Enter the values to complete the box plot of dataset 51, 52, 53, 54, 55, 56, 57, 58. (2 points)
To create the box plot, we need to find the minimum, first quartile, median, third quartile, and maximum values of the dataset.
The given dataset is: 51, 52, 53, 54, 55, 56, 57, 58.
Step 1: Arrange the data in ascending order:
51, 52, 53, 54, 55, 56, 57, 58
Step 2: Find the minimum value (smallest value):
Minimum = 51
Step 3: Find the first quartile (25th percentile):
There are 8 data points in total, so the first quartile is the median of the lower half of the data. Since there is an even number of data points, we have to take the average of the middle two values.
First quartile = (52 + 53) / 2 = 52.5
Step 4: Find the median (second quartile, 50th percentile):
There are 8 data points, so the median is the value in the middle position.
Median = 54
Step 5: Find the third quartile (75th percentile):
The third quartile is the median of the upper half of the data. Since there is an even number of data points, we have to take the average of the middle two values.
Third quartile = (56 + 57) / 2 = 56.5
Step 6: Find the maximum value (largest value):
Maximum = 58
Now, we can complete the box plot using these values:
Minimum: 51
First quartile: 52.5
Median: 54
Third quartile: 56.5
Maximum: 58
To complete the box plot of the given dataset 51, 52, 53, 54, 55, 56, 57, 58, we need to find the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. Here's how you can calculate these values:
Step 1: Sort the dataset in ascending order:
51, 52, 53, 54, 55, 56, 57, 58
Step 2: Find the minimum: The minimum value is the first value in the sorted dataset, which is 51.
Step 3: Find Q1 (lower quartile): The lower quartile (Q1) is the median of the lower half of the dataset. Since the dataset has 8 values, the lower half would be the first 4 values. So, Q1 = median(51, 52, 53, 54) = (52 + 53) / 2 = 52.5.
Step 4: Find the median (Q2): The median (Q2) is the middle value of the dataset. Since the dataset has 8 values, the middle value would be the 4th value. So, Q2 = 54.
Step 5: Find Q3 (upper quartile): The upper quartile (Q3) is the median of the upper half of the dataset. Since the dataset has 8 values, the upper half would be the last 4 values. So, Q3 = median(55, 56, 57, 58) = (56 + 57) / 2 = 56.5.
Step 6: Find the maximum: The maximum value is the last value in the sorted dataset, which is 58.
Now you have all the values to complete the box plot:
Minimum: 51
Lower Quartile (Q1): 52.5
Median (Q2): 54
Upper Quartile (Q3): 56.5
Maximum: 58