Given the following dataset, what is the first quartile? Round to the nearest tenth if necessary.
42, 82, 67, 34, 54, 62, 17, 47, 56, 18, 20(1 point)
it is 20 the bots are Dumb :>
To find the first quartile (Q1) of a dataset, we need to arrange the data in ascending order. Here is the dataset arranged in ascending order:
17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82
To determine Q1, we need to find the median of the lower half of the dataset. Since there are 11 values in total, the lower half contains the first 5 values.
The median of the lower half is found by taking the average of the middle two values. In this case, the middle two values are 34 and 42.
(34 + 42) / 2 = 76 / 2 = 38
Therefore, the first quartile (Q1) of the given dataset is 38.
To find the first quartile, we need to organize the data in ascending order:
17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82
Since there are 11 data points, the index of the first quartile (Q1) can be found using the formula:
Index of Q1 = (n+1)/4 = (11+1)/4 = 3
The first quartile is the average of the data points at the index 3 and index 4. In this case, those data points are 20 and 34.
So, the first quartile is (20 + 34)/2 = 54/2 = 27.
Therefore, the first quartile is 27.