Question

survey question
\how many minutes of screen time do 6th graders spend on a typical school night?\
population: all 6th graders at school
sample: 25 students (randomly chosen during homeroom)
raw data (minutes of screen time)
42, 60, 75, 80, 95, 100, 110, 120, 125, 130, 135, 140, 145, 150, 150, 160, 165, 170, 180, 190, 200, 210, 220, 240, 300
survey question
\what is your favorite after - school activity?\
population: all 6th graders at school
sample: 25 students (randomly chosen during homeroom)
sports: 12
video games: 5
reading: 3
hanging w/ friends: 5
using the appropriate data displays, create a pie chart, histogram, and boxplot for the data above. (histogram and boxplot are on the next page).
pie chart:
\\(\frac{12}{25}=48\\%\\)
\\(\frac{5}{25}=20\\%\\)
\\(\frac{3}{25}=12\\%\\)

Explanation:

Step1: Organize data for pie - chart

For the favorite after - school activity data, calculate the percentage of each category out of the total number of students in the sample (25).
Sports: $\frac{12}{25}=0.48 = 48\%$, Video Games: $\frac{5}{25}=0.2 = 20\%$, Reading: $\frac{3}{25}=0.12 = 12\%$, Hanging w/ Friends: $\frac{5}{25}=0.2 = 20\%$.

Step2: Create a histogram for screen - time data

1. First, determine the range of the screen - time data: $300 - 42=258$.
2. Decide on the number of bins. Let's say 5 bins. The bin width would be $\frac{258}{5}\approx52$.
3. The bins could be: $42 - 93$, $94 - 145$, $146 - 197$, $198 - 249$, $250 - 300$.
4. Count the number of data points in each bin:

• For $42 - 93$: 5 (42, 60, 75, 80, 95)
• For $94 - 145$: 8 (100, 110, 120, 125, 130, 135, 140, 145)
• For $146 - 197$: 7 (150, 150, 160, 165, 170, 180, 190)
• For $198 - 249$: 4 (200, 210, 220, 240)
• For $250 - 300$: 1 (300)

1. Plot the bins on the x - axis and the frequency on the y - axis.

Step3: Create a boxplot for screen - time data

1. Order the data: 42, 60, 75, 80, 95, 100, 110, 120, 125, 130, 135, 140, 145, 150, 150, 160, 165, 170, 180, 190, 200, 210, 220, 240, 300.
2. Find the median (Q2). Since $n = 25$, the median is the 13th value, so $Q2=145$.
3. Find the lower half of the data (the first 12 values): 42, 60, 75, 80, 95, 100, 110, 120, 125, 130, 135, 140. The median of the lower half (Q1) is the average of the 6th and 7th values: $\frac{100 + 110}{2}=105$.
4. Find the upper half of the data (the last 12 values): 150, 150, 160, 165, 170, 180, 190, 200, 210, 220, 240, 300. The median of the upper half (Q3) is the average of the 6th and 7th values: $\frac{180+190}{2}=185$.
5. The minimum value is 42 and the maximum value is 300. Draw a box from Q1 to Q3 with a line at Q2, and whiskers from the box to the minimum and maximum values.

Answer:

Pie - chart percentages for favorite after - school activities are calculated as above. Histogram and boxplot for screen - time data are constructed as described in the steps for bins and quartile calculations respectively.