quartile deviation
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QuartileDeviation
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Quantilesthe extensions of the
median concept because they are
values which divide a set of data into equal
parts.
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Quantiles
1. Median - divides the distribution into two
equal parts.s.
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Quantiles
2. Quartile - divides the distribution into
four equal parts.
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Quantiles
3. Decile - divides the distribution into ten
equal parts.
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Quantiles
4. Percentile - divides the distribution into one hundred equal
parts.
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QuartilesValues in a given set of distribution that divide the data into four equal parts. Each set of scores
has three quartiles. These values can be
denoted by Q1, Q2 and Q3.
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First quartile (Q1)
The middle number between the smallest number and the median of the data set (25th
Percentile).
Lower quartile
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Second quartile (Q2)
The median of the data that separates the lower and
upper quartile (50th Percentile).
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Third quartile (Q3)
The middle value between the median and the highest value of the data set (75th
Percentile).
Upper quartile
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The difference between the upper and lower
quartiles is called the Interquartile range.
IQR = Q3-Q1
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Quartile deviation or Semi-interquartile range is one-half the difference
between the first and the third quartiles.
QD = Q3-Q1
2
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Quartile Deviation for Ungrouped Data
A. Getting the Quartiles
1. Arrange the test scores from highest to lowest or vice versa
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Scores of 8 Students in Management Statistics
17, 26, 17, 27, 30, 31, 30, 37
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Scores of 8 Students in Management Statistics
1717262730303137
N = 8
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Quartile Deviation for Ungrouped Data
A.Getting the Quartiles
2. Assign serial numbers to each score. The first is assigned to the lowest test scores, while the last serial number is assigned to the highest test score.
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Scores of 8 Students in Management Statistics
1717262730303137N = 8
12345678
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Quartile Deviation for Ungrouped Data
A. Getting the Quartiles3. Determine the first quartile (Q1).
To be able to locate Q1, divide N by 4. Use the obtained value in locating the serial number of the score that falls under Q1. Add the value of the located serial number from the next high score.
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Scores of 8 Students in Management Statistics
N /4 = 8/4 = 2
Q1 = (17 + 26)/2
= 21.5
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Quartile Deviation for Ungrouped Data
A. Getting the Quartiles4. Determine the third quartile (Q3)
by dividing 3N by 4. Locate the serial number corresponding to the obtained answer. Add the value of the located serial number from the next high score. Opposite this number is the test score corresponding to Q3.
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Scores of 8 Students in Management Statistics
3N /4 = 3(8)/4 = 6
Q3 = (30 + 31)/2
= 30.5
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Quartile Deviation for Ungrouped Data
B. Getting the Quartile deviation
Subtract Q1 from Q3 and divide the difference by 2.
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QD = (Q3 – Q1)/2= (30.5 – 21.5)/2
= 4.5
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Quartile Deviation for Grouped Data
B. Getting the Quartiles1. Cumulate the frequencies
from bottom to top of the grouped frequency distribution.
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Quartile Deviation for Grouped Data
B. Getting the Quartiles
2. Find the First quartile using the formula:
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Q1 = L + (N/4 – CF )/f (i)
where:L = exact lower limit if the Q1 class
N/4 = locator of the Q1 class
N = total number of scoresCF = cumulative frequency before the
Q1 class
i = class size/interval
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Quartile Deviation for Grouped Data
B. Getting the Quartiles
2. Find the Third quartile using the formula:
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Q3 = L + (3N/4 – CF )/f (i)
where:L = exact lower limit if the Q3 class
3N/4 = locator of the Q3 class
N = total number of scoresCF = cumulative frequency before the
Q3 class
i = class size/interval
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@GLEChristianS