Math / Data & Statistics

Question14. A survey was done to see the average amount of money that a single adult spends on a meal eating out. The results are below. \begin{tabular}{lllllllllll} 5 & 10 & 8 & 7 & 6 & 5 & 12 & 15 & 14 & 10 & 13 \\ 15 & 20 & 25 & 14 & 7 & 6 & 8 & 9 & 10 & 12 & 14 \\ 22 & 24 & 21 & 8 & 18 & 16 & 14 & 13 & 12 & 9 & 10 \\ 15 & 10 & 7 & 8 & 9 & 14 & 13 & 16 & 12 & 14 & 18 \\ 12 & 8 & 22 & 17 & 13 & 10 & 9 & 8 & 6 & 5 & 24 \end{tabular}
Make a box and whisker plot of the data. Find the interquartile range.

Studdy Solution

STEP 1

What is this asking? We need to create a box and whisker plot from the given meal costs and find the interquartile range. Watch out! Don't forget to order the data before finding quartiles!

STEP 2

1. Order the data
2. Find key values
3. Create the box plot
4. Calculate the interquartile range

STEP 3

Alright, let's organize this delicious data!
We need to arrange the meal costs from least to greatest so we can easily find those quartiles.
This is like lining up all the tasty dishes from cheapest to most expensive!

STEP 4

Here's the ordered data: 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 20, 21, 22, 22, 24, 24, 25.
Wow, that's a lot of meals!

STEP 5

Now, let's find the minimum, maximum, and median!
The minimum is the smallest value, which is $\$5$ .
The maximum is the largest, $\$25$ .

STEP 6

To find the median, since there are 50 values (an even number), we take the average of the 25th and 26th values.
Both the 25th and 26th values are $\$12$ , so the median is $\frac{\$12 + \$12}{2} = \$12$ .

STEP 7

Next, we need the first quartile (Q1) and third quartile (Q3). $Q1$ is the median of the lower half (the first 25 values), and $Q3$ is the median of the upper half (the last 25 values).

STEP 8

The median of the lower half is the 13th value, which is $\$8$ .
So, $Q1 = \$8$ .

STEP 9

The median of the upper half is the 38th value, which is $\$14$ .
So, $Q3 = \$14$ .

STEP 10

With our key values, we can draw our box plot!
The left whisker starts at the minimum ( $\$5$ ) and extends to $Q1$ ( $\$8$ ).
The box goes from $Q1$ ( $\$8$ ) to $Q3$ ( $\$14$ ), with a line at the median ( $\$12$ ).
The right whisker goes from $Q3$ ( $\$14$ ) to the maximum ( $\$25$ ).

STEP 11

Finally, the interquartile range (IQR) is the difference between $Q3$ and $Q1$ .
So, $IQR = Q3 - Q1 = \$14 - \$8 = \$6$ .

STEP 12

The box and whisker plot has a minimum of $\$5$ , a first quartile ( $Q1$ ) of $\$8$ , a median of $\$12$ , a third quartile ( $Q3$ ) of $\$14$ , and a maximum of $\$25$ .
The interquartile range is $\$6$ .

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Studdy Solution

STEP 1

What is this asking? We need to create a box and whisker plot from the given meal costs and find the interquartile range. Watch out! Don't forget to order the data before finding quartiles!

STEP 2

1. Order the data
2. Find key values
3. Create the box plot
4. Calculate the interquartile range

STEP 3

Alright, let's organize this delicious data!
We need to arrange the meal costs from least to greatest so we can easily find those quartiles.
This is like lining up all the tasty dishes from cheapest to most expensive!

STEP 4

Here's the ordered data: 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 20, 21, 22, 22, 24, 24, 25.
Wow, that's a lot of meals!

STEP 5

Now, let's find the minimum, maximum, and median!
The minimum is the smallest value, which is $\$5$ .
The maximum is the largest, $\$25$ .

STEP 6

To find the median, since there are 50 values (an even number), we take the average of the 25th and 26th values.
Both the 25th and 26th values are $\$12$ , so the median is $\frac{\$12 + \$12}{2} = \$12$ .

STEP 7

Next, we need the first quartile (Q1) and third quartile (Q3). $Q1$ is the median of the lower half (the first 25 values), and $Q3$ is the median of the upper half (the last 25 values).

STEP 8

The median of the lower half is the 13th value, which is $\$8$ .
So, $Q1 = \$8$ .

STEP 9

The median of the upper half is the 38th value, which is $\$14$ .
So, $Q3 = \$14$ .

STEP 10

With our key values, we can draw our box plot!
The left whisker starts at the minimum ( $\$5$ ) and extends to $Q1$ ( $\$8$ ).
The box goes from $Q1$ ( $\$8$ ) to $Q3$ ( $\$14$ ), with a line at the median ( $\$12$ ).
The right whisker goes from $Q3$ ( $\$14$ ) to the maximum ( $\$25$ ).

STEP 11

Finally, the interquartile range (IQR) is the difference between $Q3$ and $Q1$ .
So, $IQR = Q3 - Q1 = \$14 - \$8 = \$6$ .

STEP 12

The box and whisker plot has a minimum of $\$5$ , a first quartile ( $Q1$ ) of $\$8$ , a median of $\$12$ , a third quartile ( $Q3$ ) of $\$14$ , and a maximum of $\$25$ .
The interquartile range is $\$6$ .

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Studdy Solution

STEP 1

What is this asking? We need to create a box and whisker plot from the given meal costs and find the interquartile range. Watch out! Don't forget to order the data before finding quartiles!

STEP 2

1. Order the data2. Find key values3. Create the box plot4. Calculate the interquartile range

STEP 3

Alright, let's **organize** this delicious data!We need to arrange the meal costs from least to greatest so we can easily find those quartiles.This is like lining up all the tasty dishes from cheapest to most expensive!

STEP 4

Here's the **ordered data**: 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 20, 21, 22, 22, 24, 24, 25.Wow, that's a lot of meals!

STEP 5

Now, let's find the **minimum**, **maximum**, and **median**!The **minimum** is the smallest value, which is $5\$5$5.The **maximum** is the largest, $25\$25$25.

STEP 6

To find the **median**, since there are 50 values (an even number), we take the average of the 25th and 26th values.Both the 25th and 26th values are $12\$12$12, so the **median** is $12+$122=$12\frac{\$12 + \$12}{2} = \$122$12+$12​=$12.

STEP 7

Next, we need the **first quartile (Q1)** and **third quartile (Q3)**. Q1Q1Q1 is the median of the lower half (the first 25 values), and Q3Q3Q3 is the median of the upper half (the last 25 values).

STEP 8

The **median of the lower half** is the 13th value, which is $8\$8$8.So, Q1=$8Q1 = \$8Q1=$8.

STEP 9

The **median of the upper half** is the 38th value, which is $14\$14$14.So, Q3=$14Q3 = \$14Q3=$14.

STEP 10

STEP 11

Finally, the **interquartile range (IQR)** is the difference between Q3Q3Q3 and Q1Q1Q1.So, IQR=Q3−Q1=$14−$8=$6IQR = Q3 - Q1 = \$14 - \$8 = \$6IQR=Q3−Q1=$14−$8=$6.

STEP 12

The box and whisker plot has a minimum of $5\$5$5, a first quartile (Q1Q1Q1) of $8\$8$8, a median of $12\$12$12, a third quartile (Q3Q3Q3) of $14\$14$14, and a maximum of $25\$25$25.The interquartile range is $6\$6$6.

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1. Order the data
2. Find key values
3. Create the box plot
4. Calculate the interquartile range

Alright, let's organize this delicious data!
We need to arrange the meal costs from least to greatest so we can easily find those quartiles.
This is like lining up all the tasty dishes from cheapest to most expensive!

Here's the ordered data: 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 20, 21, 22, 22, 24, 24, 25.
Wow, that's a lot of meals!

Now, let's find the minimum, maximum, and median!
The minimum is the smallest value, which is $\$5$ .
The maximum is the largest, $\$25$ .

To find the median, since there are 50 values (an even number), we take the average of the 25th and 26th values.
Both the 25th and 26th values are $\$12$ , so the median is $\frac{\$12 + \$12}{2} = \$12$ .

Next, we need the first quartile (Q1) and third quartile (Q3). $Q1$ is the median of the lower half (the first 25 values), and $Q3$ is the median of the upper half (the last 25 values).

The median of the lower half is the 13th value, which is $\$8$ .
So, $Q1 = \$8$ .

The median of the upper half is the 38th value, which is $\$14$ .
So, $Q3 = \$14$ .

Finally, the interquartile range (IQR) is the difference between $Q3$ and $Q1$ .
So, $IQR = Q3 - Q1 = \$14 - \$8 = \$6$ .

The box and whisker plot has a minimum of $\$5$ , a first quartile ( $Q1$ ) of $\$8$ , a median of $\$12$ , a third quartile ( $Q3$ ) of $\$14$ , and a maximum of $\$25$ .
The interquartile range is $\$6$ .