Question

sleep showdown: data + art challenge
name: _ date: _
10/1/25
step 1: plot the data
use the table below to create box plots for 8th and 9th graders sleep hours.
grade hours of sleep
8th 6, 7, 7, 8, 8, 9, 9, 10, 10, 11
9th 5, 6, 7, 7, 8, 8, 9, 10, 11, 12
instructions: 1. draw a number line for hours of sleep. 2. mark the minimum, q1, median, q3, and maximum. 3. identify any outliers. 4. draw the box plots side by side for comparison.
step 2: interpret the data
answer the questions below: 1. which grade has the most consistent sleep? how can you tell? 2. which grade has the widest variety of sleep hours? 3. are there any outliers? what do they tell us? 4. if you only looked at the median, what story would you miss?
step 3: create your sleep art
now its time to turn data into art! choose one option: - poster: show the story of sleep using drawings, icons, or colors. highlight medians, ranges, and outliers. - comic strip: create a mini - comic showing \a night in the life\ of a student from each grade. include sleep patterns and outliers. - collage: make a visual collage representing each grades sleep hours using symbols, doodles, or cut - outs
tips: - think about variability: bigger spread = more diverse sleep habits. - use visuals to show outliers clearly. - make your art tell the story without needing numbers.
step 4: share your work
· explain to a partner or the class what your visuals show about median, variability, and outliers.

Explanation:

Step1: Calculate statistics for 8th - graders

For 8th - graders data set $\{6,7,7,8,8,9,9,10,10,11\}$:

• Minimum: The smallest value is $6$.
• Q1 (First - quartile): First, find the median of the lower half. The lower half is $\{6,7,7,8,8\}$, and its median is $7$.
• Median: Since there are $n = 10$ data - points, the median is the average of the 5th and 6th ordered values. So, median$=\frac{8 + 9}{2}=8.5$.
• Q3 (Third - quartile): The upper half is $\{9,10,10,11\}$, and its median is $10$.
• Maximum: The largest value is $11$.
• Inter - quartile range (IQR): $IQR=Q3 - Q1=10 - 7 = 3$. Outliers are values less than $Q1-1.5\times IQR=7-1.5\times3=7 - 4.5 = 2.5$ or greater than $Q3 + 1.5\times IQR=10+1.5\times3=10 + 4.5 = 14.5$. There are no outliers.

Step2: Calculate statistics for 9th - graders

For 9th - graders data set $\{5,6,7,7,8,8,9,10,11,12\}$:

• Minimum: The smallest value is $5$.
• Q1: The lower half is $\{5,6,7,7,8\}$, and its median is $7$.
• Median: Since $n = 10$, the median is $\frac{8 + 8}{2}=8$.
• Q3: The upper half is $\{9,10,11,12\}$, and its median is $10.5$.
• Maximum: The largest value is $12$.
• IQR: $IQR = Q3 - Q1=10.5 - 7 = 3.5$. Outliers are values less than $Q1-1.5\times IQR=7-1.5\times3.5=7 - 5.25 = 1.75$ or greater than $Q3+1.5\times IQR=10.5 + 5.25 = 15.75$. There are no outliers.

Step3: Answer questions in Step 2

1. Most consistent sleep: The 8th - graders have more consistent sleep. We can tell by looking at the inter - quartile range. The IQR for 8th - graders is $3$ and for 9th - graders is $3.5$. A smaller IQR indicates less variability in the middle 50% of the data.
2. Widest variety of sleep hours: The 9th - graders have the widest variety of sleep hours. We can consider the range (maximum - minimum). For 8th - graders, the range is $11 - 6 = 5$, and for 9th - graders, the range is $12 - 5 = 7$.
3. Outliers: There are no outliers in either data set. Outliers can indicate unusual or extreme sleep patterns among the students.
4. Missing story when only looking at the median: If we only look at the median, we miss the information about the spread and skewness of the data. For example, we don't know how far apart the minimum and maximum values are, or how the data is distributed within the lower and upper halves.

Answer:

1. 8th - graders have more consistent sleep, as indicated by a smaller IQR.
2. 9th - graders have the widest variety of sleep hours, as indicated by a larger range.
3. There are no outliers in either data set; outliers would indicate extreme sleep patterns.
4. Looking only at the median misses information about data spread and skewness.