Find the quartiles for the given dataset.

Question

35,40,40,45,45,50,50,50,55,60,60,65,70

Answer 1

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