Asked by Yani
Find the quartiles for the given dataset.
35,40,40,45,45,50,50,50,55,60,60,65,70
35,40,40,45,45,50,50,50,55,60,60,65,70
Answers
Answered by
GPT 3.5
To find the quartiles, we first need to order the dataset in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
There are 13 numbers in the dataset, so we can find the quartiles using the formulas:
First quartile (Q1): (n+1)/4-th term
Second quartile (Q2): (n+1)/2-th term
Third quartile (Q3): 3(n+1)/4-th term
n is the number of terms, which in this case is 13.
First quartile (Q1): (13+1)/4-th term = 14/4-th term = 3.5-th term
The 3.5-th term falls between the 3rd and 4th term, which are both 40. Therefore, Q1 = 40.
Second quartile (Q2): (13+1)/2-th term = 14/2-th term = 7-th term
The 7th term is 50. Therefore, Q2 = 50.
Third quartile (Q3): 3(13+1)/4-th term = 3(14)/4-th term = 42/4-th term = 10.5-th term
The 10.5-th term falls between the 10th and 11th term, which are 55 and 60 respectively. Therefore, Q3 is the average of these two numbers: (55 + 60) / 2 = 57.5.
Therefore, the quartiles for the given dataset are:
Q1 = 40
Q2 = 50
Q3 = 57.5
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
There are 13 numbers in the dataset, so we can find the quartiles using the formulas:
First quartile (Q1): (n+1)/4-th term
Second quartile (Q2): (n+1)/2-th term
Third quartile (Q3): 3(n+1)/4-th term
n is the number of terms, which in this case is 13.
First quartile (Q1): (13+1)/4-th term = 14/4-th term = 3.5-th term
The 3.5-th term falls between the 3rd and 4th term, which are both 40. Therefore, Q1 = 40.
Second quartile (Q2): (13+1)/2-th term = 14/2-th term = 7-th term
The 7th term is 50. Therefore, Q2 = 50.
Third quartile (Q3): 3(13+1)/4-th term = 3(14)/4-th term = 42/4-th term = 10.5-th term
The 10.5-th term falls between the 10th and 11th term, which are 55 and 60 respectively. Therefore, Q3 is the average of these two numbers: (55 + 60) / 2 = 57.5.
Therefore, the quartiles for the given dataset are:
Q1 = 40
Q2 = 50
Q3 = 57.5