Math / Data & Statistics

QuestionConstruct a boxplot for the data set below. \begin{tabular}{rrrrr} \hline 32 & 29 & 19 & 5 & 8 \\ 19 & 35 & 7 & 13 & 17 \\ 17 & 11 & 17 & 17 & 5 \\ 8 & 14 & 14 & 14 & 10 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The data set consists of 20 numerical values.
2. A boxplot (box-and-whisker plot) represents the distribution of the data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
3. The data set needs to be sorted in ascending order to identify quartiles and other summary statistics.

STEP 2

1. Sort the data set in ascending order.
2. Find the minimum and maximum values.
3. Determine the first quartile (Q1), median (Q2), and third quartile (Q3).
4. Construct the boxplot using the five-number summary.

STEP 3

Sort the data set in ascending order.
$\{5, 5, 7, 8, 8, 10, 11, 13, 14, 14, 14, 17, 17, 17, 17, 19, 19, 29, 32, 35\}$

STEP 4

Identify the minimum value in the sorted data set.
$\text{Minimum} = 5$

STEP 5

Identify the maximum value in the sorted data set.
$\text{Maximum} = 35$

STEP 6

Determine the median (Q2), which is the middle value of the sorted data set. Since there are 20 values, the median is the average of the 10th and 11th values.
$\text{Median} (Q2) = \frac{14 + 14}{2} = 14$

STEP 7

Determine the first quartile (Q1), which is the median of the first half of the data set (excluding the median if the number of observations is odd). The first half consists of the first 10 values.
$\text{Q1} = \frac{8 + 10}{2} = 9$

STEP 8

Determine the third quartile (Q3), which is the median of the second half of the data set (excluding the median if the number of observations is odd). The second half consists of the last 10 values.
$\text{Q3} = \frac{17 + 17}{2} = 17$

STEP 9

Summarize the five-number summary: minimum, Q1, median (Q2), Q3, and maximum.
$\text{Five-Number Summary: } 5, 9, 14, 17, 35$

STEP 10

Construct the boxplot using the five-number summary.
- Draw a number line that includes the range from the minimum to the maximum value. - Draw a box from Q1 to Q3. - Draw a line within the box at the median (Q2). - Draw "whiskers" from the minimum to Q1 and from Q3 to the maximum.
The boxplot should look like this:
$\begin{array}{c} \text{Boxplot:} \\ \text{Min} \quad Q1 \quad Q2 \quad Q3 \quad \text{Max} \\ |-----| \quad [9 \quad | \quad 14 \quad | \quad 17] \quad |-----| \end{array}$

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QuestionConstruct a boxplot for the data set below. \begin{tabular}{rrrrr} \hline 32 & 29 & 19 & 5 & 8 \\ 19 & 35 & 7 & 13 & 17 \\ 17 & 11 & 17 & 17 & 5 \\ 8 & 14 & 14 & 14 & 10 \\ \hline \end{tabular}

Studdy Solution

STEP 1

STEP 2

1. Sort the data set in ascending order.
2. Find the minimum and maximum values.
3. Determine the first quartile (Q1), median (Q2), and third quartile (Q3).
4. Construct the boxplot using the five-number summary.

STEP 3

Sort the data set in ascending order.
$\{5, 5, 7, 8, 8, 10, 11, 13, 14, 14, 14, 17, 17, 17, 17, 19, 19, 29, 32, 35\}$

STEP 4

Identify the minimum value in the sorted data set.
$\text{Minimum} = 5$

STEP 5

Identify the maximum value in the sorted data set.
$\text{Maximum} = 35$

STEP 6

Determine the median (Q2), which is the middle value of the sorted data set. Since there are 20 values, the median is the average of the 10th and 11th values.
$\text{Median} (Q2) = \frac{14 + 14}{2} = 14$

STEP 7

Determine the first quartile (Q1), which is the median of the first half of the data set (excluding the median if the number of observations is odd). The first half consists of the first 10 values.
$\text{Q1} = \frac{8 + 10}{2} = 9$

STEP 8

Determine the third quartile (Q3), which is the median of the second half of the data set (excluding the median if the number of observations is odd). The second half consists of the last 10 values.
$\text{Q3} = \frac{17 + 17}{2} = 17$

STEP 9

Summarize the five-number summary: minimum, Q1, median (Q2), Q3, and maximum.
$\text{Five-Number Summary: } 5, 9, 14, 17, 35$

STEP 10

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QuestionConstruct a boxplot for the data set below. \begin{tabular}{rrrrr} \hline 32 & 29 & 19 & 5 & 8 \\ 19 & 35 & 7 & 13 & 17 \\ 17 & 11 & 17 & 17 & 5 \\ 8 & 14 & 14 & 14 & 10 \\ \hline \end{tabular}

Studdy Solution

STEP 1

STEP 2

1. Sort the data set in ascending order.2. Find the minimum and maximum values.3. Determine the first quartile (Q1), median (Q2), and third quartile (Q3).4. Construct the boxplot using the five-number summary.

STEP 3

Sort the data set in ascending order.{5,5,7,8,8,10,11,13,14,14,14,17,17,17,17,19,19,29,32,35}\{5, 5, 7, 8, 8, 10, 11, 13, 14, 14, 14, 17, 17, 17, 17, 19, 19, 29, 32, 35\}{5,5,7,8,8,10,11,13,14,14,14,17,17,17,17,19,19,29,32,35}

STEP 4

Identify the minimum value in the sorted data set.Minimum=5\text{Minimum} = 5Minimum=5

STEP 5

Identify the maximum value in the sorted data set.Maximum=35\text{Maximum} = 35Maximum=35

STEP 6

Determine the median (Q2), which is the middle value of the sorted data set. Since there are 20 values, the median is the average of the 10th and 11th values.Median(Q2)=14+142=14\text{Median} (Q2) = \frac{14 + 14}{2} = 14Median(Q2)=214+14​=14

STEP 7

Determine the first quartile (Q1), which is the median of the first half of the data set (excluding the median if the number of observations is odd). The first half consists of the first 10 values.Q1=8+102=9\text{Q1} = \frac{8 + 10}{2} = 9Q1=28+10​=9

STEP 8

Determine the third quartile (Q3), which is the median of the second half of the data set (excluding the median if the number of observations is odd). The second half consists of the last 10 values.Q3=17+172=17\text{Q3} = \frac{17 + 17}{2} = 17Q3=217+17​=17

STEP 9

Summarize the five-number summary: minimum, Q1, median (Q2), Q3, and maximum.Five-Number Summary: 5,9,14,17,35\text{Five-Number Summary: } 5, 9, 14, 17, 35Five-Number Summary: 5,9,14,17,35

STEP 10

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1. Sort the data set in ascending order.
2. Find the minimum and maximum values.
3. Determine the first quartile (Q1), median (Q2), and third quartile (Q3).
4. Construct the boxplot using the five-number summary.

Sort the data set in ascending order.
$\{5, 5, 7, 8, 8, 10, 11, 13, 14, 14, 14, 17, 17, 17, 17, 19, 19, 29, 32, 35\}$

Identify the minimum value in the sorted data set.
$\text{Minimum} = 5$

Identify the maximum value in the sorted data set.
$\text{Maximum} = 35$

Determine the median (Q2), which is the middle value of the sorted data set. Since there are 20 values, the median is the average of the 10th and 11th values.
$\text{Median} (Q2) = \frac{14 + 14}{2} = 14$

Determine the first quartile (Q1), which is the median of the first half of the data set (excluding the median if the number of observations is odd). The first half consists of the first 10 values.
$\text{Q1} = \frac{8 + 10}{2} = 9$

Determine the third quartile (Q3), which is the median of the second half of the data set (excluding the median if the number of observations is odd). The second half consists of the last 10 values.
$\text{Q3} = \frac{17 + 17}{2} = 17$

Summarize the five-number summary: minimum, Q1, median (Q2), Q3, and maximum.
$\text{Five-Number Summary: } 5, 9, 14, 17, 35$