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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:

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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

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