11.1 Find Measures of Central Tendency & Dispersion
Statistics - numerical values used to summarize and compare sets of data. Two important types:
1. measure of central tendency-a number used to
represent the center or middle of a set of data values.
a. mean - average - x bar, sum of numbers divided by
the number of values.
b. median - middle value, (average the middle two values
if there are an even number of values).
c. mode - the value or values that occurs most often,
no mode if all values appear once.
2. measures of dispersion - tells how dispersed, or spread
out data values are.
a. range - difference between the greatest and least
data values.
b. standard deviation - (sigma) describes the typical
difference,(or deviation),between a data value
and the mean. (see formula)
Outliers - a value that is much greater than or much less than most of the other values in the data set. Measures of central tendency and dispersion can give misleading impressions of a data set if the set contains one or more outliers.
11.2 Apply Transformations to Data
Adding a Constant to Data Values:
mean, median, and mode of the new data set can be
obtained by adding the same constant to the mean,
median, and mode of the original data set.
range and standard deviation are unchanged.
Multiplying Data Values by a Constant:
mean, median, mode, range, and standard deviation of
new data set can be found by multiplying each original
statistic by the same constant.
11.2B (See page 1008 examples)
Ways to Organize Data
1. Line Plot
2. Stem & Leaf Plot
3. Histogram (Tally chart)
4. Box and Whisker Plot
11.3 Use Normal Distributions
Normal Distribution, one type of probability distribution, is modeled by a bell-shape curve called a normal curve that is symmetric about the mean.
Areas Under a Normal Curve:
A normal distribution with mean, x-bar, and standard deviation,
sigma, has the following properties -
*the total area under the related normal curve is 1
*about 68% of the area lies within 1 SD of the mean
*about 95% of the area lies within 2 SD of the mean
*about 99.7% of the area lies within 3 SD of the
mean
Standard Normal Distribution is the normal distribution with mean 0 and standard deviation 1.
z-score - for the x-value is the number of SD the x-value lies above or below the mean.
11.4 Select & Draw Conclusions from Samples
Population - group of objects or people that you want information
about.
Sample - subset of a population. Use when it is too difficult to collect
from everyone.
self-selected sample - members of a population volunteer to be
in the sample
convenience sample - members of a population that are easy- to-
reach
systematic sample - members of a population are selected
using a rule
random sample - members of a population have an equal chance
of being selected
Bias in Sampling: (select an unbiased sample to draw accurate
conclusion)
unbiased sample - is representative of the population you want
information about.
biased sample - a sample that under representing or over
representing a part of your population
Sample size: when conducting a survey, make the size of the sample
large enough so it accurately represents the population.
Margin of error: gives a limit on how much the responses of the sample would differ from the responses of the population. As the sample size
increases, the margin of error decreases.
Margin of error = ± 1/√n
If the percent of the sample responding a certain way is p, then the percent of the population that would respond the same is likely between
p - 1/√n and p + 1/√n
11.5 Choose the Best Model from Two-Variable Data
Function General Form
Linear y = ax + b
Quadratic y = ax2 + bx + c
Cubic y = ax3 + bx2 + cx + d
Exponential y = abx
Power y = axb
1. Make a scatter plot of the data on your calculator.
2. Determine the type of function suggested by the pattern
of the graph.
3. Use the regression features of the calculator to find a
model of best fit.