![]() ![]() You might be curious: what variables in daily life can a normal distribution model. These parameters do not come from data but are part of the model. Normal models are appropriate for symmetric and unimodal distributions. The normal model has two parameters (the population mean, µ, and the population standard deviation, σ) and is often written as N(mean, sd). A normal curve is mound-shaped and symmetric. Some sets of data may be described as approximately normally distributed. You may have learned about "normal" models or bell-shaped curves in your Algebra class and through calculus. AP Statistics MCQs always will ask questions like this to trick you if you know how the shifting and rescaling affect the shape, center, and spread, so get ready to encounter such questions! □ Normal Model: More than Just a Hump What about rescaling? You may guess already that with rescaling data when we multiply or divide any number to a data set, the shape of distribution won’t change (it will just look stretched or squeezed), but everything else will change, the mean, minimum, maximum, range, IQR, and standard deviation. The center shifts with other measures of the position such as percentiles, mininum, and maximum by the same amount of value. In general, shifting data changes the distribution but leaves the shape and spread unchanged. Wait, but how does standardization affect the distribution? □ Here is the formula for z-score:Īs you see, when we are standardizing data into z-scores, we are shifting them by the mean and rescaling by the standard deviation. The further the value is from the mean, irrespective of the sign, the more unusual the value is. Negative z-scores mean that the data value is below the mean, while positive z-scores mean that the data value is higher than the mean. In sports, when the judges have to calculate the final score for athletes, they use z-scores. They can also be used to standardize data for comparison between different data sets.įor this reason, z-scores are also called standardized values. Z-scores are useful for comparing values within a data set and for determining whether a value is unusual or extreme relative to the rest of the data. This z-score of 2 means that the data point is 2 standard deviations above the mean of the data set. If a data point has a value of 70, the z-score for that data point would be calculated as follows: Where z = z-score, x = a data point, x̄ = mean value, s = standard deviationįor example, consider a data set with a mean of 50 and a standard deviation of 10. It is resistant to units, and it can be used to compare any activity. It is calculated by subtracting the mean of the data set from the value of the data point, and then dividing the result by the standard deviation of the data set. So, what exactly are z-scores? A z-score, also known as a standard score, is a measure of how many standard deviations a data point is from the mean (not median) of a data set. When I think of statistics, one of the first things that come in my mind is standard deviation and z-scores. N ( μ, σ 2 ) Īccording to Stigler, this formulation is advantageous because of a much simpler and easier-to-remember formula, and simple approximate formulas for the quantiles of the distribution.This section introduces you to z-scores. ![]()
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