In the small town of Middleton, there are only two restaurants that serve pizza- a small family-owned Italian restaurant and a new franchise pizza restaurant. In a recent review of the franchise, a food critic reported that the pizza was delicious as promised. The only negative review that the franchise received from the critic was about the inaccurate delivery time quoted during the online order process. In response to the article, the franchise owner used a program to analyze the online pizza orders that took place during the week before the review. He chose to track the orders at 6 pm each day. He recorded his results in the frequency table below.
Monday Tuesday Wednesday Thursday Friday
On-Time ||| ||
Late | ||| ||||
Use the frequency table to create a box and whisker plot of the On-Time data values. In your final answer, include all calculations necessary to create the box and whisker plot.
Use the frequency table to create a box and whisker plot of the Late data values. In your final answer, include all calculations necessary to create the box and whisker plot.
what was the answer
To create a box and whisker plot of the On-Time data values, we need to calculate the minimum, maximum, median, lower quartile (Q1), and upper quartile (Q3).
Looking at the frequency table, we can see that there are 3 on-time deliveries on Monday and 2 on-time deliveries on Tuesday.
To find the minimum value, we need to identify the day with the minimum number of on-time deliveries. In this case, it is Monday with 3 on-time deliveries.
To find the maximum value, we need to identify the day with the maximum number of on-time deliveries. In this case, it is Tuesday with 2 on-time deliveries.
Now, let's calculate the median. The median is the middle value when the data is arranged in ascending order. Since we have an even number of data points (3 + 2 = 5), the median is the average of the two middle values.
Arranging the data in ascending order, we get: 2, 2, 3.
Now we can calculate the median: (2 + 3) / 2 = 2.5.
The lower quartile (Q1) is the median of the lower half of the data. In this case, we only have two data points in the lower half, so Q1 is simply the minimum value, which is 2.
The upper quartile (Q3) is the median of the upper half of the data. In this case, we only have two data points in the upper half, so Q3 is simply the maximum value, which is 3.
Now let's summarize the values we calculated to create the box and whisker plot:
Minimum: 2
Q1: 2
Median: 2.5
Q3: 3
Maximum: 3
To create the box and whisker plot, draw a number line and plot the minimum, Q1, median, Q3, and maximum as points. Then connect the points to form a box using a solid line. Finally, draw whiskers (lines) extending from the box to the minimum and maximum values.
Now, let's move on to creating a box and whisker plot of the Late data values.
Looking at the frequency table, we can see that there are 1 late delivery on Monday, 3 late deliveries on Wednesday, and 4 late deliveries on Friday.
To find the minimum value, we need to identify the day with the minimum number of late deliveries. In this case, it is Monday with 1 late delivery.
To find the maximum value, we need to identify the day with the maximum number of late deliveries. In this case, it is Friday with 4 late deliveries.
Now, let's calculate the median. The median is the middle value when the data is arranged in ascending order. Since we have an odd number of data points (1 + 3 + 4 = 8), the median is the middle value.
Arranging the data in ascending order, we get: 1, 3, 4.
The median is 3.
The lower quartile (Q1) is the median of the lower half of the data. In this case, we have five data points in the lower half, so the median is the average of the two middle values.
Arranging the data in ascending order, we get: 1, 1, 3.
Now we can calculate the median: (1 + 3) / 2 = 2.
The upper quartile (Q3) is the median of the upper half of the data. In this case, we have three data points in the upper half, so the median is simply the maximum value, which is 4.
Now let's summarize the values we calculated to create the box and whisker plot:
Minimum: 1
Q1: 2
Median: 3
Q3: 4
Maximum: 4
To create the box and whisker plot, draw a number line and plot the minimum, Q1, median, Q3, and maximum as points. Then connect the points to form a box using a solid line. Finally, draw whiskers (lines) extending from the box to the minimum and maximum values.
That's it! You've now created box and whisker plots for both the On-Time and Late data values based on the frequency table.