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Python for Data Analytics
45 hours 3 mins
While sampling from the uniform distribution is quite useful, you can also generate random samples from other distributions, like the normal distribution. You're continuing your pricing strategy work with the online jewelry retailer. This time, you've also been asked to model potential competitor prices, which you hypothesize to be roughly normally distributed around your own mean price. Some competitors price higher, some lower, and increasingly higher or lower prices are increasingly more rare. By analyzing historical competitor data, you've found that prices for similar diamonds typically vary relatively narrowly around your client's mean price. The distribution has a standard deviation of about $750. You can use this insight to simulate realistic competitor pricing scenarios using your own mean price plus this standard deviation. This simulation can help your client estimate how often their prices may be significantly undercut by competitors and determine optimal discount levels that maintain competitiveness. Picking up where you left off in the same notebook, you've already imported your modules. You're interested in creating a simulation of 1,000 diamond prices from the normal distribution with a mean of $3,932 and a standard deviation of $750. Remember, that's the standard deviation you found based on analyzing the historical competitor data. You've already created this simulation for many confidence intervals from the uniform distribution, so you can copy this code and just change a few aspects of it. Let's start with just this section of the loop plus the end and confidence variables. The processes are quite similar since they both have a sample size, confidence level, mean, standard deviation, and so on. You actually only need to change one line of code here. Can you spot which one you'll need to change? Well, you're sampling from the normal distribution now, not the uniform one. The size argument stays the same, still $1,000, but now you have LOC and SCALE arguments, just like your confidence interval. For LOC, use the mean price for your diamonds, $3,932, and for SCALE, use the historical standard deviation, $750. For now, add a line that prints out the interval as is. Running that cell, you get 100 pairs of values. These are all your confidence intervals. They're quite narrow around the mean value. Before you take these results to your client, you can add back in the other parts of the code that print out these pretty results. Remember, the true mean is $3,932. You can change these variables to contains and does not contain mu. Then adjust the value, checking whether the mean is within the interval. It's 3,932, not 0.05. Run this cell, and cool! You get 98 intervals containing the true mean, and only two intervals that don't. Playing that back, you use the np.random.normal function to generate random samples from a normal distribution. You use the same size argument as with np.random.uniform, but this time included the LOC argument for the mean and SCALE argument for the standard deviation. Great work! You've seen how simulation can help address real-world business problems and written Python code to repeat a simulation many times. That takes you to the end of this lesson. You've covered the core inferential techniques data analysts use every day and seen how to scale them up to create hundreds of intervals at once. Coming up, you'll complete the Practice Assignment and Practice Lab for this lesson, where you'll explore housing prices in London. Once you're done with the Practice Assignment and Practice Lab, join me in the next lesson to learn a brand new inferential technique, linear regression. See you there!