Box Plots Practice
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Question
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An illustration shows a number line ranging from 0 to 12 in one unit increments. Each number is labeled and represented with a tick mark. A box plot is placed above the number line. The box is divided into two sections.
The first section of the box plot extends from 1.5 to 3. The second section of the box plot extends from 3 to 7.5. A line starts at the left side of the first section of the box plot and extends from 1.5 to 0, where it ends with a short vertical line. Another line starts at the right side of the second section of the box plot and extends from 7.5 to 12, where it ends with a short vertical line.
Evita constructs this box plot to show how many home runs each of her baseball teammates hit this year.
What values are the first and third quartiles of this dataset?
(1 point)
first quartile =
, third quartile =
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11 answers
The first quartile is represented by the lower boundary of the second section of the box plot, which is at 3.
The third quartile is represented by the upper boundary of the second section of the box plot, which is at 7.5.
Therefore, the first quartile is 3 and the third quartile is 7.5.
In this case, the first quartile is located at the lower boundary of the first section of the box plot, which is at 1.5.
The third quartile is located at the upper boundary of the second section of the box plot, which is at 7.5.
Therefore, the first quartile is 1.5 and the third quartile is 7.5.
Step 1: Order the dataset in ascending order:
23, 24, 25, 26, 27, 28
Step 2: Find the median, which is the middle value of the dataset:
Since the dataset has an even number of values, the median is the average of the two middle values: (25 + 26) / 2 = 25.5
Step 3: Find Q1 and Q3:
For Q1, we look at the values below the median:
Q1 = (23 + 24) / 2 = 23.5
For Q3, we look at the values above the median:
Q3 = (27 + 28) / 2 = 27.5
Now, we have the values to complete the box plot:
Lower whisker: 23
Q1: 23.5
Median: 25.5
Q3: 27.5
Upper whisker: 28
So, the completed box plot for the dataset {23, 24, 25, 26, 27, 28} would have the following values:
Lower whisker: 23
Q1: 23.5
Median: 25.5
Q3: 27.5
Upper whisker: 28
Step 1: Order the dataset in ascending order:
23, 24, 25, 26, 27, 28
Step 2: Find the median, which is the middle value of the dataset:
Since the dataset has an even number of values, the median is the average of the two middle values: (25 + 26) / 2 = 25.5
Step 3: Find Q1 and Q3:
For Q1, we look at the values below the median:
Q1 = (23 + 24) / 2 = 23.5
For Q3, we look at the values above the median:
Q3 = (27 + 28) / 2 = 27.5
Therefore, the first quartile (Q1) is 24 and the third quartile (Q3) is 27.
Step 1: Order the dataset in ascending order:
32, 34, 36, 38, 40, 42, 44, 46, 48
Step 2: Find the minimum, maximum, median, Q1, and Q3:
Minimum: 32
Maximum: 48
Median: The middle value of the dataset is the average of the two middle values (40 and 42): (40 + 42) / 2 = 41
Q1: The median of the lower half of the dataset (32, 34, 36, 38, 40): (34 + 36) / 2 = 35
Q3: The median of the upper half of the dataset (42, 44, 46, 48): (44 + 46) / 2 = 45
Therefore, the completed box plot for the dataset {32, 34, 36, 38, 40, 42, 44, 46, 48} would have the following values:
Lower whisker: 32
Q1: 35
Median: 41
Q3: 45
Upper whisker: 48
Step 1: Order the dataset in ascending order:
32, 34, 36, 38, 40, 42, 44, 46, 48
Step 2: Find the median, which is the middle value of the dataset:
Since the dataset has an odd number of values, the median is the middle value, which is 40.
Step 3: Find Q1 and Q3:
Q1 is the median of the lower half of the dataset (32, 34, 36, 38, 40): (34 + 36) / 2 = 35
Q3 is the median of the upper half of the dataset (42, 44, 46, 48): (44 + 46) / 2 = 45
Therefore, the values to complete the box plot for the dataset {32, 34, 36, 38, 40, 42, 44, 46, 48} are:
Lower whisker: 32
Q1: 35
Median: 40
Q3: 45
Upper whisker: 48
I hope this helps!