Identify the first quartile in the following dataset:
5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6(1 point)
Responses
6.5
6.5
4
4
0
0
2.5
@bot what is the answer
The first quartile in the given dataset is 2.5.
but why and how
To find the first quartile, we need to arrange the dataset in ascending order:
0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11, 12
Then, we need to find the median of the lower half of the data (the first quarter). Since there are 16 data points in the dataset, the median of the lower half is the middle value between the 8th and 9th number.
The 8th number is 4 and the 9th number is 5. So the median of the lower half is (4+5)/2 = 4.5. This is the first quartile.
However, since the dataset contains even number of values, some sources calculate the first quartile as the median of the first half of the data, excluding the median value itself. In this case, the first quartile would be the median of the first 8 numbers, which is (2+2)/2 = 2. Therefore, the first quartile could be reported as either 2 or 4.5 depending on the convention used.
their are 15 data pointss
I apologize for the error. Since there are 15 data points in the given dataset, to find the first quartile, we follow the same steps. We arrange the dataset in ascending order:
0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11
Then, we need to find the median of the lower half of the data (the first quarter). Since there are 15 data points in the dataset, the median of the lower half is the middle value, which is the 8th value.
The 8th value is 4. Therefore, the first quartile is 4.
Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
(1 point)
Responses
6.5
6.5
8
8
13.5
13.5
21.5
To find the interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3).
To find Q1:
1. Arrange the data set in ascending order: 11, 13, 14, 15, 17, 21, 22, 27
2. Find the median of the lower half of the data set. Since there are 8 values, we find the median of the first 4: (13+14)/2 = 13.5
Therefore, Q1 = 13.5
To find Q3:
1. Arrange the data set in ascending order: 11, 13, 14, 15, 17, 21, 22, 27
2. Find the median of the upper half of the data set. Since there are 8 values, we find the median of the last 4: (21+22)/2 = 21.5
Therefore, Q3 = 21.5
Now we can find the interquartile range:
IQR = Q3 - Q1
IQR = 21.5 - 13.5
IQR = 8
Therefore, the interquartile range of the given dataset is 8.
Consider the following dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25. What is the third quartile’s value? Round to the nearest tenth if necessary.(1 point)
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 first need to arrange the dataset in ascending order:
17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82
The dataset has 11 values, so Q1 will be the median of the first half of the dataset.
Q1 = median of {17, 18, 20, 34, 42}.
The median of this dataset can be obtained as follows:
median = (20+34)/2 = 27
Therefore, the first quartile is 27 (rounded to the nearest whole number).
incorrect
I apologize for the error in my previous response.
To find the first quartile, we first need to arrange the dataset in ascending order:
17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82
The dataset has 11 values, so Q1 will be the median of the first half of the dataset.
Q1 = median of {17, 18, 20, 34, 42}
The median of this dataset can be obtained as follows:
median = (20 + 34)/2 = 27
Therefore, the first quartile is 27 (rounded to the nearest whole number).
I apologize for any confusion caused by my previous response.
he 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 the given dataset, we need to subtract the smallest value in the dataset from the largest value.
In this case, the smallest value is 4.16 and the largest value is 26.51.
Therefore, the range of the dataset is calculated as follows:
Range = Largest value - Smallest value
Range = 26.51 - 4.16
Range = 22.35
So, the range of the given dataset is 22.35 inches.
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 need to first compute the first quartile (Q1) and the third quartile (Q3).
1. To find Q1, we need to find the median of the lower half of the dataset. The dataset has an even number of values, so we take the average of the two middle values. First, we need to arrange the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
The lower half of the dataset is {35.6, 38.1, 41.0}. Since this set has an odd number of values, the median is simply the middle value, which is 38.1. Therefore, Q1 = 38.1.
2. To find Q3, we need to find the median of the upper half of the dataset. The upper half of the dataset is {43.0, 44.2, 44.4}. This set has an odd number of values, so the median is the middle value, which is 44.2. Therefore, Q3 = 44.2.
Now that we have Q1 and Q3, we can find the interquartile range (IQR) as follows:
IQR = Q3 - Q1
IQR = 44.2 - 38.1
IQR = 6.1
Therefore, the interquartile range of the given dataset is 6.1.
To find the third quartile, we need to find the median of the upper half of the dataset.
1. First, we need to find the median of the entire dataset. To do this, we arrange the data in numerical order:
18, 20, 22, 22, 24, 25, 29, 30, 31
The median of this dataset is the middle value, which is 24.
2. Next, we split the dataset into two halves: one with values below the median and one with values above the median:
Dataset below median (first quartile):
18, 20, 22, 22, 24
Dataset above median:
25, 29, 30, 31
3. To find the third quartile (Q3), we need to find the median of the upper half of the dataset:
Median of the dataset above the median = (29 + 30)/2 = 29.5
So the third quartile (Q3) is 29.5.
Therefore, the third quartile’s value is 29.5.