Magkano ba bayan

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Magkano ba bayan??? (A Math 12 Statistical
Project)
Group members Cabrera, Christina Flaviano,
Elaine Rossel Francisco, Sharris Gayle Gozum,
Therese Nicole Paraiso, Cecilia Angela Tatel,
Christcel
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A sample of 100 Freshmen students, male and
female, ranging from 17-19 years of age, from the
Ateneo de Manila University is surveyed to
determine the amount of allowance they receive
every week.
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Every allowance amount received weekly by each
person is not less than P500 and not greater than
P2000. Upon analyzing the raw scores, we have
decided to set the size of the class intervals to
150.
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FREQUENCY DISTRIBUTION TABLE
Class Intervals Frequency Relative
Frequency lt Cumulative gtCumulative
Frequency Frequency 500-650 32
32/100 8/25 0.32 32 100 650-800
17 17/100 0.17 49
68 800-950 12 12/100 3/25 0.12 61
51 950-1100 24 24/100 6/25
0.24 85 39 1100-1250 7
7/100 0.07 92 15 1250-1400 0
0 92 8 1400-1550 4
4/100 1/25 0.04 96 8 1550-1700
0 0 96 4 1700-1850 1
1/100 0.01 97 4 1850-2000 3
3/100 0.03 100
3 TOTAL 100 100/100 1.0
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MEAN ( ? )/n, where xi class mark
of the ith interval fi
frequency of the ith interval
n number of observations
n1 number of class intervals
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From the raw scores given it can be observed that
Ungrouped data
MEAN x (84950)/100 849.50
Grouped data
MEAN x (87500)/100 875
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n100 n/2 100/2 50 The MEDIAN is the
average of the 50th and 51st value. 800 (50th
value) 800 (51st value) 1600 1600/2 800
MEDIAN
FINDING THE MEDIAN
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For Ungrouped Data Since SD v? (xi-x)2/n
SD v(12226250)/ 100 349.67 From here, we
can expect that most students have P875 or
P349.67 as their weekly allowance.
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or another formula for finding the SD of
ungrouped data
SD vn?(xi)2 (?xi)2/n2
SD v100(83872500)-(84950)2/ 100
34216.18769/ 100 342.16 The results of the
first and second computations of SD, P349.67 and
P342.16 respectively, are close in value. From
here, we can determine the certainty of these two
formulas.
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For Grouped Data
Since SD v? (xi-x)2fi/n
?(xi-x)2fi 9990000 SD v(9990000)/ 100
316.07 From here, we can expect that most
students have P875 or P316.07 as their weekly
allowance.
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or another formula SD vn?(fixi2)
(?fixi)2/n2
SD v100(86552500)-(87500)2/ 10000
v999000000/ 10000 316.07 The results
of the first and second computations of SD are
both P316.07. From here, we can determine the
certainty of these two formulas.
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Analysis

• Our survey of 100 freshmen students shows that
  they receive a weekly allowance of 500-2000
  pesos.
• The mean or average for ungrouped data is
  849.50 pesos.
• The mean for grouped data is 875 pesos.
• The median is 800 pesos.

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• The modal class is the class interval of 500-650
  pesos.

• The standard of deviation for ungrouped data are
  349.67 and 342.16 (we used the two formulas)
• The standard of deviation for grouped data are
  316.07 and 316.07

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Given the standard of deviation, we can expect
majority of the students to receive 349.67 more
or less than 875 pesos. Majority of the students
therefore receive an allowance within the range
of 525-1225 pesos. Our frequency distribution
table supports this. 92 of the students receive
an allowance within the range of 500-1250 pesos.
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The large value of the standard of deviation
indicates that the observations are more
scattered from the mean. Again, our tables
support this. The mean 875 falls within the
800-950 class interval. 32 of our sample fall
under the 500-650 class interval, 24 fall under
the 950-1100 class interval.
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If students wish to ask for a raise in their
allowance, it would be advisable for them to use
the mean or the median as opposed to the modal
class. The computed values of the mean and
median are much higher compared to the modal
class. Moreover, it is pointless to use the
modal class since it represents the lowest class
interval.
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One may also suppose that a weekly allowance
within the range of 500-1250 pesos is sufficient
for a freshman student since .92 of the sample
receive this amount.