Biased/Unbiased Samples
To determine whether students have heard about New Product X, a research company surveys randomly selected students from a computer-generated list. Is this simple, stratified, or systematic?
simple random sample
A football coach is planning on purchasing training videos for each player who misses his summer camp. He randomly asks 15 players, and 4 of them say they will miss the camp. How many players out of 75 can the coach expect to miss the summer camp?
20 players
1. The dot plot on the board displays data from 20 random samples, each consisting of 60 households. Each dot represents the mean number of pieces of mail per day by households in the sample. (Example 1)
a. Which number best represents the mean number of pieces of mail?
2.05 pieces of mail
The double dot plot shows the average cost per meal in dollars at different types of restaurants. Give me the mean and variability for the Mexican restaurant.
Mean: Mexican restaurant $14
Variability: $1
The double dot plot shows the number of minutes two girls spent practicing softball pitching on random days this month. The table gives the mean and mean absolute deviation for each girl.
Hannah Bayley
Mean 45 55
Mad 4.5 4.5
a. How many measures of variability separate the means of the samples?
about 2.22 measures of variability
To determine whether there is enough interest in starting a high school water polo team, a coach surveys 15 randomly selected junior high students from the swim team and dive team.
stratified random sample
A high school principal is planning to start a new elective class. He randomly surveys 60 students to ask whether they would take the class, and 7 said they would. How many students can the principal expect to take the class if there are 540 students in the high school?
63 students
1. The dot plot displays data from 20 random samples, each consisting of 60 households. Each dot represents the mean number of pieces of mail per day by households in the sample. (Example 1)
b. Find and interpret the variability in the distribution.
0.77 per piece
The double dot plot shows the average cost per meal in dollars at different types of restaurants. Give me the Mean and Variability of the Italian restaurant.
A. Mean Italian restaurant $17
B. Variability $1.29
The double dot plot shows the number of minutes two girls spent practicing softball pitching on random days this month. The table gives the mean and mean absolute deviation for each girl.
Hannah Bayley
Mean 45 55
Mad 4.5 4.5
Make an inference as to whether the means of the two populations are likely to be different.
A ratio greater than two suggests that the means are likely to be different. Because 2.2 > 2, the populations in this situation are likely to be different.
To select a new school mascot, all students are invited to take a survey. The responses will determine the new mascot. Is this convenience sample or voluntary response sample?
voluntary response sampling
A teacher is planning on buying materials for a project all her classes will complete. She randomly surveys 24 students about what method they will use to present their project. The table shows the results. How many poster boards can the teacher expect to buy if she has 96 students in total?
Material for Project: # students
poster board 11
electronic 7
construction paper 6
44 poster boards
. The dot plot displays data from 17 random samples, each consisting of 23 scores on a 5-point quiz taken by eighth-grade students. Each dot represents the mean score by students in the sample. (Example 1)
a. Which number best represents the mean score?
b. Find and interpret the variability in the distribution.
A. 3.6 points
B. 0.89 point
The double dot plot shows the average cost per meal in dollars at different types of restaurants. What are some appropriate inferences you can make about the data? (Example 1)
Overall, the Italian restaurants are more expensive with a greater variation. You can infer that a randomly selected meal at an Italian restaurant is likely to be more expensive than a randomly selected meal at a Mexican restaurant.
The double dot plot shows the number of minutes that two diving teams train. The table gives the mean and mean absolute deviation for each team.
Team A Team B
Mean 66 76
MAD 6.2 6.2
a. How many measures of variability separate the means of the samples?
about 1.61 measures of variability
A travel agent surveys local clients to determine how many people in the state are planning on taking a vacation in the upcoming year. The responses will determine the agency’s marketing strategy. Is this voluntary response or convenience sample?
convenience sample
An employer is planning to buy lunch for all his employees. The table shows the results of a random survey of his employees’ lunch preferences. How many Italian sandwiches can the employer expect to buy if he has 84 employees?
Sandwich Preference Percent
Italian 25%
Veggie 20%
Turkey 55%
21 Italian sandwiches
The dot plot displays data from 16 random samples, each consisting of 13 gymnasts. Each dot represents the mean score on balance beam for the season by gymnasts in the sample. (Example 1)
a. Which number best represents the mean score on beam?
b. Find and interpret the variability in the distribution.
A. score of 8.5
B. 0.5 points
The double dot plot shows the average hours of sleep per night for teenagers and adults. Compare their centers and variability. What are some appropriate inferences you can make about the data? (Example 1)
The double dot plot shows the number of minutes that two diving teams train. The table gives the mean and mean absolute deviation for each team.
Team A Team B
Mean 66 76
MAD 6.2 6.2
Make an inference as to whether the means of the two populations are likely to be different.
A ratio less than two suggests that the means are likely to be the same. Because 1.61 < 2, the number of minutes that Team A and Team B train are likely to be the same.
Identify the sample method used and whether it is biased or unbiased. Then determine whether the inference is valid. To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie.
systematic random sample; unbiased; The inference is valid.
The table for payment methods at a grocery store are shown in the graph. Predict how many customers will pay with their phones if 800 customers visit the store.
Payment Method: Percent:
Cash 26%
Check 8%
Credit 52%
Phone 14%
112 people
The dot plot displays data from 16 random samples, each consisting of 25 high school students. Each dot represents the mean number of hours worked in after-school jobs per week by students in the sample. (Example 1)
a. Which number best represents the mean number of hours worked?
b. Find and interpret the variability in the distribution.
A. 11.8 hours
B. 0.88 hour
The double box plot shows the number of campers per session for day camps and resident camps. What are some appropriate inferences you can make about the data? (Example 2)
Sample answer: The median for the resident camp data is 150 campers with a variation of 100 campers. The median for the day camp data is 225 campers per session with a variation of 75 campers. Overall, the day camps have more campers per session with less variation. You can infer that a randomly selected day camp is likely to have more campers per session than a randomly selected resident camp.
The double dot plot shows the sample number of birds that visit two feeders with different seed types on random days this month. The table gives the mean and mean absolute deviation for each seed type. (Example 1)
Sunflower Millet
Mean 14.5 11.5
MAD 1.1 1.1
a. How many measures of variability separate the means of the samples?
b. Make an inference as to whether the means of the two populations are likely to be different.
a. about 0.91 measures of variability
b. A ratio less than two suggests that the means are likely to be the same. Because 0.91 < 2, the populations of birds in this situation are likely to be the same.