Bell Curve

[Susan Altemus]

I would like to determine a bell curve using performance ratings for our employees. Would someone be able to assist me?

I currently have 2 columns as shown below. The lowest rating someone could receive is a zero and the highest a five.

<TABLE style="WIDTH: 163pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=218 border=0 x:str><COLGROUP><COL style="WIDTH: 92pt; mso-width-source: userset; mso-width-alt: 4498" width=123><COL style="WIDTH: 71pt; mso-width-source: userset; mso-width-alt: 3474" width=95><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 92pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=123 height=17>Employee</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 71pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=95>Rating</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>A</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.25</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>B</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.15</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>C</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.00</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>D</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2.75</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>E</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.20</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>F</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.00</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>G</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.10</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>H</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2.85</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>I</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>4.50</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>K</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>5.00</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>L</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.50</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>M</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.75</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>N</TD><TD class=xl23 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3.85</TD></TR></TBODY></TABLE>

Thank you,
Susie

 

[xenou]

Have you heard of "There are three kinds of lies: lies, damned lies, and statistics?"

Mark Twain attributed the quote to Benjamin Disraeli but it might have been Charles Wentworth Dilke.

A good quote. I'll have to see what kind of damned lies I can get out of this ... if I can find some time to play with it.

Quote:
Originally Posted by xenou
If I may ask out of curiosity, why would you do this? For the sake of argument, let's say the data is not a normal curve. What do we gain by "forcing" it into a normal curve (whatever that means)?

The normal curve is really nice looking :P and is easy to work with (for example, you can use the central limit theorem). Furthermore, after collecting a large enough sample of data, the distribution will be very very close to a normal distribution (regardless of the individual distribution of the ratings). Note that it is an APPROXIMATION (but as stated, so easy to work with)

Quote:
Originally Posted by xenou
Also curious on this point, what does it mean to use values representing ratings? What has happened to the real ratings?

If you use your actual data (with a small sample), the graph won't look like a normal curve. Therefore, you plot a large amout of possible values, all corresponding to a normal distr.

Hope this helps.

I'm sorry to say I'm still puzzled -- I'm assuming that the OP has real data, which cannot be altered or added to (that is, we have a list of 13 actual employee ratings). So what do you mean by "plotting a large amout of possible values, all corresponding to a normal distr" ... what possible values? Aren't we assuming that the curve is normal? Why not assume it's skewed right or skewed left? Couldn't we be making a mistake by "trying" to find a normal curve when perhaps that's not what our population would actually look like ...

Just my thoughts - please realize I am no expert in statistics. I am curious though. I'll have to try some of these suggestions but I'm not at all sure I understand them!

 

[samfolds]

"plotting a large amout of possible values, all corresponding to a normal distr"

To make the graph look nicer : it makes it "smooth" :P... But that's how you make a graphic in any circumstances. Try plotting a quadratic function with just 4 points..!!! Now try with a dozen, 100. See how smooth it becomes.

As you're saying, on a small sample, it's probably not a good idea to approximate our data with a normal curve. Unless OP wanted to compare her actual data with the corresponding normal distribution, I don't know why she wanted to do that.

Don't hesitate if it's still blurry

Samfolds

 

[xenou]

Okay - I'll see if I can learn something from all this now! If I come up with anything interesting I'll post back.