The following data are the numbers of cars thefts that occurred in a city in the past 11 days. 6 3 7 11 4 3 8 7 2 6 9.
calculate the values for the first and third quartiles. construct a box plot for the given data.
To calculate the first and third quartiles, we need to arrange the data in ascending order first:
2, 3, 3, 4, 6, 6, 7, 7, 8, 9, 11
Now, to find the first quartile (Q1), we need to determine the median of the lower half of the data set. Since there are an odd number of data points (11), the median will be the value in the middle, which is 6.
To find the third quartile (Q3), we need to determine the median of the upper half of the data set. Again, since there are an odd number of data points (11), the median will be the value in the middle, which is 8.
So, Q1 = 6 and Q3 = 8.
Now, let's construct a box plot for the given data:
First, determine the minimum and maximum values:
Minimum value = 2
Maximum value = 11
Next, locate the median, which is 6. Draw a vertical line through the box plot to represent the median.
Then, draw a box around the range between the first quartile (Q1 = 6) and the third quartile (Q3 = 8).
Finally, draw horizontal lines (whiskers) extending from the box to the minimum value (2) and the maximum value (11).
The resulting box plot should visually represent the distribution of the data, showing the median, quartiles, and any outliers present.