The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.
Numbers for the box&whisker: 51,54,57,60,63,66,69,72,75,78,81,84
You can do a box&whisker here:
alcula box plot
Which statement about the temperatures in Orlando must be true?
A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.
It’s B
D. The hottest day in December was 75 degrees.
To determine which statement about the temperatures in Orlando must be true, we can analyze the given box-and-whisker plot. Here is a step-by-step explanation:
Step 1: Identify the minimum and maximum values
Looking at the plot, the "whiskers" (the lines extending from the box) show the minimum and maximum values. In this case, the minimum value is 51 degrees, and the maximum value is 84 degrees.
Step 2: Identify the first and third quartiles
The box in the plot represents the interquartile range (IQR), which contains the middle 50% of the data. The line in the middle of the box represents the median, which divides the data in half. In this case, the first quartile is 60 degrees, and the third quartile is 78 degrees.
Step 3: Answer the question
Now that we have the relevant values, we can determine which statement must be true:
A. About half of the days in January had average temperatures above 75 degrees.
This statement is false. The box is located between the first quartile (60 degrees) and the third quartile (78 degrees), which contains the middle 50% of the data. Therefore, only about 25% of the data, or one quarter of the days, had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
This statement is also false. The box does not start at 66 degrees; instead, it starts at 60 degrees. Therefore, it is not accurate to say that about 50% of the days had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
This statement is false. The minimum value in the plot is 51 degrees, which means that the coldest day in January was colder than 66 degrees.
D. The hottest day in December was 75 degrees.
This statement is true. The maximum value in the plot is 84 degrees, which means that the hottest day in January had a temperature of 75 degrees.
Therefore, the correct answer is option D. The hottest day in December was 75 degrees.
To answer this question, let's analyze the given box-and-whisker plot.
First, we need to understand how to interpret a box-and-whisker plot. A box-and-whisker plot displays the distribution of a dataset and provides information about its median, quartiles, and any outliers. The plot consists of a box that represents the middle 50% of the data, with the median inside the box. The whiskers extend from the box and represent the range of the data, excluding any outliers.
Looking at the given box-and-whisker plot, we can identify the following information:
- The lower quartile (Q1) is represented by the left side of the box, which is around 57.
- The median (Q2) is represented by the line inside the box, which is around 66.
- The upper quartile (Q3) is represented by the right side of the box, which is around 75.
- The whiskers extend from the box to the minimum and maximum data points, which are 51 and 84, respectively.
Now, let's evaluate each statement:
A. About half of the days in January had average temperatures above 75 degrees.
To determine if this statement is true, we need to check if the median (Q2) is above 75 degrees. In this case, the median is around 66 degrees, so it can be concluded that this statement is NOT true.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
To determine if this statement is true, we need to check if the range of temperatures between Q2 (66) and Q3 (75) covers the middle 50% of the data. Since the box represents the middle 50% and Q2 and Q3 fall within that range, this statement is TRUE.
C. The coldest day in January was 66 degrees.
To determine if this statement is true, we need to check if the minimum value in the dataset is 66 degrees. In this case, the minimum is 51 degrees, so it can be concluded that this statement is NOT true.
D. The hottest day in December was 75 degrees.
The given data is for January, not December. Therefore, this statement is not relevant to the information provided.
In summary, the statement that MUST be true based on the given box-and-whisker plot is:
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.