2.3: tomato plants: box plot\na box - plot can also be used to represent the distribution of numerical…

2.3: tomato plants: box plot\na box - plot can also be used to represent the distribution of numerical data.\n1. using the same data as in the previous activity for tomato plants, find the median, and add it to the table. what does the median represent for these data?\n2. find the median of the least 15 values to split the data into the first and second quarters. this value is called the first quartile. add this value to the table under q1. what does this value mean in this situation?\n3. find the value (the third quartile) that splits the data into the third and fourth quarters, and add it to the table under q3. add the minimum and maximum values to the table.\n|minimum|q1|median|q3|maximum|\n|----|----|----|----|----|\n|45|62|70|80|90|

2.3: tomato plants: box plot\na box - plot can also be used to represent the distribution of numerical data.\n1. using the same data as in the previous activity for tomato plants, find the median, and add it to the table. what does the median represent for these data?\n2. find the median of the least 15 values to split the data into the first and second quarters. this value is called the first quartile. add this value to the table under q1. what does this value mean in this situation?\n3. find the value (the third quartile) that splits the data into the third and fourth quarters, and add it to the table under q3. add the minimum and maximum values to the table.\n|minimum|q1|median|q3|maximum|\n|----|----|----|----|----|\n|45|62|70|80|90|

Answer

Explanation:

Step1: Recall median definition

The median is the middle - value of a data set. For an ordered data set with (n) values, if (n) is odd, the median is the (\left(\frac{n + 1}{2}\right))-th value; if (n) is even, the median is the average of the (\frac{n}{2})-th and (\left(\frac{n}{2}+1\right))-th values. In a box - plot, the median divides the data set into two halves.

Step2: Answer question 1

The median represents the middle - value of the data set. It splits the data into two equal - sized parts (half of the data values are less than or equal to the median and half are greater than or equal to the median).

Step3: Recall first - quartile definition

The first quartile ((Q1)) is the value that splits the lower half of the data into two equal parts. It represents the 25th percentile of the data set, meaning 25% of the data values are less than or equal to (Q1).

Step4: Answer question 2

Adding the first - quartile value to the table under (Q1) and considering the context, the value of (Q1) (62) means that 25% of the data values for tomato plants are less than or equal to 62. In this situation, it is the value that marks the boundary of the first 25% of the ordered data values.

Step5: Recall third - quartile definition

The third quartile ((Q3)) is the value that splits the upper half of the data into two equal parts. It represents the 75th percentile of the data set, so 75% of the data values are less than or equal to (Q3).

Step6: Answer question 3

The value of (Q3) (80) splits the data into the third and fourth quarters. When we add the minimum (45) and maximum (90) values to the table, we have a complete five - number summary for the data set of tomato plants.

Answer:

  1. The median represents the middle - value of the data set for tomato plants. It divides the data into two equal halves such that 50% of the data values are less than or equal to it and 50% are greater than or equal to it.
  2. The value of (Q1 = 62) means that 25% of the data values for tomato plants are less than or equal to 62. In the context of splitting the data into quarters, it marks the boundary of the first 25% of the ordered data values.
  3. The value of (Q3 = 80) splits the data into the third and fourth quarters. Adding the minimum value 45 and the maximum value 90 to the table gives a complete five - number summary for the data set of tomato plants.