Find Q1 and Q3 for this set of values:
36, 38, 42, 47, 51, 56, 62, 69, 70, 74.
Q1 (first quartile) is the median of the lower half of the data set.
To find Q1:
1. Put the numbers in order from least to greatest:
36, 38, 42, 47, 51, 56, 62, 69, 70, 74
2. Find the median of the lower half of the data set.
The lower half of the data set is: 36, 38, 42, 47, 51
So the median of the lower half is the middle number, which is 42.
Therefore, Q1 is 42.
Q3 (third quartile) is the median of the upper half of the data set.
To find Q3:
1. Put the numbers in order from least to greatest:
36, 38, 42, 47, 51, 56, 62, 69, 70, 74
2. Find the median of the upper half of the data set.
The upper half of the data set is: 56, 62, 69, 70, 74
So the median of the upper half is the middle number, which is 69.
Therefore, Q3 is 69.
To find Q1 and Q3 for this set of values, you need to follow these steps:
Step 1: Arrange the numbers in ascending order:
36, 38, 42, 47, 51, 56, 62, 69, 70, 74
Step 2: Find the median of the lower half of the data set (Q1):
Since there are an even number of values (10), the median of the lower half will be the average of the 5th and 6th values.
Q1 = (42 + 47) / 2 = 44.5
Step 3: Find the median of the upper half of the data set (Q3):
Q3 = (62 + 69) / 2 = 65.5
Therefore, Q1 is 44.5 and Q3 is 65.5 for this data set.
To find Q1 and Q3 for a set of values, we need to first arrange the values in ascending order:
36, 38, 42, 47, 51, 56, 62, 69, 70, 74
Q1 represents the lower quartile, which splits the lower 25% of the data from the rest. To find Q1, we need to first find the position of Q1 in the ordered set. The position of Q1 can be calculated using the formula:
Position of Q1 = (25/100) * (n+1)
where 'n' is the total number of values in the set. In our case, n = 10.
Position of Q1 = (25/100) * (10+1) = (25/100) * (11) = 2.75
Since the position is not a whole number, we need to take the average of the values at the 2nd and 3rd position to find Q1.
The 2nd position is the value at index 2, which is 38.
The 3rd position is the value at index 3, which is 42.
Q1 = (38 + 42) / 2 = 80 / 2 = 40
Therefore, Q1 for this set of values is 40.
Similarly, Q3 represents the upper quartile, which splits the upper 25% of the data from the rest. To find Q3, we can use the same approach.
Position of Q3 = (75/100) * (n+1)
Position of Q3 = (75/100) * (10+1) = (75/100) * (11) = 8.25
Again, since the position is not a whole number, we take the average of the values at the 8th and 9th position.
The 8th position is the value at index 8, which is 69.
The 9th position is the value at index 9, which is 70.
Q3 = (69 + 70) / 2 = 139 / 2 = 69.5
Therefore, Q3 for this set of values is 69.5.