Quartile Deviation

QuartileDeviation

Quantilesthe extensions of the

median concept because they are

values which divide a set of data into equal

parts.

Quantiles

1. Median - divides the distribution into two

equal parts.s.

Quantiles

2. Quartile - divides the distribution into

four equal parts.

Quantiles

3. Decile - divides the distribution into ten

equal parts.

Quantiles

4. Percentile - divides the distribution into one hundred equal

parts.

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.

First quartile (Q1)

The middle number between the smallest number and the median of the data set (25th

Percentile).

Lower quartile

Second quartile (Q2)

The median of the data that separates the lower and

upper quartile (50th Percentile).

Third quartile (Q3)

The middle value between the median and the highest value of the data set (75th

Percentile).

Upper quartile

The difference between the upper and lower

quartiles is called the Interquartile range.

IQR = Q3-Q1

Quartile deviation or Semi-interquartile range is one-half the difference

between the first and the third quartiles.

QD = Q3-Q1

2

Quartile Deviation for Ungrouped Data

A. Getting the Quartiles

1. Arrange the test scores from highest to lowest or vice versa

Scores of 8 Students in Management Statistics

17, 26, 17, 27, 30, 31, 30, 37

Scores of 8 Students in Management Statistics

1717262730303137

N = 8

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.

Scores of 8 Students in Management Statistics

1717262730303137N = 8

12345678

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.

Scores of 8 Students in Management Statistics

N /4 = 8/4 = 2

Q1 = (17 + 26)/2

= 21.5

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.

Scores of 8 Students in Management Statistics

3N /4 = 3(8)/4 = 6

Q3 = (30 + 31)/2

= 30.5

Quartile Deviation for Ungrouped Data

B. Getting the Quartile deviation

Subtract Q1 from Q3 and divide the difference by 2.

QD = (Q3 – Q1)/2= (30.5 – 21.5)/2

= 4.5

Quartile Deviation for Grouped Data

B. Getting the Quartiles1. Cumulate the frequencies

from bottom to top of the grouped frequency distribution.

Quartile Deviation for Grouped Data

B. Getting the Quartiles

2. Find the First quartile using the formula:

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

Quartile Deviation for Grouped Data

B. Getting the Quartiles

2. Find the Third quartile using the formula:

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

THANK YOU AND GOD BLESS!

@GLEChristianS