QUARTILE AND DECILE OF GROUPED DATA

The steps in computing the median are similar to that of Q1 and Q3
. In finding the median,
we need first to determine the median class. The Q1 class is the class interval where
the 𝑁
4
th score is contained, while the class interval that contains the 3𝑁
4
𝑡ℎ
score is the Q3 class.
Formula :𝑄𝑘 = LB +
𝑘𝑁
4
−𝑐𝑓𝑏
𝑓𝑄𝑘
𝑖
LB = lower boundary of the of the 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 = the value of quartile being asked
The interquartile range describes the middle 50% of values when
ordered from lowest to highest. To find the interquartile range (IQR),
first find the median (middle value) of the upper and the lower half of
the data. These values are Q1 and Q3
. The IQR is the difference
between Q3 and Q1
.
Interquartile Range (IQR) = Q3 – Q1
The quartile deviation or semi-interquartile range is one-half the
difference between the third and the first quartile.
Quartile Deviation (QD) =
𝑄3−𝑄1
2
The formula in finding the kth decile of a distribution is
𝐷𝑘 = 𝑙𝑏𝑑𝑘 +
(
𝑘
10)𝑁 − 𝑐𝑓
𝑓𝐷𝑘
𝑖
𝐿𝐵𝑑𝑘 − 𝐿𝑜𝑤𝑒𝑟 𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑁 − 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
𝑐𝑓 − 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝐹𝑑𝑘 − 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒

1. Q4-WEEK 5 & 6 WELCOME MATHEMATICS CLASS FOR GRADE 10 10th grade

2. RE CALL It is a method that is used to divide a distribution into ten equal parts. is a quantile that divides a set of scores into 100 equal parts. the proportion of scores in a distribution that a specific score is greater than or equal to. DECILE QUARTILE PERCENTILE PERCENTILE RANK Quartiles are the values which divide the whole distribution into four equal parts.

3. QUARTILE FOR GROUPED DATA The steps in computing the median are similar to that of Q 1 and Q 3 . In finding the median, we need first to determine the median class. The Q 1 class is the class interval where the score is contained, while the class interval that contains the score is the Q 3 class .   Formula : = LB +   LB = lower boundary of the of the class N = total frequency = cumulative frequency of the class before the class = frequency of the class i = size of the class interval k = the value of quartile being asked  

4. EXAMPLE 1: Calculate Q 1 , Q 2 and Q 3 of the Mathematics test scores of 50 students. Class interval (scores) Frequency (f) 50-54 4 45-59 8 40-44 11 35-39 9 30-34 12 25-29 6 cf               = LB +                         Q 1 = 32.21: 25% of the students have a score less than or equal to 32.21.

5. EXAMPLE 1: Calculate Q 1 , Q 2 and Q 3 of the Mathematics test scores of 50 students. Class interval (scores) Frequency (f) 50-54 4 45-59 8 40-44 11 35-39 9 30-34 12 25-29 6 cf               = LB +                           Q 2 = 38.39: 50% of the students have a score less than or equal to 38.39

6. EXAMPLE 1: Calculate Q 1 , Q 2 and Q 3 of the Mathematics test scores of 50 students. Class interval (scores) Frequency (f) 50-54 4 45-59 8 40-44 11 35-39 9 30-34 12 25-29 6 cf               = LB +                             Q 3 = 44.27: 75% of the students have a score less than or equal to 44.27

7. The interquartile range describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the upper and the lower half of the data. These values are Q 1 and Q 3 . The IQR is the difference between Q 3 and Q 1 . Interquartile Range (IQR) = Q 3 – Q 1 The quartile deviation or semi-interquartile range is one-half the difference between the third and the first quartile. Quartile Deviation (QD) =            

8. ACTIVITY Class Interval Frequency(f) 88 – 96 9 80 – 87 10 72 – 79 15 64 – 71 13 56 – 63 9 48 – 55 9 Consider the distribution of scores of the students in Math. Find: a) Q 1 b) Q 3 c) IR, d) QD cf 65 56 46 31 18 9   Q 1 class   Q 3 class                   Interquartile Range (IR) = Q 3 – Q 1 = 81.70 – 61.94 = 19.76 Quartile Deviation (QD) = 19.76/2 = 9.88

9. The formula in finding the kth decile of a distribution is   DECILES FOR GROUPED DATA

10. Let the table be scores of 45 students in a long test in Math. EXAMPLE Solve for (a) D 1 and (b) D 6 Class f 30-34 5 25-29 11 20-24 13 15-19 6 10-14 10 LB cf                                            

11. Let the table be scores of 45 students in a long test in Math. EXAMPLE Solve for (a) D 1 and (b) D 6 Class f 30-34 5 25-29 11 20-24 13 15-19 6 10-14 10 LB cf                                              

12. ACTIVITY 100 students are given a 50-item assessment in Mathematics 10 to determine who will be qualified to apply for club membership. The results of the assessment are shown in the table below.   Scores F 46-50 19 41-45 18 36-40 12 31-35 17 26-30 14 21-25 15 16-20 3 11-15 2 LB 45.5 40.5 35.5 30.5 25.5 20.5 15.5 10.5 cf 100 81 63 51 34 20 5 2   i                      

13. ACTIVITY 100 students are given a 50-item assessment in Mathematics 10 to determine who will be qualified to apply for club membership. The results of the assessment are shown in the table below.   Scores F 46-50 19 41-45 18 36-40 12 31-35 17 26-30 14 21-25 15 16-20 3 11-15 2 LB 45.5 40.5 35.5 30.5 25.5 20.5 15.5 10.5 cf 100 81 63 51 34 20 5 2   i                        

14. RE CAP QUARTILE Formula : = LB +   DECILE  

15. ANY QUESTIONS?

16. THANK YOU!