Center and variability
Find the mean of the following set of data: 13, 23, 21, 20, 21, 24, 18
mean is 20
Find the MAD of this data set:
5, 3, 8, 2, 1, 11
Mean = 6
MAD = (1+3+2+4+5+5)/6
MAD =3.33
In a representative sample of dentists, 8 out of 10 dentists recommend using an electric toothbrush.
What percent of all dentists would you expect to recommend using an electric toothbrush?
80%
A company wants to find the percentage of the adults in Massachusetts that have a dog.
What is the population?
All adults in Massachusetts
Which would be the better measure of center to use with this data, mean or median. Why?
10, 10, 10, 10, 9, 9, 9, 8, 8, 7, 1, 0
Median because the data is skewed.
Find the mean absolute deviation of the following data set: 5, 6, 7, 4, 3
MAD is: 1.2
Find the interquartile range for the data set: 12, 14, 11, 10, 9, 10, 9
What is the IQR = 3 - put the numbers in order from least to greatest - find the median - find the difference between the first quartile (9) and third quartile (12)
A company wants to find the percentage of the adults in Massachusetts that have a dog.
What is a possible sample that could be used to estimate this?
Answer must describe a subset of all adults in Massachusetts.
Find a possible missing value in the set of data if the range is 20.
14, 8, 17, 21, ____, 11, 3, 13
What is 1 or 23
Can you find the MAD from a box plot? Why or why not?
No, the mean of data is not displayed in a box plot so you can't find the MAD.
A solution used to kill bacteria is tested The solution kills the following percentages of bacteria in six trials: 85, 84, 87, 86, 90, 80
What is the median and IQR?
Median: 85.5
IQR: 87-84 =3
A pet food store wants to know how many pets each household owns within a five-town region.
The store mails a survey to all residents who live within 3 blocks of the store asking how many pets they own.
Is this a representative sample? Why or why not.
Not representative because the sample is not random. The households are not randomly selected from the five towns.
Is there a meaningful difference in the ages of two groups of children? Support your answer.
Group 1: Mean = 8.2 and MAD = 2
Group 2: Mean = 10 and MAD = 1.1
There is NO meaningful difference. The difference is the means is less than two of the larger MADs.
0.9 < 2
Which groups' scores have a higher typical value and a lower variability. Why?
Group A: Mean = 10.8 and MAD = 4.1
Group B: Mean = 8.2 and MAD = 2.3
Group C: Mean = 10.8 and MAD = 2.3
Group C because it has the highest mean with the lowest MAD.
In a sample of 20 people, 3 of them like horror movies. If the population has 800 people, how many of them would you expect to like horror movies?
120 people
A middle school teacher works at a school with 600 students. He wants to know what percentage of the students have more than two siblings. He asks 75 students randomly selected from all grades at the school.
What is the sample?
the 75 students he asked
What is the definition of the Mean Absolute Deviation? What does a large MAD mean about the data?
The average distance the data points are away from the mean.
A large MAD means that the data is spread out/has great variability.
If data is symmetric and without outliers, which measure of center and measure of variability should you use?
Mean and MAD
There are 200 students in the seventh grade at our school. A random sample of 50 seventh graders at our school is asked if social studies is their favorite subject. 12 students respond that social studies is their favorite.
Based on this sample, how many seventh graders at our school would you expect to have social studies as their favorite?
48 seventh graders
A middle school teacher works at a school with 600 students. He wants to know what percentage of the school has more than two siblings.
Describe a way that he can get a representative sample of the students?
The sample described should be random. Each student should have an equal chance of being selected.