![THE QUARTILE FOR GROUPED DATA
1. THE FOLLOWING FORMULA IS USED IN FINDING THE QUARTILES
OF GROUPED DATA
kN
cfb-
Qk = LB +
4
FQK[ ]i
Where: LB = lower boundary of Qk class
N = total frequency
cfb = cumulative frequency of the
class before the Qk class
FQk = frequency of the Qk class
i = size of the class interval
k = nth quartile, where n = 1, 2, and 3](https://image.slidesharecdn.com/groupeddata-190131043414/75/QUARTILES-MEASURES-OF-POSITION-FOR-GROUPED-DATA-4-2048.jpg)
![THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
STEP 2: SOLVE Q1 USING THE FORMULA
N
cfb-
Q1 = LB +
4
FQ1[ ]i
N = 50
cfb = 6
fQ1 = 12
LB = 25.5
i = 5](https://image.slidesharecdn.com/groupeddata-190131043414/75/QUARTILES-MEASURES-OF-POSITION-FOR-GROUPED-DATA-11-2048.jpg)
![THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
Therefore, 25% of the students have a score less than or equal to 28.21
50
6-
Q1 = 25.5 + 4
12[ ]5
Given: N = 50
cfb = 6
fQ1 = 12
LB = 25.5
i = 5
Q1 = 28.21 Final answer](https://image.slidesharecdn.com/groupeddata-190131043414/75/QUARTILES-MEASURES-OF-POSITION-FOR-GROUPED-DATA-12-2048.jpg)
Uploaded byChuckry Maunes
QUARTILES : MEASURES OF POSITION FOR GROUPED DATA
This document discusses how to calculate quartiles, deciles, and percentiles from a set of grouped data. It provides a formula to find the quartiles of grouped data which involves determining the lower boundary, cumulative frequency, and frequency of the quartile class. An example is shown calculating the first, second, and third quartiles of mathematics test scores from 50 students grouped into classes. The first quartile is calculated to be 28.21 using the provided formula.
In this document
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Introduction to measures of position: quartiles, deciles, percentiles, and calculation of the 90th percentile.
Explains what quartiles are, the formulae to find quartiles in grouped data, and how to calculate Qk class.
Step-by-step example using mathematics test scores of 50 students to calculate Q1, Q2, and Q3, including determination of lower boundaries and cumulative frequency.
Introduction to measures of position: quartiles, deciles, percentiles, and calculation of the 90th percentile.
Expression of gratitude for attention and information about educational programs.
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QUARTILES : MEASURES OF POSITION FOR GROUPED DATA
- 2. OBJECTIVES •ILLUSTRATE THE FOLLOWINGMEASURES OF POSITION: QUARTILES, DECILES AND PERCENTILES •CALCULATE SPECIFIED MEASURE OF POSITION (E.G. 90TH PERCENTILE) OF A SET OF DATA.
- 3. QUARTILE FOR GROUPEDDATA •THE QUARTILES ARE THE SCORE POINTS WHICH DIVIDE A DISTRIBUTION INTO FOUR EQUAL PARTS.
- 4. THE QUARTILE FORGROUPED DATA 1. THE FOLLOWING FORMULA IS USED IN FINDING THE QUARTILES OF GROUPED DATA kN cfb- Qk = LB + 4 FQK[ ]i Where: LB = lower boundary of Qk class N = total frequency cfb = cumulative frequency of the class before the Qk class FQk = frequency of the Qk class i = size of the class interval k = nth quartile, where n = 1, 2, and 3
- 5. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA 2. FORMULA TO CALCULATE THE QK CLASS Qk class= kN 4 Where: N = total frequency k = nth quartile, where n = 1, 2, and 3
- 6. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA EXAMPLE CALCULATE THE Q1, Q2, AND Q3 IF THE MATHEMATICS TEST SCORES OF 50 STUDENTS SCORES FREQUENCY 46-50 4 41-45 8 36-40 11 31-35 9 26-30 12 21-25 6
- 7. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA STEP 1.A: DETERMINE THE LOWER BOUNDARIES SCORES FREQUENCY Lower Boundaries (LB) 46-50 4 41-45 8 36-40 11 31-35 9 26-30 12 25.5 21-25 6 20.5 To solve for LB subtract 0.5 to the smallest number per class interval 21 – 0.5 = 20.5 30.5 35.5 40.5 45.5
- 8. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA STEP 1.B: DETERMINE THE CUMULATIVE FREQUENCY SCORES FREQUENCY Lower Boundaries (LB) Less than Cumulative Frequency (<cf) 46-50 4 45.5 41-45 8 40.5 36-40 11 35.5 31-35 9 30.5 27 26-30 12 25.5 18 21-25 6 20.5 6 Copied from the frequency 6 + the frequency of the class interval 18 + the frequency of the class interval 38 46 50
- 9. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA Q1 class= N 4 STEP 2.A: CALCULATE THE Q1 CLASS N = 50 k = 1Given: Q1 class = 50 4 =12.5 This means that we need to find the class interval where the 12.5th score is contained
- 10. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE Q1 CLASS IS SITUATED SCORES FREQUENCY Lower Boundaries (LB) Less thanCumulative Frequency (<cf) 46-50 4 45.5 50 41-45 8 40.5 46 36-40 11 35.5 38 31-35 9 30.5 27 26-30 12 25.5 18 21-25 6 20.5 6 (7th to 18th score) Q1 class The Q1 class is class interval 26-30 N = 50 cfb = 6 fQ1 = 12 LB = 25.5 i = 5 Σ f = 50 Cfb = fQ1 = LB = i = 5
- 11. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA STEP 2: SOLVE Q1 USING THE FORMULA N cfb- Q1 = LB + 4 FQ1[ ]i N = 50 cfb = 6 fQ1 = 12 LB = 25.5 i = 5
- 12. THE MEASURE OFPOSITION QUARTILE FOR GROUPED DATA Therefore, 25% of the students have a score less than or equal to 28.21 50 6- Q1 = 25.5 + 4 12[ ]5 Given: N = 50 cfb = 6 fQ1 = 12 LB = 25.5 i = 5 Q1 = 28.21 Final answer
- 13. OBJECTIVES •ILLUSTRATE THE FOLLOWINGMEASURES OF POSITION: QUARTILES, DECILES AND PERCENTILES •CALCULATE SPECIFIED MEASURE OF POSITION (E.G. 90TH PERCENTILE) OF A SET OF DATA.
- 14.