily mathematics test results below :
Solution :
 R = 92 – 40 = 52
 K = 1 + 3,3.logN
= 1 + 3,3.log40
= 6,29
K 6

i 9
Value
40
49
58
67
76
85
–
–
–
–
–
–
fi
48
57
66
75
84
93
Midpoint
44
53
62
71
80
89
Turus
IIII
III
IIII
IIII
II
IIII
I
IIII IIII
IIII
I
Frequency
6
3
14
9
2
6
40
Adaptif
Cumulative Frequency Distribution Table of less than (fk )
Definition :
Cumulative frequency of less than is number of frequency of all values that
are less than or equal to the value in each class.
Cumulative Frequency Distribution Table of more than (fk )
Definition :
Cumulative frequency of more than is number of frequency of all values that
are more than or equal to the value in each class.
Cumulative relative frequency is the frequency presentase cumulative size
of the data.
cumulative frequency
Cumulative relative frequency 
x 100%
data size
Adaptif
Value
Midpoint
40 – 48
44
IIII I
6
49 – 57
53
III
3
58 – 66
62
IIII IIII IIII
67 – 75
71
IIII IIII
9
76 – 84
80
II
2
85 – 93
89
IIII I
6
fi
Turus
Frequency
14
40
Lower bound edge = lower bound – 0,5.10-n
Upper bound edge = upper bound + 0,5.10-n
with “n” = the number of digits behind the comma
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Example :
Cumulative frequency distribution table
Cumulative
relative
frequency
Cumulative
frequency
of more
than
Cumulative
relative
frequency
Value
Frequency
Cumulative
frequency of
less than
40 – 48
6
6
15 %
40
100 %
49 – 57
3
9
22,5 %
34
85 %
58 – 66
14
23
57,5 %
31
77,5 %
67 – 75
9
32
80 %
17
42,5 %
76 – 84
2
34
85 %
8
20 %
85 – 93
6
40
100 %
6
15 %
fi
40
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Bar Chart
Is diagram presented in the form of a rectangle, so that it can describe a
situation.
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Pie Chart
Is diagram presented in the form of the circle, so that it can describe a
situation.
Adaptif
Line Graph
Is diagram presented in the form of a line, so that it can describe a
situation.
Adaptif
Pictogram
is diagram showing the data by using tools such as visual images.
Diagram interest from many students read the Education Level in Kecamatan “Melek" Year 2009
Level of Education
Count
TK
200
SD
200
SMP
400
SMA
600
Information :
100 people representing
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Histogram
is the form of a bar chart but the width is the width of stem intervals while
the class of limit - the stem is a class edge, so that each stem coincide with
each other
14
9
6
3
2
39,5
48,5
57,5
66,5
75,5
84,5
93,5
Adaptif
Polygon
is broken line connecting the coordinates of each point made from the
middle class with frequency.
14
9
6
3
2
44
53
62
71
80
89
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Ogive
is smooth curve earned based on the cumulative frequency distribution.
There are two types of ogive :
1. Ogive positive, that is kurva list based on the cumulative frequency distribution of
less than.
2. Ogive negative, namely kurva list based on the cumulative frequency distribution
of more than .Ogive positive
Ogive negative
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Central Tendency
Centralising of data describe the place or the value of which tends to gather data.
1. Mean
is average value of data.
Mean a single data
Mean weight single data
n
n
x 
Mean group data
 xi
i 1
n
x 
 f .x
i 1
n
i
f
i 1
i
i
n
x 
 f .x
i 1
n
i
f
i 1
i
i
Adaptif
Central Tendency
Centralising of data describe the place or the value of which tends to gather data.
2. Median
Is middle value after the data sorted.
Median a single data
If n odd, is the median value of the datum to-
( n  1)
2
n
n 
datum to     datum to    1
2
2 
If n even, median is the value of the datum to2
Median group data
1

 .n  f kk 
.i
Median  tbb   2
f


m




Adaptif
Central Tendency
Centralising of data describe the place or the value of which tends to gather data.
3. Mode
is the value in the data that most often appear.
Mode a single data
From the data presented the value of the search appear at most.
Modus group data
 d1 
.i
Mode  tbb  
d

d
2 
 1
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The size of the how far the observation (data) from the average spread - ratanya referred to as
the size of Diversity / Distribution.
1.
Range
is the biggest datum difference with the smallest.
Range = xmaks – xmin
2. Average Deviation
Average Deviation a single data :
n
SR 
x
i 1
i
x
n
Average Deviation group data :
n
SR 

i 1
f i . xi  x
n

i 1
fi
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3. Variance and Standard Deviation
variance a single data :
 x  x 
n
S 
2
standard deviation a single data :
i
i 1
S
n
 x  x 
n
2
2
i
i 1
n
or
n
S2 
x
i 1
n
2
i
n
x
2
S
x
i 1
n
2
i
x
2
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4. Semiinterquartile range atau quartile deviation
Kuartil is to share data Ascending into four sections the same lot.
i
 n  f kk
Qi  tbbi   4
f Qi





.i



interquartile range or overlay :
H = Q3 – Q1
Semiinterquartile range atau quartile deviation :
Qd = ½.(Q3 – Q1) =
½.H
5. Decile
Decile is to share
into ten sections the same lot.
 i data Ascending

n  f kk 

.i
Di  tbbi   10
f Di






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6. Percentile range
Percentile istoishare data
 Ascending into one hundred sections the
n  f kk 

same lot.
.i
Pi  tbbi   100
f Pi






Percentile range :
JP = P90 – P10
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Standard score (z-test) is a number that indicates the position of a data
against the average - the average in the group.
xx
z
S
Variation coefficient is a number that high diversity (variation) of data in a group.
S
KV 
x100%
x
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