Biased or Unbiased
A school surveys every 8th person leaving a public library about their favorite book genre. Biased or unbiased?
Unbiased — a systematic random sample; no group is favored.
Find the mean of 4, 6, 8, 10.
7
A dot plot shows pets per family: 0 pets has 4 dots, 1 pet has 6 dots, 2 pets has 3 dots, 3 pets has 2 dots. How many families were surveyed?
15
A box plot has minimum 8, first quartile 15, median 22, third quartile 30, maximum 38. What is the median?
22
Two classes both have a mean score of 80. Class A has a MAD of 2 and Class B has a MAD of 9. Which class's scores are more spread out?
Class B (a bigger MAD means more spread)
A store asks shoppers at a skateboard shop about their favorite sport. Biased or unbiased?
Biased — it favors people who already like skateboarding.
Find the median of 5, 9, 3, 11, 7.
7
Using that same dot plot, what is the mode?
1 pet
Using that same box plot, find the range.
30
Find the MAD of 6, 8, 10. The mean is 8. Give your answer to the nearest tenth.
1.3
A town wants opinions on a new bike lane, but surveys only people riding bikes in the park. Biased or unbiased, and why?
Biased — it only reaches people who already bike, so it favors one side.
Find the mode of 12, 15, 12, 18, 15, 12, 20.
12
A histogram of quiz scores has intervals 60-69: 4 students, 70-79: 9 students, 80-89: 7 students, 90-99: 3 students. Which interval has the most students, and how many students took the quiz?
70-79 has the most; 23 students total
Using that same box plot, find the interquartile range (IQR).
15
Find the MAD of 4, 7, 9, 12.
2.5
A principal wants to know if students like the new schedule. She surveys all students in the jazz band. Biased or unbiased? Give one reason.
Biased — one group only; the jazz band does not represent the whole school.
Data: 20, 24, 18, 30, 22, 26. Find the mean to the nearest tenth and the median.
Mean 23.3, median 23
Test scores: 55, 62, 68, 71, 59, 64, 77, 73, 66, 81. Give the frequencies for intervals 50-59, 60-69, 70-79, 80-89.
50-59: 2; 60-69: 4; 70-79: 3; 80-89: 1
Using that same box plot, what percent of the data lies between 15 and 30?
50%
Salaries: 28,000; 30,000; 32,000; 31,000; 150,000. Which measure — mean, median, or mode — best represents a typical salary, and why?
Median (31,000) — the 150,000 salary is an outlier that pulls the mean (54,200) way up, and there is no mode.
A researcher wants to estimate how many hours middle schoolers sleep. She picks 200 students at random from all three grades, but only 40 reply, and most of them are 8th graders. Is the result trustworthy? Why?
No — most of the sample did not respond, and the replies overrepresent 8th graders, so the sample no longer fairly represents all grades.
Scores: 72, 78, 75, 80, 76, 74, 35. Find the mean with the outlier and without it, to the nearest tenth. What does the outlier do?
With the outlier 70.0; without it 75.8; the outlier pulls the mean down
A histogram has intervals 0-9, 10-19, 20-29, 30-39 with frequencies 5, 11, 8, 2. A student says the data has no gaps. Is the student right? And what percent of the data falls in 10-19?
Yes, no gaps (no interval is empty, so the bars all touch); 42.3% in 10-19
Store A prices: min 10, Q1 20, median 35, Q3 50, max 70. Store B prices: min 15, Q1 25, median 30, Q3 40, max 55. Which store has the higher median, and which has the smaller IQR? What does the smaller IQR tell you?
Store A has the higher median (35 vs 30). Store B has the smaller IQR (15 vs 30), which means Store B's middle half of prices is less spread out — they cluster more tightly.
Two data sets both have mean 50. Set X: 48, 50, 52. Set Y: 30, 50, 70. Find the MAD of each and explain what the comparison tells you.
Set X MAD is about 1.3; Set Y MAD is about 13.3. Even though the means are equal, Set Y is much more spread out than Set X.