Activities

1. Below is the data collected from a random sample of 100 graduating seniors on the number of college applications they submitted in their senior year. What inferences would you draw about the senior class as a whole?

2. A teacher does not have time to grade every students' test, but she wants to get a general sense of how her students did. She shuffles her papers, picks 10 papers at random and grades them. The results are in the table below.  What inferences would you draw about the performance of her students?

3. The ages of five children in a family are 3, 3, 5, 8, and 21.  Write a statement that compares the mean and the median.  Show your work.

4. Two research teams are investigating water quality in a pond. TS Research collects two samples with 100 measurements in each sample. AB Research collects two samples with 50 measurements in each sample. 
   Part A) Which team's estimate would you expect to be more representative?
   Part B) Which pair of samples would you expect to show less variation? Explain.

5. In the time trials for the 400-meter run at the state sectionals, the 20 runners recorded the times shown in the accompanying table. What was the mean absolute deviation of the running times in seconds?  Round to the nearest tenth and show your work.

6. The bar graph shows the favorite dinners of a group of people.  What percent of the people prefer pasta? (Round to the nearest percent)

Answer Key/Rubric

1. Most of the students filled out between 5 and 9 applications to college.

2. Most of the students did well on the test.  The majority that she graded have a grade “A”

3. The mean is greater than the median or the median is less than the mean.
   
   Mean: 3 + 3 + 5 + 8 + 21 = 40
               40 ÷5 = 8.
   
   Median: 3  3  5  8  21
   Middle number is 5

4. Part A) I think that the team that collected more water would be more representative.
   Part B)  I think that AB research would have results that show less variation because they have smaller water samples that would not give as much data as the other company that took larger samples.

5. The MAD for the running times rounded to the nearest tenth is 0.8.  Student work might include but is not limited to,
   
   Find the mean running time
   Mean:
   50+50+51+52+52+52+52+52+53+53+53+53+53+53+54+54+54+54+55+55 = 1055
   1055 ÷ 20 = 52.75
   52.75 ≈ 52.8 seconds
   
   Find the deviations:

            16.6 ÷ 20 = 0.83
            0.83 ≈ 0.8 MAD

6. The percent of people that prefer pasta rounded to the nearest percent is 28%.  Student work might include but is not limited to,

• Find the total amount of people that took the survey by adding the amount of people in each dinner category
• 13 + 8 + 5 + 2 + 1 = 29
• Out of the 29 people in the survey 8 picked pasta as a favorite meal.
• = 0.2758…
• ≈28%