This video discusses how to calculate quartiles, deciles, and percentiles for discrete, simple, and grouped frequency distributions. It demonstrates calculating the third quartile, sixth decile, and 70th percentile for a discrete data set. For a grouped frequency distribution, it shows how to find the median, lower quartile, upper quartile, third decile, and 95th percentile. The key steps shown are arranging the data in ascending order, determining the cumulative frequency, and using formulas to calculate the values of interest based on the total sample size.

1. SUMAN MATHEWS
GRADE 11 MATH
COLLEGE MATH

2. PREVIEW
THIS VIDEO WOULD BE USEFUL FOR GRADE 11 STUDENTS STUDYING MATHEMATICS.
IT WOULD ALSO BE USEFUL FOR STUDENTS AT THE COLLEGE LEVEL STUDYING STATISTICS.
HERE WE SHOW HOW QUARTILES, DECILES AND PERCENTILES CAN BE CALCULATED
.
CALCULATION OF THE ABOVE IS DONE FOR DISCRETE, SIMPLE AND GROUPED
FREQUENCY DISTRIBUTIONS

3. IF A GIVEN SET IS ARRANGED IN ASCENDING OR DESCENDING ORDER OF MAGNITUDE,
• MEDIAN DIVIDES THE SET INTO 2 EQUAL PARTS.
• QUARTILES DIVIDE THE SET INTO 4 QUARTERS. THERE ARE 3 QUARTILES 𝑄1, 𝑄2, 𝑄3
• DECILES DIVIDE THE SET INTO 10 EQUAL PARTS. THERE ARE 9 DECILES, 𝐷1, 𝐷2,------𝐷9
PERCENTILES DIVIDE THE SET INTO 100 EQUAL PARTS.
THERE ARE 99 PERCENTILES
𝑃1, 𝑃2, −−−−−−− −𝑃99

4. 𝑄1 =
𝑁 + 1
4
𝑇𝐻 𝑉𝐴𝐿𝑈𝐸
FOR A DISCRETE DISTRIBUTION OR A SIMPLE FREQUENCY DISTRIBUTION
𝑄2 =
𝑁 + 1
2
𝑇𝐻 𝑉𝐴𝐿𝑈𝐸
𝑄3 = 3
𝑁 + 1
4
𝑇𝐻 𝑉𝐴𝐿𝑈𝐸
=MEDIAN
𝐷𝑟 =
𝑟(𝑛+1) 𝑡ℎ
10
value
𝑃𝑟 =
𝑟(𝑛 + 1) 𝑡ℎ
100
𝑣𝑎𝑙𝑢𝑒

5. Question 1
Calculate the 3rd quartile, 6th decile and 70th percentile
28, 17, 12, 25,26, 19, 13, 27, 21,16
We first arrange in ascending order
12, 13, 16, 17, 19, 21, 25,26, 27, 28
𝑄3 = 3
11
4
𝑡ℎ. Value = 8.25th value
= 8𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + 0.25 9𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 − 8𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 = 26 + 0.25 27 − 26 = 26.25

6. 𝐷6 =
6(11)
10
𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 = 6.6𝑡ℎ 𝑣𝑎𝑙𝑢𝑒
𝐷6 = 6𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + 0.6 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 − 6𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 = 21 + 0.6 25 − 21 = 23.4
𝑃70 =
70
100
11 𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 = 7.77𝑡ℎ 𝑣𝑎𝑙𝑢𝑒
= 25 + .77 8𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 − 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 = 25 + 0.77 26 − 25 = 25.77

7. Question 2
For the following frequency distribution , find 𝑄1, 𝑄3, 𝐷6, 𝑃45
𝒙𝒊 𝒇𝒊
18 15
19 18
20 25
21 27
22 40
23 25
24 19
25 16
26 8
27 7

8. 𝒙𝒊 𝒇𝒊
18 15
19 18
20 25
21 27
22 40
23 25
24 19
25 16
26 8
27 7
We calculate the cumulative frequencycfcf
15
33
58
85
125
150
169
185
193
200

9. 201
4
= 50.25
From the table, we look at the cf greater than 50.25 ie 58
Value of x corresponding to 58 is 20
𝑄1 = 20
3(201)
4
= 150.75
𝑄3 = 24
𝐷6 = 22
45
201
100
= 90.45
𝑃45 = 22
6
201
10
= 120.6

10. QUESTION 3
For the following table, find the median, lower quartile, upper quartile, 3rd decile, 95th percentile
C I f
600-700 40
700-800 68
800-900 86
900-1000 120
1000-1100 90
1100-1200 40
1200-1300 26

11. For a grouped frequency distribution, we use n instead of n+1
𝑄1 = 𝑙 + (
𝑛
4
− 𝑐𝑓
𝑓
) × 𝑐
Where l = lower boundary of the class in which
𝑄1 𝑙𝑖𝑒𝑠
cf = cumulative frequency of the class
preceeding this class
f = frequency of the class in which 𝑄1 𝑙𝑖𝑒𝑠
𝑐 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑙𝑎𝑠𝑠 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
𝑄2 = 𝑙 +
(
𝑛
2
− 𝑐𝑓
𝑓
) × 𝑐
𝑄3 = 𝑙 + (
3𝑛
4
− 𝑐𝑓)
𝑓
× 𝑐

12. 𝐷𝑟 = 𝑙 + (
𝑟𝑛
10 − 𝑐𝑓)
𝑓
× 𝑐
𝑃𝑟 = 𝑙 + (
𝑟𝑛
100
− 𝑐𝑓)
𝑓
× 𝑐

13. C I f c f
600-700 40 40
700-800 68 108
800-900 86 194
900-1000 120 314
1000-1100 90 404
1100-1200 40 444
1200-1300 26 470
470
4
= 117.5
We take 800 -900 as the class in which 𝑄1 𝑙𝑖𝑒𝑠
𝑄1 = 800 + (
117.5 − 108
86
) × 100
= 811.04

14. 𝑄2 =
470
2
= 235900 +
(235 − 194
120
) × 100 = 934.17
3(470)
4
= 352.5
𝑄3 = 1000 + (
352.5−314
90
) × 100 =1042.78
3(470)
10
= 141

15. 𝐷3 = 800 +
141 − 108
86
× 100 = 838.37
95(470)
100
= 446.5
𝑃95 = 1200 +
446.5 − 444
26
× 100 = 1209.62

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