Solved on Oct 22, 2023

Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: $7, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 55$ .

STEP 1

Assumptions1. The data set is7,21,28,18,29,31,47,18,40,29,32,36,48,46,55. The problem solving method to be used is to be determined from the options A. Be Systematic, B. Guessing is OK, C. Draw Pictures, D. The Order Principle3. The five-number summary includes the minimum, first quartile (Q1), median (Q), third quartile (Q3), and maximum.
4. The box-and-whisker plot is a graphical representation of the five-number summary.

STEP 2

The problem solving method to use in this case is A. Be Systematic. This is because we need to organize the data in a systematic way to find the five-number summary and draw the box-and-whisker plot.

STEP 3

First, we need to arrange the data in ascending order.
$7,18,18,21,28,29,29,31,32,36,40,46,47,48,55$

STEP 4

To find the five-number summary, we first need to find the minimum value. This is the smallest number in the data set.
$Minimum =7$

STEP 5

Next, we find the first quartile (Q1). This is the median of the lower half of the data (not including the median of the entire data set if the number of data points is odd). Since we have15 data points, the lower half is the first7 numbers.
$Q1 = Median\, of\, (7,18,18,21,28,29,29)$

STEP 6

Calculate the first quartile (Q1).
$Q1 =21$

STEP 7

The median (Q2) is the middle number of the data set. Since we have15 data points, the median is theth number.
$Q2 =31$

STEP 8

The third quartile (Q3) is the median of the upper half of the data (not including the median of the entire data set if the number of data points is odd). Since we have15 data points, the upper half is the last7 numbers.
$Q3 = Median\, of\, (32,36,40,46,47,48,55)$

STEP 9

Calculate the third quartile (Q3).
$Q3 =46$

STEP 10

Finally, the maximum is the largest number in the data set.
$Maximum =55$

STEP 11

The five-number summary of the data set is therefore $Minimum =7$ $Q =21$ $Q =31$ $Q3 =46$ $Maximum =55$

STEP 12

To draw the box-and-whisker plot, we first draw a number line that includes the range of our data set.

STEP 13

We then mark the five numbers from our five-number summary on the number line.

STEP 14

Next, we draw a box from Q to Q3 and draw a line through the box at Q2 (the median).

STEP 15

Finally, we draw lines (whiskers) from the box to the minimum and maximum values.
The box-and-whisker plot gives a visual representation of the five-number summary and the distribution of the data set.

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Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: $7, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 55$ .

STEP 1

STEP 2

The problem solving method to use in this case is A. Be Systematic. This is because we need to organize the data in a systematic way to find the five-number summary and draw the box-and-whisker plot.

STEP 3

First, we need to arrange the data in ascending order.
$7,18,18,21,28,29,29,31,32,36,40,46,47,48,55$

STEP 4

To find the five-number summary, we first need to find the minimum value. This is the smallest number in the data set.
$Minimum =7$

STEP 5

Next, we find the first quartile (Q1). This is the median of the lower half of the data (not including the median of the entire data set if the number of data points is odd). Since we have15 data points, the lower half is the first7 numbers.
$Q1 = Median\, of\, (7,18,18,21,28,29,29)$

STEP 6

Calculate the first quartile (Q1).
$Q1 =21$

STEP 7

The median (Q2) is the middle number of the data set. Since we have15 data points, the median is theth number.
$Q2 =31$

STEP 8

The third quartile (Q3) is the median of the upper half of the data (not including the median of the entire data set if the number of data points is odd). Since we have15 data points, the upper half is the last7 numbers.
$Q3 = Median\, of\, (32,36,40,46,47,48,55)$

STEP 9

Calculate the third quartile (Q3).
$Q3 =46$

STEP 10

Finally, the maximum is the largest number in the data set.
$Maximum =55$

STEP 11

The five-number summary of the data set is therefore $Minimum =7$ $Q =21$ $Q =31$ $Q3 =46$ $Maximum =55$

STEP 12

To draw the box-and-whisker plot, we first draw a number line that includes the range of our data set.

STEP 13

We then mark the five numbers from our five-number summary on the number line.

STEP 14

Next, we draw a box from Q to Q3 and draw a line through the box at Q2 (the median).

STEP 15

Finally, we draw lines (whiskers) from the box to the minimum and maximum values.
The box-and-whisker plot gives a visual representation of the five-number summary and the distribution of the data set.

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Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: 7,21,28,18,29,31,47,18,40,29,32,36,48,46,557, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 557,21,28,18,29,31,47,18,40,29,32,36,48,46,55.

STEP 1

STEP 2

The problem solving method to use in this case is A. Be Systematic. This is because we need to organize the data in a systematic way to find the five-number summary and draw the box-and-whisker plot.

STEP 3

First, we need to arrange the data in ascending order.7,18,18,21,28,29,29,31,32,36,40,46,47,48,557,18,18,21,28,29,29,31,32,36,40,46,47,48,557,18,18,21,28,29,29,31,32,36,40,46,47,48,55

STEP 4

To find the five-number summary, we first need to find the minimum value. This is the smallest number in the data set.Minimum=7Minimum =7Minimum=7

STEP 5

STEP 6

Calculate the first quartile (Q1).Q1=21Q1 =21Q1=21

STEP 7

The median (Q2) is the middle number of the data set. Since we have15 data points, the median is theth number.Q2=31Q2 =31Q2=31

STEP 8

STEP 9

Calculate the third quartile (Q3).Q3=46Q3 =46Q3=46

STEP 10

Finally, the maximum is the largest number in the data set.Maximum=55Maximum =55Maximum=55

STEP 11

The five-number summary of the data set is thereforeMinimum=7Minimum =7Minimum=7Q=21Q =21Q=21Q=31Q =31Q=31Q3=46Q3 =46Q3=46Maximum=55Maximum =55Maximum=55

STEP 12

To draw the box-and-whisker plot, we first draw a number line that includes the range of our data set.

STEP 13

We then mark the five numbers from our five-number summary on the number line.

STEP 14

Next, we draw a box from Q to Q3 and draw a line through the box at Q2 (the median).

STEP 15

Finally, we draw lines (whiskers) from the box to the minimum and maximum values.The box-and-whisker plot gives a visual representation of the five-number summary and the distribution of the data set.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine the appropriate problem-solving method to find the five-number summary and draw a box-and-whisker plot for the given data: $7, 21, 28, 18, 29, 31, 47, 18, 40, 29, 32, 36, 48, 46, 55$ .

First, we need to arrange the data in ascending order.
$7,18,18,21,28,29,29,31,32,36,40,46,47,48,55$

To find the five-number summary, we first need to find the minimum value. This is the smallest number in the data set.
$Minimum =7$

Calculate the first quartile (Q1).
$Q1 =21$

The median (Q2) is the middle number of the data set. Since we have15 data points, the median is theth number.
$Q2 =31$

Calculate the third quartile (Q3).
$Q3 =46$

Finally, the maximum is the largest number in the data set.
$Maximum =55$

The five-number summary of the data set is therefore $Minimum =7$ $Q =21$ $Q =31$ $Q3 =46$ $Maximum =55$

Finally, we draw lines (whiskers) from the box to the minimum and maximum values.
The box-and-whisker plot gives a visual representation of the five-number summary and the distribution of the data set.