How do I sketch distributions? I think I'm doing it wrong. Is there an option my friends stats-calc(her calcultor is very tempremental, so i don't know if it'll work) I can utiilzie that'll sketch things for me? thanks.
-Sketch a normal distribution with (mu)
m =80 and standard deviation of (greek letter s) 20.
a)Locate each of the following scores in your sketch, and indicate whether you consider each score to be an extreme vaule(high or low) or a central value:
65,55,40,47
b)Make another sketch showing a distribution with mu=50, but this time with a standard deviation of 2. Now locate each four scores in the new distribution, and indicate whether they are extreme or central.
How do I sketch distributions? I think I'm doing it wrong. Is there an option my stats-calc I can utiilzie that'll sketch things for me? thanks.
They gave you the mean and the standard deviation. That is all you need for an accurate sketch (bell curve) if the distribution is normal. If the standard deviation is small, the bell curve will be very narrow. If it is big, the bell curve will be wide. So the first curve will be fat, centerered on the mean, and the second one will be very narrow, centered on the mean.
In your book, you should be able to find a table of values for a normal distribution in terms of (x-mu)/sigma. That table would allow you to graph the curves very accurately. Notice that x-mu and sigma define the whole thing. All that matters is how far you are from the mean and what the standard deviation, sigma, is.
For starters, the probability of being between the mean minus one sigma and the mean plus one sigma is .68, so if your mean is 80 and sigma is 20, 68 percent of your curve will be within 20 of the mean, 80 or between 60 and 100.
Then look at the second one with mean 80 and sigma of 2
In this case, 68 percent will be beteen 48 and 52, pretty sinny and most of those values given will be pretty unlikely. 47 is the only one that is in really likely range.
To sketch a distribution, you can utilize a graphing tool or software that can plot a normal distribution curve based on the mean (μ) and standard deviation (σ) values you have.
If your friend's stats calculator is not working well, you can consider using online tools or software like Excel, SPSS, or GraphPad Prism to sketch the distributions. These tools usually have options to plot normal distribution curves based on the mean and standard deviation you provide.
For the first part of your question, sketching a normal distribution with μ = 80 and σ = 20, you can follow these steps:
1. Calculate the Z-scores for the given values using the formula: Z = (X - μ) / σ, where X represents each individual score.
- For X = 65: Z = (65 - 80) / 20 = -0.75
- For X = 55: Z = (55 - 80) / 20 = -1.25
- For X = 40: Z = (40 - 80) / 20 = -2.00
- For X = 47: Z = (47 - 80) / 20 = -1.65
2. Once you have the Z-scores, use a normal distribution table or a graphing tool to locate these Z-scores on the curve. A Z-score indicates how many standard deviations a score is away from the mean.
- A Z-score of -0.75 is relatively close to the mean, so consider it a central value.
- A Z-score of -1.25 is moderately far from the mean, so consider it closer to an extreme value.
- A Z-score of -2.00 is significantly far from the mean, so consider it an extreme value.
- A Z-score of -1.65 is moderately far from the mean, so consider it closer to an extreme value.
For the second part of your question, sketching a distribution with μ = 50 and σ = 2, follow the same steps:
1. Calculate the Z-scores for the given values:
- For X = 65: Z = (65 - 50) / 2 = 7.5
- For X = 55: Z = (55 - 50) / 2 = 2.5
- For X = 40: Z = (40 - 50) / 2 = -5.0
- For X = 47: Z = (47 - 50) / 2 = -1.5
2. Use a normal distribution table or a graphing tool to locate these Z-scores on the curve.
- A Z-score of 7.5 is extremely far from the mean, so consider it an extreme value.
- A Z-score of 2.5 is moderately far from the mean, closer to an extreme value.
- A Z-score of -5.0 is significantly far from the mean, so consider it an extreme value.
- A Z-score of -1.5 is moderately far from the mean, so consider it closer to an extreme value.
Remember that extreme or central values are subjective and can depend on the context and purpose of the analysis. The above categorization is based on the relatively common definition that values beyond 2 standard deviations from the mean can be considered extreme.