Graphs
A class collects data on favorite colors and turns it into sections of a circle. What graph type is used?
Pie Chart
An error that causes data to lean to one side
Bias
If the highest score is 95 and the lowest is 70, what is the range?
25
A teacher compares two classes’ test scores. Class A scores are very close to the mean, while Class B scores are very spread out. Which class has the larger standard deviation?
Class B
This is the middle value when data is ordered.
Median
A bar graph shows students prefer dogs (20), cats (18), and hamsters (5). What conclusion can you make from the graph?
Dog is the most popular pet choice; hamsters are the least popular.
A survey about school lunches is given to students eating in the cafeteria. Is this sample biased?
Yes
This value divides a data set into four equal parts.
Quartiles
DAILY DOUBLE!!!!
A data set has a standard deviation of 0. What can you say about all the values?
All values are the same
Find the mode: 5, 7, 7, 8, 9
7
A bar graph shows the number of books read by students:
How many more books did Jordan read than Taylor, and who read the same number of books as Jordan?
5 more, Casey
A district surveys students about technology use by emailing the survey link, but only students with regular internet access respond. Is this sample biased? Explain the type.
Yes, because those without internet can't do it.
This is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR
A teacher adds 10 points to every student’s test score. What happens to the standard deviation of the scores? Explain.
The standard deviation does not change because adding the same constant to every value does not change the spread of the data
Find the mean: 10, 20, 30, 40
25
A graph shows two lines: one for homework time and one for test scores. Both increase together. What can you conclude about the relationship?
There is a positive relationship (positive correlation) between homework time and test scores
A teacher surveys students by handing a questionnaire to the first 25 students who finish a math test. Is this sample biased? Explain.
Biased because it is a convenience sample and may overrepresent faster test-takers
This is what the IQR is not effected by.
Outliers
Which set has the greater standard deviation?
A: 10, 10, 10, 10, 10
B: 0, 5, 10, 15, 20
B
DAILY DOUBLE!!!!!!
Which measure (mean, median, or mode) is most affected by an outlier in this set: 5, 6, 7, 8, 100?
Mean
A line graph is used to show students’ quiz scores over time. The graph’s x-axis is labeled “Student Names,” and the y-axis is labeled “Score.”
Is this graph appropriate? If not, what is the problem and what should be changed?
The graph is not appropriate because line graphs are used for change over time or ordered data; the x-axis should represent time (or ordered sequence like quiz 1, quiz 2, etc.), not student names.
A district wants to estimate the average amount of time students spend on homework. They randomly select 200 students from the school roster. The survey is sent by email and is open for 24 hours. Only 60 students respond, and most of them are students enrolled in honors or AP classes.
Is this study biased? Explain.
It is biased because the more advanced students were the ones who filled it out.
Find the interquartile range (IQR) of this data set:
2, 4, 5, 7, 8, 9, 10, 12
6
Two classes have the same mean of 75 on a test. Class A scores are: 70, 72, 75, 78, 80. Class B scores are: 40, 60, 75, 90, 110. Which class has the larger standard deviation and why?
Class B because its scores are much more spread out from the mean, showing greater variability
A data set has a mean of 40 and a median of 45. One new value of 200 is added to the data set. What happens to the mean and median, and which one changes more? Explain.
The mean increases significantly because it is affected by extreme values (outlier), while the median changes very little or not at all; the mean changes more than the median.