Math  /  Data & Statistics

Question(1) Find Q1;Q2Q3Q_{1} ; Q_{2} \leqslant Q_{3} of the following sets of data a) 21,27,23,25,23,26,29,28,29,2821,27,23,25,23,26,29,28,29,28 b) 113,119,115,114,118,117,16,115,119113,119,115,114,118,117,16,115,119 c) 58,51,59,54,51,57,56,51,53,58,5258,51,59,54,51,57,56,51,53,58,52 d) 2,11,9,13,15,19,3,7,4,12,16,18,172,11,9,13,15,19,3,7,4,12,16,18,17

Studdy Solution

STEP 1

1. Q1 Q_1 is the first quartile, Q2 Q_2 is the median, and Q3 Q_3 is the third quartile.
2. The data sets need to be ordered to find the quartiles.
3. Quartiles divide the data into four equal parts.

STEP 2

1. Order each data set.
2. Calculate Q1 Q_1 , Q2 Q_2 , and Q3 Q_3 for each data set.

**For Set a) 21,27,23,25,23,26,29,28,29,28 21,27,23,25,23,26,29,28,29,28 **

STEP 3

Order the data set:
21,23,23,25,26,27,28,28,29,29 21, 23, 23, 25, 26, 27, 28, 28, 29, 29

STEP 4

Calculate Q1 Q_1 :
- Q1 Q_1 is the median of the first half: 21,23,23,25,26 21, 23, 23, 25, 26 - Median of this set is 23 23 .

STEP 5

Calculate Q2 Q_2 (median of the entire set):
- Median of the ordered set is the average of 5th and 6th values: 26+272=26.5 \frac{26 + 27}{2} = 26.5 .

STEP 6

Calculate Q3 Q_3 :
- Q3 Q_3 is the median of the second half: 27,28,28,29,29 27, 28, 28, 29, 29 - Median of this set is 28 28 .
Quartiles for set a):
Q1=23,Q2=26.5,Q3=28 Q_1 = 23, \quad Q_2 = 26.5, \quad Q_3 = 28
**For Set b) 113,119,115,114,118,117,116,115,119 113,119,115,114,118,117,116,115,119 **

STEP 7

Order the data set:
113,114,115,115,116,117,118,119,119 113, 114, 115, 115, 116, 117, 118, 119, 119

STEP 8

Calculate Q1 Q_1 :
- Q1 Q_1 is the median of the first half: 113,114,115,115 113, 114, 115, 115 - Median of this set is 114.5 114.5 .

STEP 9

Calculate Q2 Q_2 (median of the entire set):
- Median of the ordered set is the 5th value: 116 116 .

STEP 10

Calculate Q3 Q_3 :
- Q3 Q_3 is the median of the second half: 117,118,119,119 117, 118, 119, 119 - Median of this set is 118.5 118.5 .
Quartiles for set b):
Q1=114.5,Q2=116,Q3=118.5 Q_1 = 114.5, \quad Q_2 = 116, \quad Q_3 = 118.5
**For Set c) 58,51,59,54,51,57,56,51,53,58,52 58,51,59,54,51,57,56,51,53,58,52 **

STEP 11

Order the data set:
51,51,51,52,53,54,56,57,58,58,59 51, 51, 51, 52, 53, 54, 56, 57, 58, 58, 59

STEP 12

Calculate Q1 Q_1 :
- Q1 Q_1 is the median of the first half: 51,51,51,52,53 51, 51, 51, 52, 53 - Median of this set is 51 51 .

STEP 13

Calculate Q2 Q_2 (median of the entire set):
- Median of the ordered set is the 6th value: 54 54 .

STEP 14

Calculate Q3 Q_3 :
- Q3 Q_3 is the median of the second half: 56,57,58,58,59 56, 57, 58, 58, 59 - Median of this set is 58 58 .
Quartiles for set c):
Q1=51,Q2=54,Q3=58 Q_1 = 51, \quad Q_2 = 54, \quad Q_3 = 58
**For Set d) 2,11,9,13,15,19,3,7,4,12,16,18,17 2,11,9,13,15,19,3,7,4,12,16,18,17 **

STEP 15

Order the data set:
2,3,4,7,9,11,12,13,15,16,17,18,19 2, 3, 4, 7, 9, 11, 12, 13, 15, 16, 17, 18, 19

STEP 16

Calculate Q1 Q_1 :
- Q1 Q_1 is the median of the first half: 2,3,4,7,9,11 2, 3, 4, 7, 9, 11 - Median of this set is 6 6 .

STEP 17

Calculate Q2 Q_2 (median of the entire set):
- Median of the ordered set is the 7th value: 12 12 .

STEP 18

Calculate Q3 Q_3 :
- Q3 Q_3 is the median of the second half: 13,15,16,17,18,19 13, 15, 16, 17, 18, 19 - Median of this set is 16.5 16.5 .
Quartiles for set d):
Q1=6,Q2=12,Q3=16.5 Q_1 = 6, \quad Q_2 = 12, \quad Q_3 = 16.5

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