1 spreadsheet problem solving applied statistics table lookup
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Spreadsheet Problem Solving applied statistics
table lookup
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Using Excel for statistical calculations
Broad capabilities, well beyond the scope of this course[ChE’s will learn many more features in
Applied Data Analysis (CHEN 3010)]
Built-in functions (COUNT, AVERAGE, STDEV, . . . )
Data Analysis toolbox (Descriptive Statistics, Histogram,Regression, . . . )
We will concentrate today on descriptive statistics
Trendline curve-fitting feature
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Characterizing a set of data
1 2 ny , y , , y iy , i 1,2, ,n
Central value or tendency(most likely value, estimate of true value)
Sample average
n
ii 1
yy
n
Median
n+1
2
in 2 n 2 1
n odd: y
y with y sorted in ascending ordery yn even:
2
Mode most frequently occurring value in the series
there are others: geometric mean, harmonic mean,m-estimator, first moment
[ AVERAGE(•) ]
[ MEDIAN(•) ]
[ MODE(•) ]
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Spread or dispersion of the data (describes uncertainty)
Range max minR y y
Inter-quartile range (iqr) 75%ile 25%ileiqr y y
Sample standard deviation n
2
ii 1
y yS
n 1
Resolution decimal place farthest to the right to whicha measurement may be reliably read
Standard error of the mean estimate y
SS
n
There are others, e.g., median absolute deviation.
[ MAX(•) - MIN(•) ]
[ STDEV(•) ]Note: sample variance issquare of S, [ VAR(•) ]
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Other quantities of use in statistical calculations
sample count n
sample sumn
ii 1
y
sample sum of squaresn
2i
i 1
y
“corrected” sum of squares n
2
ii 1
y y
[ COUNT(•) ]
[ SUM(•) ]
[ SUMSQ(•) ]
[ VAR(•) * (n-1) ]
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Example data set:
Measurements taken on a silicon wafer used for makingmicrocircuits
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Sample statistics using formulas
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8Finding the median andquartiles
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Using the Data Analysis toolbox
Note: if the Data Analysis . . .item is not on the Tools menu,you will have to go to the Add-insmenu and activate the checkboxfor Analysis Toolpak. If the AnalysisToolpak item is not on the Add-inslist, it will have to be installed fromMicrosoft Office Set-up.
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Setting up for descriptive statistics
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Results from Descriptive Statistics
Format AutoFormat OK
reformat table adjust display forappropriatesignificant figures
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Table Look-up
A great deal of information is organized in the form oftables and Excel provides a number of built-in functionsthat allow for the extraction of appropriate data from tables.
Excel’s lookup functions are:
LOOKUP
VLOOKUP
HLOOKUP
MATCH
INDEX
OFFSET
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LOOKUP(Lookup_value,Lookup_vector,Result_vector)
search downthe lookupvector
find eithera matchingvalue, ora valuegreater thanthe lookupvalue, whicheveroccurs first
go to the same position inthe result vector, and extractthe value there
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Example of LOOKUP use
text inalphabeticalorder
create name“material”for this column
this columnwill be the“lookup vector”
numerical valuesof bulk density
create name“density” forthis column
this column willbe the“result vector”
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Create LOOKUP functionformulas
this cell is named “choice”
Lookup_value,Lookup_vector,Result_vector
What happens when our choice is not in the lookup vector?
LOOKUP goes down listuntil it finds a name > “potash”,“salt” in this case, then it backsup one to “oyster shells” andreturns the answer for that
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Important: the lookup vector must be in ascending order. For text labels,this means alphabetic order. Upper- or lower-case letters don’t matter.
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VLOOKUP(Lookup_value,Table_array,col_index_num,Range_lookup)
searchdownleftcolumnoftablearraytofindmatch
Which column number forextraction of result? 1, 2, 3 or 4?
result
optional argument:if FALSE, requiresan exact match
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Example of VLOOKUP use
Table of properties of various granular materials
named “MaterialTable”
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Need to sort the table in ascending (alphabetical) order forfirst column
Using VLOOKUP to extract information from the table:
What if our choice value has a typo?
cell named“choice”
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typo, should be “Millet”
result shown as invalid
With 4th argument as TRUE, or absent, you would see:
results for “Flaxseeds”,next earlier item in table
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Application of VLOOKUP: Linear interpolation from atable of physical properties
For any %HNO3
from 0 to 90, wewant an automaticestimate of theheat capacity
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Create index columns to the right and left of the table
name this“NitricTable2” name this
“NitricTable1”
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Create an input cell and name it “input”
Enter a formula using VLOOKUP todetermine the row index for the“lower bracketing value”
Enter a simple “add 1 to the above” formula for the rowindex of the “higher bracketing value”
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Enter VLOOKUP functions based on “NitricTable2” andusing the low and high row indices to extract the bracketingvalues of %HNO3 and Heat Capacity.
Using Insert Name Create, transfer the 6 labelsin column F over as names on the cells to the right incolumn G
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LowPct HighPct
LowHC
HighHC
linear approximationbetween to locationsin the table
input%HNO3
HeatCapestimate
input LowPct
HeatCap HighHC LowHC LowHCHighPct LowPct
Enter this formula in a cell to compute the estimatedheat capacity
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Automatic linear interpolationformula and results
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Change values of the input to get different results[including bad results when input outside of
acceptable range]
the good the bad and the ugly!
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Other lookup functions:
HLOOKUP like VLOOKUP, except horizontalrather than vertical looks acrosstop row of table and then extracts fromindexed row
MATCH does not extract a value, but, instead, returnsa relative location (position number) of avalue in a lookup array
INDEX extracts a value from a table (2-dimensionalarray of cells with rows and columns) giventhe column index and the row index
OFFSET extracts a cell address or range from a tablegiven the offset location from the upper-left-hand corner of the table
See “Help” for more details on these