A movie theater recorded the number of tickets sold daily for a popular movie during the month of June. A box-and-whisker plot represents the number of tickets sold.
minimum-100
maximum-8
1st quartile-300
median-400
3rd quartile-600
Which conclusion can be made using this plot?
a. the second quartile is 600.
b. the mean of the attendance is 400.
c. the range of the attendance is 300 to 600.
d. twenty-five percent of the attendance is between 300 and 400.
The answer is d., but I don't know why
First of all, some of your information is reversed. The maximum (most) = 100 and the minimum (least) = 8.
Also, if the 3rd quartile is 600, the maximum must be greater than 600. Does the maximum = 1000? Especially with math problems, you need to be more accurate in providing your information.
Each quartile is 25% (one quarter) of the scores. The median is the second quartile (50%).
I hope this helps. Thanks for asking.
thanks
To understand why the correct answer is d., let's first review some basic concepts related to box-and-whisker plots:
- The minimum value represents the lowest data point, in this case, 100 tickets.
- The maximum value represents the highest data point, in this case, 800 tickets.
- The first quartile (Q1) represents the median of the lower half of the data, and in this case, it is 300 tickets.
- The third quartile (Q3) represents the median of the upper half of the data, and in this case, it is 600 tickets.
- The median (also known as the second quartile, Q2) represents the middle value of the data set when it is arranged in order, and in this case, it is 400 tickets.
Now, let's analyze the given options:
a. The second quartile is 600: This is not correct because the second quartile, or median, is given as 400 tickets, not 600.
b. The mean of the attendance is 400: The box-and-whisker plot does not provide information about the mean (average) of the data, so this option cannot be determined based on the given plot.
c. The range of the attendance is 300 to 600: The range is calculated as the difference between the maximum and minimum values. In this case, the range is 800 - 100 = 700, not 300 to 600. Therefore, this option is incorrect.
d. Twenty-five percent of the attendance is between 300 and 400: This is the correct answer. Since the first quartile (Q1) is given as 300 tickets and the median (Q2) is given as 400 tickets, we know that 25% of the data falls between these two values. Therefore, this option is the correct conclusion that can be made based on the given plot.
Overall, the correct conclusion based on the box-and-whisker plot is that twenty-five percent of the attendance is between 300 and 400 tickets.
To determine the answer, let's go through the provided information and understand each statistic in the box-and-whisker plot.
The box-and-whisker plot provides a visual representation of the distribution of the data, including five key statistics: minimum, maximum, quartiles (including the median).
- Minimum: The minimum value in the dataset is 100, indicating that the lowest number of tickets sold on any given day in June was 100.
- Maximum: The maximum value in the dataset is 800, indicating that the highest number of tickets sold on any given day in June was 800.
- 1st Quartile: The 1st quartile is 300, which means that 25% of the data falls below this value. In other words, 25% of the days in June had ticket sales of 300 or less.
- Median: The median is 400, which represents the middle value of the dataset when arranged in ascending order. It divides the data into two equal halves, indicating that 50% of the days had ticket sales below 400, and 50% had ticket sales above 400.
- 3rd Quartile: The 3rd quartile is 600, which means that 75% of the data falls below this value. In other words, 75% of the days in June had ticket sales of 600 or less.
Now, let's analyze the options given:
a. The second quartile is 600: This statement is not accurate because the median (second quartile) is given as 400, not 600.
b. The mean of attendance is 400: The mean (average) of the attendance is not given in the information provided, so we cannot determine whether this statement is true or false.
c. The range of attendance is 300 to 600: The range of attendance is calculated as the difference between the maximum and minimum values, which is 800 - 100 = 700. Therefore, this statement is false.
d. Twenty-five percent of attendance is between 300 and 400: This statement is accurate because the 1st quartile is given as 300 and the median (2nd quartile) is given as 400. Since the quartiles represent dividing the data into 25% intervals, it is true to say that 25% of the attendance is between 300 and 400.
Therefore, the correct conclusion from the box-and-whisker plot is that twenty-five percent of the attendance is between 300 and 400 (option d).