Given the following dataset, what are the extremes?
58, 32, 8, 25, 13, 12, 3, 11, 22, 10(1 point)
The smallest extreme value is
.
The largest extreme value is
.
The smallest extreme value is 3.
The largest extreme value is 58.
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)
To find the first quartile, we need to arrange the dataset in ascending order:
17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82
There are 11 numbers in the dataset, so the first quartile is located at the (11 + 1)/4 = 3rd data point.
The first quartile is 20.
The amounts of rainfall measured in inches in downtown Los Angeles during the six rainy seasons from 2000 to 2006 are given as a dataset.
15.56, 4.16, 10.38, 8.61, 26.51, 10.89
Find the range of this dataset.
(1 point)
The range of this dataset is
.
To find the range of a dataset, we need to subtract the smallest value from the largest value.
In this dataset, the smallest value is 4.16 and the largest value is 26.51.
Therefore, the range of the dataset is 26.51 - 4.16 = 22.35.
The average temperatures in December in Washington, D.C., from 1993 to 1998 are given as a dataset.
38.1, 44.2, 35.6, 43.0, 41.0, 44.4
Find the interquartile range of the dataset.
(1 point)
The interquartile range of the dataset is
.
To find the interquartile range of a dataset, we first need to find the values of the first quartile (Q1) and the third quartile (Q3).
To do that, we need to arrange the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
There are 6 numbers in the dataset, so the first quartile is located at the (6 + 1)/4 = 1.75th data point. Since it is not an integer, we can use linear interpolation to estimate the value of Q1.
Q1 = 38.1 + 0.75 * (41.0 - 38.1) = 38.1 + 0.75 * 2.9 = 38.1 + 2.175 = 40.275
The third quartile is located at the 3 * (6 + 1)/4 = 3.75th data point. Using linear interpolation:
Q3 = 43.0 + 0.75 * (44.2 - 43.0) = 43.0 + 0.75 * 1.2 = 43.0 + 0.9 = 43.9
Finally, the interquartile range is calculated as Q3 - Q1:
Interquartile range = 43.9 - 40.275 = 3.625.
wrong
Apologies for the mistake. Let's try again to find the interquartile range of the given dataset.
To find the interquartile range, we need to first find the first quartile (Q1) and the third quartile (Q3).
To do that, we need to arrange the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
Next, we need to find the median (Q2), which is the value right in the middle of the dataset. Since we have an even number of values, we find the median by taking the average of the two middle values:
(Q2) = (41.0 + 43.0) / 2 = 42.0
Next, we find the first quartile (Q1), which is the median of the lower half of the dataset:
Q1 = (35.6 + 38.1) / 2 = 36.85
Finally, we find the third quartile (Q3), which is the median of the upper half of the dataset:
Q3 = (44.2 + 44.4) / 2 = 44.3
The interquartile range is calculated as Q3 - Q1:
Interquartile range = 44.3 - 36.85 = 7.45