Find the quartiles for the given dataset.
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
(2 points)
Q1:
;
To find the quartiles, we need to divide the dataset into four equal parts.
Firstly, we need to find the median, which is the middle value of the dataset.
In this case, the median is the value in the middle of the dataset, which is the 7th value, 50.
Next, we need to find the lower quartile (Q1), which is the median of the lower half of the dataset.
The lower half of the dataset is 35, 40, 40, 45, 45, and 50.
To find the median of this lower half, we take the average of the middle two values, which are 40 and 45.
So, Q1 is 42.5.
Similarly, we need to find the upper quartile (Q3), which is the median of the upper half of the dataset.
The upper half of the dataset is 50, 55, 60, 60, 65, and 70.
To find the median of this upper half, we again take the average of the middle two values, which are 60 and 60.
So, Q3 is 60.
Therefore, the quartiles for the given dataset are:
Q1: 42.5
Q3: 60
To find the quartiles for the given dataset, we first need to organize the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Step 1: Identify the position of the first quartile (Q1).
Q1 = (n + 1) / 4
where n is the total number of data points.
In this case, n = 13.
Q1 = (13 + 1) / 4
Q1 = 14 / 4
Q1 = 3.5
Since Q1 is not an integer, we need to interpolate between the values at positions 3 and 4 to find Q1.
Step 2: Interpolate to find Q1.
Q1 = value at position 3 + (position of Q1 - position of value at position 3) * (value at position 4 - value at position 3)
Q1 = 40 + (3.5 - 3) * (45 - 40)
Q1 = 40 + 0.5 * 5
Q1 = 40 + 2.5
Q1 = 42.5
So, Q1 is 42.5