24 - 25 - 27 statistics Flashcards
what is the mean?
the average
what is the mean of this list of numbers: 5,6,2,2,2,7?
(5+6+2+2+2+7)/6 = 4
what is the median
the number in the middle the list is in order
what is the median of this list of numbers: 5,6,2,2,2,7?
the median is the average of the two middle numbers:
(2+5)/2 = 3.5
what is the median of 1,2,3?
take half of 3 to get 1.5 and round it up to 2
what is the median of 1,2,3,4?
the median is the average of the second and third numbers:
take half of 4 to get 2 and round 2 up to 3
these are the two numbers that contribute to the median.
what is the mode?
the number that shows up the most often
what is the mode of this list of numbers: 5,6,2,2,2,7?
it’s 2
what is the range?
the difference between the biggest number in the list and the smallest number
what is the range of this list of numbers: 5,6,2,2,2,7?
7 - 2 = 5
define
what is the standard deviation?
a measure of how spread out a list of numbers is OR how much they deviate from the mean
example
which has higher standard deviation: 5,6,2,2,2,7 OR 5,5,5,5,6,7?
5,6,2,2,2,7 ha shigher standarad deviation.
define
what is an outlier?
an extreme data point that is far outside where most of the data lies
function
how does an outlieraffect the average(mean), the range, and the median?
If an outlier is greater than the rest of the data, it increases the average (mean) and increasese the range since there is a larger gap between the minimun and the maximum. The median istypically unaffected.
outliers typically affect the mean but not the median
technique
when dealing with average questions on the SAT,
think in terms of sums or totals
technique
you can always find the sum by
multiplying the average with the number of subjects
example
the higher the standard deviation,
the more spread out from the mean
example
the lower the standard deviation,
the more clustered toward the mean
recognizing type of questions: reading data
given graphs and charts to
interpret graphs
confusing concept
maximum capacity of a truck=
maximum weight when reached maximum capacity - initial weight of truck when empty
define/key formula
probability of a certain outcome
number in target group
/
number in group under consideration
define
what is the goal of statistics
to be able to make predictions and estimations based on limited time and information
technique
what is one common theme in statisctics and SAT questions?
using a sample mean to predict something about the entire population
define
what is a confidence interval
the mean of your estimate plus and minus the variation in that estimate
example
if the mean price of an apartment in Malden is $150,000 with a margin of error of $10,000, thi simplies that the true mean price of all apartments in Madlen is likely between $140,000 and $160,000. What is this interval known as?
Confidence interval
confusing concept
the margin of error depends on two factors:
- sample size
- variability in data (often measured by standard deviation)
recognizing type of questions:
“based on the design and results of the study, which of the following is an appropriate conclusion?”
association(correlation) vs. causation question
confusing concept
True or False
Because students who exercise get better exam scores than those who do not, the exercise causes an improvement in scores.
False - exercise is associated with improvement
confusing concept
in order for researchers to see whether exercise does cause an improvement in exam scores, they must
they should implement random assignment; that is, instead of randomly selecting 200 students from one group who already exercise and 200 others that do not, they should have just randomly selected 400 students. Then randomly assign each student to exercise or not and see the difference in the two groups’ performance
confusing concept
- subjects not selected at random
- subjects not randomly assigned
Conclusions:
- results cannot be generalized to the population
- cause and effect cannot be proven
confusing concept
- subjects not selected at random
- subjects randomly assigned
- results cannot be generalized to the population
- cause and effect can be proven
confusing concepts
- subjects tested at random
- subjects not randomly assigned
- results can be generalized to the population
- cause and effect cannot be proven
confusing concepts
- subjects selected at random
- subjects randomly assigned
- results can be generalized to the population
- cause and effect can be proven
key idea
if sample was not randomoly selected from the general population
it cannot make a generalization on the population
key idea
if the subjects are not randomly assigned,
cause and effect relationship cannot be established
confusing concept
True or False
A confidence interval applies to an individual data point or group of data points.
False - a confidence interval applies only to the mean, which is a statistical measure, not an individual data point.
cofusing concept
what does it mean in statistics to be 95% confidenct in something?
If the experiment were repeated again and again, each with 40 water samples, 95% of those experiments would give us a confidence interval that contains the true mean. So the 95% pertains to all the confidence intervals generated by repeated experiments, NOT the chance that any one confidence interval contains the true mean.
key formula
Volume
Area of base x height
example
volume of a cube
s^3
example
volume of a rectangular prism
V = lwh
key formula
volume of a cylinder
πr^2 h
key formula
volume of a cone
1/3πr^2h
key formula
volume of a sphere
4/3πr^3
