How do you know when to use which statistical distribution?
Quick and dirty in Excel:1) Chart it. Use an XY Scatterplot - what do you see? Histograms are also often a quick tell.2) Using the Analysis Toolpack Addin from the Data Analysis menu/ribbon run a regression on the data. Select the checkboxes to plot residuals. If they look like a random scatterplot it is normally distributed. Other patterns suggest other distributions.3) Using the Analysis Toolpack Addin from the Data Analysis menu/ribbon run Descriptive Statistics on the data. Look particularly at the values for Skewness and Kertosis. Good basic description of these two pasted below from this page: http://www.princeton.edu/~otorre..."Skewness measures the asymmetry of the data, when in an otherwise normal curve one of the tails is longer than the other. It is a roughly test for normality in the data (by dividing it by the SE). If it is positive there is more data on the left side of the curve (right skewed, the median and the mode are lower than the mean). A negative value indicates that the mass of the data is concentrated on the right of the curve (left tail is longer, left skewed, the median and the mode are higher than the mean). An indicator of a normal curve shows a skew of +2 to –2. A normal distribution has a skew of 0.""Kurtosis measures the peak of the distribution. It is also an indicator of normality. Positive kurtosis indicates too few cases in the tails o a tall distribution (leptokurtic), negative kurtosis too many cases in the tails or a flat distribution (platykurtic). The range for normality should go, in general, from +2 or to –2. A normal distribution has a kurtosis of 0 (given a correction of –3, otherwise it will have a kurtosis of 3)."
What type of statistical distribution I have to use?
I would say either uniform or a very simple linear function.Uniform[math]f(x) = \begin{cases} \frac {1}{8} & \text{if }4.5 \le x \le 8 \text { with a step of 0.5} \\ 0 & \text {otherwise} \end{cases}[/math]Simple linear function.[math]f(x) = \begin{cases} \frac {5}{48} + \frac {x}{300} & \text{if }4.5 \le x \le 8 \text { with a step of 0.5} \\ 0 & \text {otherwise} \end{cases}[/math]Considering the slope of the linear function is so small, the uniform one is probably just as good. The difference in probabilities of the 2 end values is just [math]\frac {3.5}{300} = \frac {7}{600} \approx 0.0117[/math] which can easily be explained by random variance.
What type of distribution to use? (In terms of statistics)?
A cloth manufacturer knows that faults occur randomly in the production process at a rate of 3 every 15 metres. i) Find the probability that there are of exactly 4 faults in a 15-metre length of cloth. ii)Calculate the probability of at least 2 faults in a 60-metre length of cloth. I think it is a geometric distribution, what are your thoughts, is it binomial, geometric or Poisson?
What does center of distribution mean in statistics?
ok well i just started stats and i'm just learning all the terms, what does center of distribution mean? this is an example i'm stuck on The population of the United States is aging, though less rapidly than in other developed countries. Here is a stemplot of the percents of residents aged 65 and older in the 50 states, according to the 2000 census. The stems are whole percents and the leaves are tenths of a percent. There are two outliers: Alaska has the lowest percent of older residents, and Florida has the highest. 6 8 7 8 8 9 79 10 08 11 15566 12 012223444457888999 13 01233333444899 14 02666 15 23 16 8 whats the center of distribution?
Another statistics question from April 14?
For any normal random variable X with mean μ and standard deviation σ , X ~ Normal( μ , σ ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( μ , σ² ). Most software denotes the normal with just the standard deviation.) You can translate into standard normal units by: Z = ( X - μ ) / σ Where Z ~ Normal( μ = 0, σ = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed with mean μ and standard deviation σ /√(n) An applet for finding the values http://www-stat.stanford.edu/~naras/jsm/... calculator http://stattrek.com/Tables/normal.aspx how to read the tables http://rlbroderson.tripod.com/statistics... In this question we have Xbar ~ Normal( μ = 1100 , σ² = 6400 / 400 ) Xbar ~ Normal( μ = 1100 , σ² = 16 ) Xbar ~ Normal( μ = 1100 , σ = 80 / sqrt( 400 ) ) Xbar ~ Normal( μ = 1100 , σ = 4 ) Find P( 1097 < Xbar < 1104 ) = P( ( 1097 - 1100 ) / 4 < ( Xbar - μ ) / σ < ( 1104 - 1100 ) / 4 ) = P( -0.75 < Z < 1 ) = P( Z < 1 ) - P( Z < -0.75 ) = 0.8413447 - 0.2266274 = 0.6147174
What is raw data in the term of statistics?
The original measured values or scores, without any manipulation, except perhaps sorting in the case of quantitative data. Any manipulation should be completely "non-lossy", so histogram binning and frequency calculations, for instance, would not comply (as discussed in response to your previous question about small differences in calculated summary statistics based upon raw data or upon frequencies).
Questions in Statistics!! Please Help!!?
1) --- b 2) --- d 3) --- total f of last 3 classes --- (0+1+2) --- d 4) --- d 5) --- b 6) a) f : 0 3 5 3 1 b) 3 c) 12 d) --- c 7) --- b 8) --- a
What is a normal distribution in laymens terms?
Gaussian Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. Height is one simple example of something that follows a normal distribution pattern: Most people are of average height, the numbers of people that are taller and shorter than average are fairly equal and a very small (and still roughly equivalent) number of people are either extremely tall or extremely short.This distribution is maintain not only in Economic aspects but also Biological aspect, Random velocity of Gaseous Particles, Electrical Circuit etcThis naturally leads us to ask the question why mathematics is so effective at describing our universe – a question asked many times before by a number of great minds.Importance of Normal Distribution :First reason the normal distribution is important is that many psychological and educational variables are distributed approximately normally. Measures of reading ability, introversion, job satisfaction, and memory are among the many psychological variables approximately normally distributed. although the distributions are only approximately normal, they are usually quite close.It is very helpful in forecasting .We can calculate the estimated length of the bones of animals and woods and leaves . because if animals are one type their numbering is normally distributed .Second reason the normal distribution is so important is that it is easy for mathematical statisticians to work with.Normal distribution is very useful for controlling the quality in business. With this we can fix the limit of quality . that will helpful for controlling the quality .If we take one sample out of the universe and calculate the mean size of growing then it will normal distribution This means that many kinds of statistical tests can be derived for normal distributions. Almost all statistical tests discussed in this text assume normal distributions. Fortunately, these tests work very well even if the distribution is only approximately normally distributed. Some tests work well even with very wide deviations from normality.Finally, if the mean and standard deviation of a normal distribution are known, it is easy to convert back and forth from raw scores to percentiles.For more query:Normal DistributionThe Gaussian/normal distributionNormal DistributionImportance of the Normal Distribution
Probability and Statistics Question?
(a) You need the area under the normal distribution curve that lies above 135 given that the mean = 137.2 and standard dev = 1.6. This represents 1.375 SDs from the mean (i.e. 2.2 / 1.6). Use the normal dist. tables for this area. The area between 135 and 137.2 is 0.4154. But you add the total area above the mean to this, giving the total area above 135 as 0.9154. So that the proportion of the area above 135 is 91.54 per cent of the whole area under the curve. Probability that one jar contains more than 135 oz is 91.54%. (b). Select 10 at random. You now have a binomial distribution with p = .9154 and q = .0846, with 10 trials. This is (p+q)^10 . Probability that exactly 8 contain more than 135 oz is 10C8 p^8. q^2 Pr that exactly 9 contain more than 135 oz is 10C9 p^9.q Pr that all 10 contain more than 135 oz is p^10. So the Pr that at least 8 contain more than 135 oz is the sum of these three. 10C8 = 45, 10C9 = 10. 0.9154^8 = 0.4930, 0.0846^2 = 0.00716 0.9154^9 = 0.4513, 0.9154^10 = 0.4131. Pr(8) = 45 x 0.4930 x 0.00716 = 0.1941 Pr(9) = 10 x 0.4513 x 0.0846 = 0.0382 Pr(10) = 0.00716 Sum of these 3 = 0.2395. The probability that at least 8 out of the 10 exceed 135 oz is therefore 0.2395 or 23.95 per cent. (c) Mean stays at 137.2 but you want 95 % to exceed 135. This implies the half (i.e. 50%) above the mean and 45% below the mean. From the same tables, this is 1.645 SDs below the mean. If the stated contents is to be 135 again, this implies that the SD = 2.2 / 1.645 = 1.337. So the SD would need to be 1.337.
Statistics question. Please help/explain. :o)?
All human blood can be typed as one of O, A, B, or AB, but the distribution if the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American. Blood type O A B AB Probability 0.45 0.25 0.14 ? (a) What is the probability of type AB blood? (b) Maria has type B blood. She can safely receive blood transfusions from people with types O and B. What is the probability that a randomly chosen black American can donate blood to Maria?