Chapter 3 Stats

Front 1

Chapter 1Distinguish between population and sample, parameter and statisticGood sampling methods: simple random sample, collect in appropriate ways

Back 1

INfo

Front 2

Frequency distribution: summarizing dataGraphs designed to help understand dataCenter, variation, distribution, outliers, changing characteristics over time

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INfo

Front 3

Two measures of center used as tools for analyzing data.

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Mean and median

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The value at the cneter or middle of data set.

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Measure of center

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What is the mean

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the measure of center obtained by adding the values and dividing the total by the number of values.

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This letter in the equation is the sum of a set of values. All the values added at the top.

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E

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this letter is the variable usually used to represent the individual data values. usually added together

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x

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This letter represents the number of data values in a sample.

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n

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this number represents the number of data values in a population.

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N

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_ Ex
x= --------
n
___
x is pronounced ‘x-bar’ and denotes the mean of a set of sample values

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Mean of a sample values

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µ= --------
N

µ is pronounced ‘mu’ and denotes the mean of all values in a population

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mean of all values in a population

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MEAN
T or F. Is relatively reliable, means of samples drawn from the same population don't vary as much as other measures of center. takes every data value into account

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True

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Disadvantages of MEAN

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Is sensitive to every data value, one extreme value can affect it dramatically, is not a resistant measure of center

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the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

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Median

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median is denoted by the ___ with a ___ mark over it called the x-tilde

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X squiggle

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why is the advantage of using Median as a center of measure?

True or False

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it is not affected by an extreme value - it is a resistant measure of the center

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How to find the median if the data value is odd?

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The exact middle of the list

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if the number of data values is even the median is found how?

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by computing the mean of th two middle numbers

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The value that occurs with the greatest frequency.

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Mode

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True of False
Data set can have one, more than one, or no mode

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True

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two data values occur with the same greatest frequency

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Bimodal

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more than two data values occur with the same greatest frequency

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Multimodal

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No data value is repeated

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No mode

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Mode is the only measure of central tendency that can be used with nominal data

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True

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Which is mode, bimodal and no mode?
a. 5.40 1.10 0.42 0.73 0.48 1.10
b. 27 27 27 55 55 55 88 88 99
c. 1 2 3 6 7 8 9 10

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Mode
Bimodal
no mode

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the value midway between the maximum and minimum values in the original data set

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Midrange

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what is the midrange calculation

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Midrange=Max value + minimum Value/ 2

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Midrange is sensitive to extremes. Because it uses only the maximum and minimum values, so rarely used

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Info

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Redeeming features for midrange.
Very easy to compute
reinforces that there are several ways to define the center
avoids confusion with median

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info

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the value at the center or middle of a data set?

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Measure of center

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4 ways to figure measure of center

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Mean, median, mode, midrange

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The most important of all numerical measurements used to describe data, and it is what most people call an average

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Mean

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a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing magnitude

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Median

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Never use the term average when referring to measure of center.. use the correct term such as mean or median

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Info

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Mode is the only measure of center that can be used with data at the nominal level of measurement

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True

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This measurement applies to data that consists of names, labels, or categories.

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Nominal level of measurement

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We use this rule for mean, median and mid-range

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Round off rule for measures of center

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What is the round-off rule for measures of center

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Carry one more decimal place than is present in the original set of values

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Nominal data is data such as labels, names, categories.. there is no point in statistics for these things

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info

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Assume that all sample values in each class are equal to the class midpoint

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Mean from a frequency distribution

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Mean from a frequency distribution
__ E(f*x)
x= ----------
Ef

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Find the class midpoint, multiply the class midpoint by the frequency add the totals and divide by the sum of the frequency

Front 42

Frequency distribution yields an approximation of
-
x because it is not based on the exact original list of sample values.

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Info

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A=4 points b=3 points c= 2 points d=1 point f= 0 points
I Took a 3 credit course got an A, 4 got an A, 3 got an b, 3 got a C and 1 got an F
__ E(w*x)
x=----------------
E(w)

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(3*4)+ (4*4)+(3*3)+(3*2)+(1*0)
________________________________
3+4+3+3+1

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Distribution of data is symmetric if the left half of its histogram is roughly a mirror image of its right half

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symmetric

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Distribution of data is skewed if it is not symmetric and extends more to one side than the other

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skewed

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(also called negatively skewed) have a longer left tail, mean and median are to the left of the mode

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Skewed to the left

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(also called positively skewed) have a longer right tail, mean and median are to the right of the mode

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Skewed to the right

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The mean and median cannot always be used to identify the shape of the distribution.

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True

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The range of a set of data values is the difference between the maximum data value and the minimum data value.

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Example

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Range=

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Maximum value- minimum value

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Range is is very sensitive to extreme values; therefore not as useful as other measures of variation.

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Info

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Round off rule for measures of variation

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When rounding the value of a measure of variation, carry one more decimal place than is present in the original set of data.

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Round only the final answer, not values in the middle of a calculation.

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True

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a set of sample values, denoted by s, is a measure of variation of values about the mean.

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Standard deviation

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a measure of variation of all values from the mean.

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Standard deviation

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The value of the standard deviation s is usually positive.

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True

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The value of the standard deviation s can increase dramatically with the inclusion of one or more outliers (data values far away from all others).

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True

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The units of the standard deviation s are the same as the units of the original data values.

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True