Find the quartiles for the given dataset.
35,40,40,45,45,50,50,50,55,60,60,65,70
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
To find the quartiles for the given dataset, we can follow these steps:
Step 1: Arrange the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Step 2: Find the median, which is the middle value of the dataset. Since there are 13 values, the median will be the 7th value and the 7th and 8th values divided by 2.
Median = (50 + 50) / 2 = 50
Step 3: Find the lower quartile (Q1). The lower quartile is the median of the lower half of the dataset.
To find the lower quartile, we first create a new dataset with the values below the median:
35, 40, 40, 45, 45
Now we find the median of this new dataset:
Lower quartile (Q1) = (40 + 40) / 2 = 40
Step 4: Find the upper quartile (Q3). The upper quartile is the median of the upper half of the dataset.
To find the upper quartile, we create a new dataset with the values above the median:
55, 60, 60, 65, 70
Now we find the median of this new dataset:
Upper quartile (Q3) = (60 + 60) / 2 = 60
So, the quartiles for the given dataset are:
Lower quartile (Q1) = 40
Median (Q2) = 50
Upper quartile (Q3) = 60