what are the quartiles for the given dataset?
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
To find the quartiles, we first need to put the data in order from smallest to largest:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
1. To find the first quartile (Q1), we find the median of the lower half of the data. Since we have 13 data points, the median is the 7th value:
Q1 = 125
2. To find the third quartile (Q3), we find the median of the upper half of the data. Again, since we have 13 data points, the median is the 7th value starting from the end:
Q3 = 136
3. To find the second quartile (Q2), we find the median of the entire data set. This is given by:
Q2 = (125 + 128) / 2 = 126.5
So the quartiles for the given dataset are Q1 = 125, Q2 = 126.5, and Q3 = 136.
To find the quartiles for the given dataset, follow these steps:
Step 1: Put the data in ascending order:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Step 2: Calculate the position of the first quartile (Q1):
n = total number of data points = 13
Q1 position = (n + 1) / 4 = (13 + 1) / 4 = 3.5
Note: Since the position is not a whole number, we need to take the average of the values at positions 3 and 4.
Step 3: Find Q1:
Q1 = (Value at position 3 + Value at position 4) / 2
= (120 + 122) / 2
= 121
Step 4: Calculate the position of the second quartile (Q2), also known as the median:
Q2 position = (n + 1) / 2 = (13 + 1) / 2 = 7
Step 5: Find Q2:
Q2 = Value at position 7
= 127
Step 6: Calculate the position of the third quartile (Q3):
Q3 position = 3 * (n + 1) / 4 = 3 * (13 + 1) / 4 = 10.5
Note: Again, since the position is not a whole number, we need to take the average of the values at positions 10 and 11.
Step 7: Find Q3:
Q3 = (Value at position 10 + Value at position 11) / 2
= (132 + 136) / 2
= 134
Therefore, the quartiles for the given dataset are:
Q1 = 121
Q2 = 127
Q3 = 134