USING EXCEL ON THE COMPUTER TO FIND THE MEAN AND
STANDARD
DEVIATION AND TO DO LINEAR REGRESSION ANALYSIS AND GRAPHING
Dr. Susan Petro
 |
Click here for printer friendly version |
TABLE OF
CONTENTS
USING EXCEL ON THE COMPUTER TO FIND THE MEAN AND
STANDARD
DEVIATION AND TO DO LINEAR REGRESSION ANALYSIS AND GRAPHING
Dr. Susan Petro
|
Click here for printer friendly version |
Topic
a)
Inserting
a ° symbol
b) Inserting a Δ symbol
c) Subscripts and superscripts
d) Significant figures
e) Merging cells
4. Making your graph
a) Deciding
how to set the y intercept
b) Adding the correlation coefficient ( r ) to your graph
c) Formatting your graph
a) To solve for x when you know y
b) To solve for y when you know x
6. Formatting your table
10. Calculating
the Standard Deviation
11. How to add a
mean and standard deviation line to a histogram
12. How to embed your Excel graphs and tables into a Word document
13. Examples of Graphs
c)
Histogram
On
Following Directions
From We
Took to the Woods by Louise Dickinson Rich
I'm a good knitter, and I'm
proud of it. I can make up my own directions, or I can follow
printed directions, which apparently is the harder thing to do,
although I don't see why it should be.
I think the difficulty with people who can't
follow printed directions for knitting or anything else is that they
try to understand them. They read the whole thing through and it
doesn't make sense to them, so they start with a defeatist
attitude. They try to relate the first few steps to the whole,
and there is no obvious relation, so they get discouraged and say, "Oh,
I can't learn things out of books...."
You don't have to understand directions.
All you have to do is follow them; and you can follow them only one
step at a time. What you need is not intelligence, but a blind
faith. I never read directions through. I never read beyond
the operation I am engaged in, having a simple trust that the person
who wrote them knew what he was doing. That trust is usually
justified. Oh, there's no trick to following directions, and if I
don't teach my children one other thing, I'm going to teach them
that. I think it's important.
Click on Programs.
Click on MSOffice.
Click on Microsoft Excel.
Decide
what data should go on the x
axis (the determinate axis) and what data
should go on the y
axis (the
indeterminate axis). The information you knew before you ran the
experiment goes on
the x axis
and the information you got by doing the experiment goes on the y
axis.
For example
if you are
measurieng the absorbance of a number of dye concentrations the dye
concentrations
will be on
the x axis since you decided
on and prepared the concentrations you
wanted
to test.
You didn't
know what the absorbances would be until you put the various
concentrations
in the
spectrophotometer,
so absorbance would go on the y
axis.
Type in
the
heading for the x axis in the
A1 box e.g. concentration (mg/ml). If the
heading is too
long to fit
in the box, you may increase the box width by placing the cursor on the
line between
A and B so
you get a double headed arrow 1
and dragging to the width you want.
To have
your
data in columns, type in the heading for the y axis e.g. absorbance in
the B1 box.
To have your
data in rows, type in heading for the y
axis e.g. absorbance in the
next
box in the
column,
A2. Remember your page width only goes through I so if you have rows to
the right of
I they will
not show up on your page when you print it. Also if you have increased
the width of
a box, your
page width will not go as far as I anymore.
Enter the
values
for x (numbers only, no
letters or symbols) in the A column
under
your
heading if
you are doing your data in columns.
Enter values
for x in the1 row following
your heading if you are doing your data in
rows.
For data
in
columns, enter values for y (numbers
only, no letters or symbols)
under the y axis
heading e.g.
enter values in B2, B3, etc.
For data in
rows, enter values for y in
boxes to the right of your y axis heading
e.g.
B2, C2, D2,
E2, etc.
DO NOT enter values for your unknown in the table at this point.
To insert
a
degree (° ) symbol hold down the Alt key
and type 248 on the number pad. (If you are
using a
Macintosh
computer hold down the Alt key, shift key and hit the number 8
key.)
To insert
a Δ symbol open up a Microsoft Word document.
Click on insert on the task bar.
Click on symbol.
Find the Δ
symbol on the table and select it. Click
on Insert then click on Close. Now
select the
Δ and click on Edit on the task bar.
Click on cut or copy. Open your
Excel document and click on
Edit and then Paste.
To
insert
a superscript or subscript in Excel click on Format on the menu
bar.
Then click on
Cells.
A window will open. In the lower left of the window it says
Effects.
Click on the box
to the left
of subscript or superscript. A check mark will appear. Now
click on OK. Type
in your
superscript
or subscript. To exit super/subscript mode repeat the process
above.
When you
click
on the box with the check mark it will disappear. Click on OK.
To have all your data values have the
same number of spaces to the right of the decimal point
select all the cells containing
numbers. Click on Format. Click on Cells. Click on
Number.
Click on Number under Category. Decide
the number of spaces you want to the right of the
decimal point based on the significant
figures you used for your measurements. Click on OK.
Merging
cells
To merge cells select the cells you want to merge and then click on the
merge icon on the toolbar
Select the entire table including the headings.
Click on
Chart
Wizard on the standard toolbar (top row of icons). This icon looks like
a
multi-colored
bar graph.
Chart Wizard Step 1 of 4 - Chart Type will appear.
Click on XY (scatter) line under Chart Type.
Under Chart subtype click on the top chart if it is not already selected.
Click on Next.
Chart Wizard Step 2 of 4 - Chart Source Data will appear.
If the data in your table is in columns click on columns, if it is in rows click on rows
Click on Next.
Chart Wizard Step 3 of 4 - Chart Options will appear.
On the
Title
card enter chart title (e.g. The Effect of Concentration on the
Absorbance
of Methylene
Blue Dye at Wavelength of 675nm).
Enter X axis title e.g. Concentration (mg/ml) of Methylene Blue Dye.
Enter Y axis title e.g. Absorbance (Abs units) of Methylene Blue Dye .
Click on Next.
Chart Wizard Step 4 of 4 - Chart Location will appear.
Decide if
you
want your chart as a new sheet or as an object on the sheet with your
table.
For
Fundamentals
of Biology have the table on the same page as the chart for ease in
correcting
so click on as an object in the sheet.
Click on Finish.
Click on
the
chart area. Small boxes will appear along the borders.
Click
on the white
area of the
graph so a four-sided arrow appears. Holding down the left mouse
button
drag the
chart
below your table. Now click on one of the small boxes on the
bottom
edge
of your
graph
so a double-sided arrow appears. Drag the bottom of the graph
down
to
number
42.
Click on one of the small boxes on the right side of your graph
so
a
double-sided
arrow appears. Drag the right side of the graph to the letter
I
if you haven't
increased
the size of the cells.
Double
click
on the plot area. Format Chart Area will appear. To change the
background
color of the
plot area click on the box under Area that is the color you want. I
prefer
a
white
background
for maximum contrast so click on none. Click on OK.
Click on
one
of the points on your graph. All the points in the line to which that
point
belongs
will become
larger squares.
Click on Chart on the menu bar.
Click on Add Trendline.
Click on Linear box if it is not already highlighted.
Click on Options card behind Type card.
Click on
Set
Intercept when dealing with linear regression data where y was zero
when
x was zero for
example in labs using
the spectrophotometer
to measure absorbance.
(The spectrophotometer is
blanked; set to zero
absorbance
at zero concentration of the
substance whose absorbance
is to be measured).
Otherwise don’t click on Set Intercept.
Set Intercept will set the y
intercept at zero so
when your formula (y = bx + a)
comes
up the a
value will be zero and
not
appear.
Click on
'Display
equation on chart'. The formula y =
bx + a with appropriate values for
b (slope)
and a (y intercept) will
appear on your graph
Click on
'Display
R-squared
value on chart'. R2 is the correlation of
determination.
Values for the correlation
of determination range from zero to one. The higher the
correlation of determination
(the closer to one) the better the regression line is in
explaining the variation
of the data.
Click on OK.
To move
formulas
where they can be more easily seen, click on the formula. A hatched
border will
appear around the formula. Click on the border so a four-sided arrow
appears
and drag it
where you want it.
The
default
point size of the formulas is quite large so to change the point size,
click the
down arrow
next to the displayed point size in the Formatting toolbar and choose a
smaller
point
size.
To add the correlation coefficient ( r ) to your graph:
Type in =sqrt(the R2
value
from your graph) e.g. if
R2
was 0.949 then type
=sqrt(0.949). Hit Enter. The r value will appear
in the cell.
Now click on the graph so the hatched border appears
around
the plot area
of the graph and the word ‘plot area’ appears in the
Name box.
Click in the formula bar that is to the right of the
Name
box. Three icons will
appear. Now type in r = whatever you got above e.g. r
= 0.974. If your slope
value (b) was
positive the r value is positive, if your
slope value was negative
then the r value will be negative. So if your
slope
was negative type a negative
sign in front of your r value.
Click on the check mark icon. What you typed will
appear
on your graph
surrounded by a hatched box.
Drag the box so it is under your other formulas.
To change the font or point size of the r value
click
on Format. Click on
Selected Data Labels. Click on Font and choose size and
font to match your
other formulas.
| The correlation coefficient indicates how
closely the
points on your graph fit a straight line. A value of +1 or -1 indicates a perfect direct or indirect relationship between x and y. If your correlation coefficient is not close to +1 or -1 your data is not linear. (Perhaps it is logarithmic, exponential or polynomial). If this is the case you wouldn’t use linear regression for graphing your data. Link to visual aide on correlation coefficient. |
Sometimes
as
you are working on the following formatting the r = equation will
seem to
disappear
from your graph. Click on the spot where the equation was
and it will
reappear.
Click
twice on the item to be changed. (Note : this is not a
double
click, but two
separate clicks.) The cursor will appear and you can make your
changes.
Alternatively
Click on the item you want to change. A hatched border will appear around it.
Put the cursor in the formula bar that is to the right of the Name
box.
Three icons
will appear. Type in the orrections you want to make.
Click on the green check mark icon.
Double click on the title. A Format Chart Title dialog box will appear.
Click on Font. Choose the size you want.
Alternatively
Click on the title. A hatched border will appear around the title.
Click on Format.
Click on Selected Chart Title.
Click on Font.
Choose font, font style and size you want.
Double click on the axis label. A Format Title dialog box will appear.
Click on Font. Choose the size you want for your axis label.
Alternatively
Click on the axis label. A hatched border will appear around the label.
Click on Format.
Click on Selected Axis Title.
Click on Font.
Choose font, font style and size you want.
To format the axes numbers or axes lines
Put the
cursor
on the axis whose numbers you wish to format. If the cursor is correctly
positioned
over the axis it will read Value (X) axis or Value (Y) axis.
Double click on the axis line. A Format Axis dialog box will appear.
Click on Font. choose the size you want your axis numbers to be.
Click on Patterns. Choose the weight you want for your axis line.
Alternatively
Place the cursor as above and single click.
Handles will appear on each end of the axis line.
Click on Format.
Click on Selected axis.
Click on Font.
Choose font, font style and size you want.
To remove
borderlines
you don't want e.g. the border around the legend or around
the plot
area
or around the entire graph.
Double
click
on the area inside the border. A Format dialog box will appear.
On the
Patterns
card click on None under Border.
The default line is quite thick so you may want to choose a lighter weight line.
Double click on the trendline.
A Format Trendline dialog box will appear.
On Patterns click on the
down arrow beside Weight and choose the thickness you want
for your line.
Alternatively
Click on the line. Handles will appear on each end.
Click on Format.
Click on Selected Trendline.
Click on Weight and
choose
the line you want.
| Click outside graph and scroll back to your table. |
Solving for Unknown x or y
To solve for x when you know y.
Type in the word ‘unknown’ in the empty space at the end of the y column.
If your data is in
columns
enter the y value you got for
the unknown in the box
below the one where you
typed ‘unknown’.
Move pointer to the empty
space at the end of the x
column. Type in the word
'unknown'. Now move pointer
to the box below the one where you just typed
‘unknown’.
Type = then a parenthesis
then the y value you just entered. ( If the number is very
long you can just type the
letter and number of the cell e.g. D11 to save time.) Now
type - then the a
value (y intercept) from the
formula on your graph and a closing
parenthesis. (If your y
intercept was zero you only need to type the y value without
parentheses.)
Now
type in / and the b value
(slope) from the equation on your graph.
Suppose the equation on
your graph is y = 29.514x. This would mean a, the y intercept,
is zero since it doesn’t
appear and b is 29.514. You
would type
=D11(or the number in the D11 cell)/29.514.
Then hit Enter and that will give you your x value at that y.
To solve for y when you know x.
Type in the word 'unknown' in the empty space at the end of the x column.
Now enter the x value for
the unknown in the box below the one where you
typed ‘unknown’.
Move pointer to the empty
space at the end of the y
column. Type in the word 'unknown'.
Now move the pointer to
the cell below the one where you just typed ‘unknown’
in the y column.
Type = then type a
parenthesis
then the b value (slope) from
the equation on your
graph, then * and the
x value you just typed under
'unknown' in the x column.
(If the x value is very
long you may type the letter and number of the cell containing
the x vallue you just
entered
e.g. A12) Now type the closing parenthesis then + then
the a value (y intercept)
from your graph. then the closing parenthesis then + then the
a value (y
intercept)
from your graph.
Hit Enter and that will give you your y value for that x.
Suppose the equation on
your
graph was y = - 0.421x + 27.98. You would type
=(-0.421*A12)+27.98
Formatting Your Table
Select the entire table.
Click on the Center icon or
Click on Format on the menu bar.
Click Center under Horizontal.
Click OK.
Select just the table headings.
Click on the B (bold) icon if you want the table headings bold.
Click on Format on the menu bar.
Click on Cells.
Click on card heading that reads Font.
Choose font, font style and size you want.
Click on OK.
Highlight the entire table.
Click on Format on the menu bar.
Click on Cells.
Click on card heading that reads Border.
Click on Outline and Inside boxes.
Choose a style for your borderline. Click in that box.
BEFORE PRINTING YOUR GRAPH be sure to click
outside
the graph area
itself. Otherwise only the graph and and not
the accompanying table will be printed.
To see what your graph will look like prior to
printing,
click on File and click on Print Preview.
Click to see an example of a single
line graph.
Say you want to chart several lines on the same
graph
- for example the effect of temperature
on the calories of energy consumed by several
bird
species say the English sparrow, the purple
finch and the pine siskin.
Type in heading for x axis data in the A1 cell - Temperature (°C).
Say you wanted your data in rows. In the A2 cell
type
in Calories English sparrow, in the A3
cell type in Calories purple finch and in the A4 box
type in Calories pine siskin.
Your temperature values will be typed in the 1 row e.g. B1, C1, D1, etc.
The calories for the English sparrow will be typed in the 2 row e.g. B2, C2, D2, etc.
The calories for the purple finch will be typed in the 3 row e.g. B3, C3, D3, etc.
The calories for the pine siskin will be typed in the 4 row e.g. B4, C4, D4, etc.
Select the table
Follow directions using Chart Wizard as previously
explained.
The only difference is that
you must repeat the "Click on one of the points on your
graph" sequence for each line.
When one has several lines the formulas may be
crowded
and it may be difficult to see
which formula goes with which line so click on
the formulas one at a time and drag them
away from the lines.
Make titles for each formula by clicking on the
graph
so a hatched border appears around
the plot area of the graph and the word 'plot area'
appears
in the Name box.
Put your cursor in the formula bar to the right of
the
Name box. Three icons will appear.
Now type in the legend title for that line e.g. English
sparrow.
Click on the green check mark icon. What you
typed
will appear on your graph surrounded
by a hatched box. Drag the box so it is above the
formulas for that line.
Repeat for the remaining lines.
To put the symbol used for each line next to the
title
above each formula you will have
to draw it in by hand after you print the graph.
The computer will choose different colors for the
points
of each line. If you are not using
a color printer the light colors will show up poorly
when printed by a black and white printer.
Double click on one of the points of the trendline
whose
marker color you want to change.
A Format Data Series dialog box will appear.
Click
on Patterns. Under Marker click the
down arrow next to Foreground. Click on black on
the pop-up palette. Now click on the
down arrow next to Background. Click on black on
the pop-up palette. Click on OK.
Click to see an example of a multi-line
graph.
To have your
histogram bars represent ranges.
Below are the water volume measurements for the histogram at the end of this document. These were used to make a histogram with five equal bars.
| Water volume (ml) |
|
| |
35.80 |
| 37.90 |
|
| 38.00 |
|
| 38.20 |
|
| 38.20 |
|
| 38.50 |
|
| 38.90 |
|
| 39.10 |
|
| 39.50 |
|
| 40.60 |
|
| Mean = 38.47 |
|
| Standard deviation = ±1.25 |
To get five bars (or any other number you want) on your histogram:
| Subtract lowest value from largest. For the numbers above that would be 40.60 - 35.80 = 4.80. | |
|
|
Now divide your answer by the number of bars you want . If you want three bars divide by 3. Since we want five bars divide as follows: 4.89/5 = 0.96 |
| Add this number to your lowest
value to get your first range. So 35.80 + 0.96 = 36.76.
First range is thus 35.80-36.76. |
|
| For the second range begin with
36.77, because if you use 36.76 and one of the measurements happens to
be exactly that you won't know whether to count it in the first range
or the second range when you determine the frequencies. Now add
0.96 to the end of the first range value (36.76) to get the upper value
of the second range. Second range is thus 36.77-37.72.
Third range is 37.73-38.68 and so on. |
Follow previous directions for making a table. Put range values
(or individual numbers depending on type of histogram) in first column
and frequencies in second column.
If your x
values are ranges as above then select the entire table.
If your x values are not ranges but single
numbers. DO NOT select the entire table. Select only the y value column of the table.
Click on Chart Wizard.
Chart Wizard Step 1 of 4 - Chart Type will appear.
Click on Column box.
Click on upper left chart under subtype if it is not highlighted already.
Click on Next.
Chart Wizard Step 2 of 4 - Chart Source Data will appear.
Click on columns if your data is in columns, click on rows if your data is in rows.
Click on Next.
Chart Wizard Step 3 of 4 - Chart Options will appear.
Enter Chart title and label x and y axes.
Click on Legend if you want the legend somewhere other than to the right.
Click on Next.
Chart Wizard Step 4 of 4 - Chart Location will appear.
If you want the chart as a new sheet, click on 'as
new
sheet'. If you want it as an object
in the same sheet click on 'as an object'
Click on finish.
How to format your histogram.
Double click on the plot area of your graph. Format
Plot
Area will appear. Click
on 'none' under Area so background will be white.
Click on one of the bars of the graph. Handles will appear on all the bars.
Click on Format. Click on Selected Data Series.
Choose
a color for the area inside
the bars. Don't click on OK yet. Click on
Options.
Set overlap at zero and gap width at 10.
Click OK.
To format the title, legend, axes and the table, see the directions on pages 4-7.
Click to see an example of a histogram.
Enter Microsoft Excel as previously described
Type in heading e.g. water volume in ml in A1 box
Enter values in A column
Skip down a few rows in A column and type in Mean.
Go down to next row and type in =average(range of
boxes
containing your data) and hit
Enter key e.g. if you entered data in box A2, A3, A4,
A5, A6 you would type
=average(a2:a6) or after the first parenthesis
simply highlight all the boxes containing
the data and the range will appear automatically.
Add the closing parenthesis and hit Enter.
Follow all directions for mean as above.
Now skip down a couple rows in column A and type in Standard Deviation.
Go down to the next row and type in =stdev(range of
boxes
containing your data)
and hit Enter. E.g. if you entered data in boxes A2,
A3, A4, A5, A6 you would type
=stdev(a2:a6) and hit the Enter key or after
the
first parenthesis simply highlight all
the boxes containing the data and the range will appear
automatically. Add the
closing parenthesis and hit Enter.
To insert a ± sign in front of your standard
deviations
move the cursor down one cell,
hold down the Alt key and type 241 on your number pad.
(If you are using a
Macintosh computer hold down the Alt key, the shift key
and hit the + key.).
Now type in the standard deviation value you obtained.
HOW
TO INSERT A MEAN AND STANDARD DEVIATION LINE ON A HISTOGRAM
First you need to have the Draw Toolbar visible.
Click on View on the Menu Bar
Click on Toolbars
Click on Drawing. Draw Toolbar will
appear.
Click on the stright line icon \ on the Draw Toolbar.
Draw a vertical line above where the mean would fall.
Click on the straight line icon again to draw a
horizontal line from the minus to the plus end of the standard
deviation range.
Click on the straight line icon to make the
end bar for each end of the horizontal line.
Now click on the plot area. Put your cursor in
the formula bar to the right of the Name box which now says plot
area. Three icons will appear. Type in the mean and
standard deviation.
