mean for grouped data
TRANSCRIPT
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Measures of Central Tendency
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Grouped Data
MEAN
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Determine the mean of the following.
Determine the mean of the following.
a. 2, 4, 1, 4 and 6
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a. 2, 4, 1, 4 and 6
answer: 3.4 5
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b. 77, 80, 90, 65, 77, 89, 80
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b. 77, 80, 90, 65, 77, 89, 80 answer: 79.71
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c. 1299,2580, 4098, 9100, 1100
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c. 1299,2580, 4098, 9100, 1100
answer: 3635.4
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d. 50, 50, 51, 58, 60
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answer: 53.8d. 50, 50, 51, 58, 60
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e. 34, 39, 39, 52, 38, 60
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answer: 43.67e. 34, 39, 39, 52, 38, 60
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Measures of Central Tendency of
MEANGROUPED DATA
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Grouped Data
Grouped data are the data or scores that are arranged in a frequency distribution.
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Grouped Data
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Mean
The mean (also known as the arithmetic mean) is the most commonly used measure of central position. It is used to describe a set of data where the measures cluster or concentrate at a point.
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Mean
Formula:
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mfXXn
f frequency
mX classmark n sum of frequency
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X meanmfXX
nWhere
:
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Illustrative Example:Calculate the mean of the Mid-year Scores of Students in Mathematics.
Score Frequency
41-45 136-40 831-35 826-30 1421-25 716-20 2
Mid-year Test scores of students in Mathematics
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 136-40 831-35 826-30 1421-25 716-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 831-35 826-30 1421-25 716-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 8 3831-35 826-30 1421-25 716-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 8 3831-35 8 3326-30 1421-25 716-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 8 3831-35 8 3326-30 14 2821-25 716-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 8 3831-35 8 3326-30 14 2821-25 7 2316-20 2
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Solution1. Find the midpoint or class mark ( ) of each class or category.
mX
2mLL ULX
Scores
41-45 1 4336-40 8 3831-35 8 3326-30 14 2821-25 7 2316-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 4336-40 8 3831-35 8 3326-30 14 2821-25 7 2316-20 2 18
30
Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 3831-35 8 3326-30 14 2821-25 7 2316-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 3326-30 14 2821-25 7 2316-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 2821-25 7 2316-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 2316-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 23 16116-20 2 18
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Solution2. Multiply the frequency and the corresponding class mark . fXm
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 23 16116-20 2 18 36
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Solution
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 23 16116-20 2 18 36
3. Find the sum of the results in step 2. fXm
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Solution3. Find the sum of the results in step 2.
Scores Frequency
(f )41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 23 16116-20 2 18 36
fXm
Solution4. Solve the mean using the formula. Scores Frequenc
y(f )
41-45 1 43 4336-40 8 38 30431-35 8 33 26426-30 14 28 39221-25 7 23 16116-20 2 18 36
n=40
Substitution
Therefore, the mean of Mid-year test is 30.
mfXXn
1, 20040
30X
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Let’s practice: Find the mean weight of Grade 8 Students.
Weight in kg Frequency75-79 170-74 465-69 1060-64 1455-59 2150-54 1545-49 1440-44 1
Weight in kg
Frequency (f)
75-79 170-74 465-69 1060-64 1455-59 2150-54 1545-49 1440-44 1
40
Weight in kg
Frequency (f)
75-79 1 7770-74 465-69 1060-64 1455-59 2150-54 1545-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 1060-64 1455-59 2150-54 1545-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 1455-59 2150-54 1545-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 14 6255-59 2150-54 1545-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 14 6255-59 21 5750-54 1545-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 14 6255-59 21 5750-54 15 5245-49 1440-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 14 6255-59 21 5750-54 15 5245-49 14 4740-44 1
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Weight in kg
Frequency (f)
75-79 1 7770-74 4 7265-69 10 6760-64 14 6255-59 21 5750-54 15 5245-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 7265-69 10 6760-64 14 6255-59 21 5750-54 15 5245-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 6760-64 14 6255-59 21 5750-54 15 5245-49 14 4740-44 1 42
50
Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 6255-59 21 5750-54 15 5245-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 5750-54 15 5245-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 5245-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 52 78045-49 14 4740-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 52 78045-49 14 47 65840-44 1 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 52 78045-49 14 47 65840-44 1 42 42
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Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 52 78045-49 14 47 65840-44 1 42 42
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Therefore, the mean weight is 57.25
Weight in kg
Frequency (f)
75-79 1 77 7770-74 4 72 28865-69 10 67 67060-64 14 62 86855-59 21 57 119750-54 15 52 78045-49 14 47 65840-44 1 42 42
mfXXn
458080
57.25X
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Generalization
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GeneralizationThe mean (also known as the arithmetic mean) is the most commonly used measure of central position. It is used to describe a set of data where the measures cluster or concentrate at a point.
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Formula
mfXXn
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Group Work
CRITERIA
5 4 3 2 1
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Group WorkCRITERIA
5 4 3 2 1
ACCURACY
100% of the steps and solutions have no mathematical errors.
Almost all (90-99%) of the steps and solutions have no mathematical errors.
Almost all (85-89%) of the steps and solutions have no mathematical errors.
Most (75-84%) of the steps and solutions have no mathematical errors.
Less than 75% of the steps and solutions have mathematical errors.
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Group Work
CRITERIA
5 4 3 2 1
ORGANIZATION
It uses an appropriate and complete strategy for solving the problem. Uses clear and effective diagrams and/or tables.
It uses complete strategy for solving the problem. Uses creative diagrams and/or tables.
It uses strategy for solving the problem. Uses diagrams and/or tables.
It uses an inappropriate strategy or application of strategy unclear. There is limited use or misuse of diagrams and/or tables.
It has no particular strategy for solving the problem. It does not show use of diagrams nor tables.
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Group Work
CRITERIA
5 4 3 2 1
DELIVERY There is a clear and effective explanation of the solution. All steps are included so the audience does not have to infer how the task was completed. Mathematical representation is actively used as a means of communicating ideas, and precise and appropriate mathematical terminology.
There is a clear explanation and appropriate use of accurate mathematical representation. There is effective use of mathematical terminology.
There is explanation and mathematical representation. There is mathematical terminology
There is an incomplete explanation; it is not clearly represented. There is some use of appropriate mathematical representation and terminology to the task.
There is no explanation of the solutions. The explanation cannot be understood, or is unrelated to the task. There is no use or inappropriate use of mathematical representation and terminology to the task.
TIMER10 minutes
End
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Assignment1.A telecommunications company is conducting
a study on the average number text messages send per day by high school students in Marikina. A random sample of 50 college students from the said area is taken. Find the mean of the data set. Class Interval Frequency
30-34 825-29 1020-24 1615-19 910-14 7
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2. Study on Median for Grouped Dataa.Describe Median.b.What is the formula in computing the median for grouped data?Reference: Mathematics Learner’s Module by Emmanuel P. AbunzoPages 564-580
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