The following data are the numbers of car 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 qualities. construct a box plot for the given data.
To calculate the values for the first and third quartiles, you need to organize the data in ascending order.
The data: 6, 3, 7, 11, 4, 3, 8, 7, 2, 6, 9
Step 1: Arrange the data in ascending order:
2, 3, 3, 4, 6, 6, 7, 7, 8, 9, 11
Step 2: Calculate the median (Q2) of the data:
Since we have an odd number of data points, the median is the middle value, which is 6.
Step 3: Calculate the first quartile (Q1):
Since we have an odd number of data points before the median, we take the middle value of the lower half, which is 3.
Step 4: Calculate the third quartile (Q3):
Since we have an odd number of data points after the median, we take the middle value of the upper half, which is 8.
The values for the first and third quartiles are Q1 = 3 and Q3 = 8, respectively.
Now, let's construct a box plot using this information:
Step 1: Draw a number line to represent the range of the data.
Step 2: Mark the minimum and maximum values. In this case, the minimum is 2, and the maximum is 11.
Step 3: Draw a box from Q1 to Q3, and draw a line inside the box to represent the median (Q2).
Step 4: Extend lines, called whiskers, from the box to the minimum and maximum values.
Step 5: Add any outliers as separate points outside the whiskers. An outlier is a value that falls significantly outside the range of the other values. In this case, there are no outliers.
Step 6: Label the axis and provide a title for the box plot.
Your completed box plot represents the distribution of car thefts for the given data.