The Central Limit Theorem is a statistical theory which states that the shape of a sampling distribution is approximately normal no matter the shape of the population when graphed. This theory works as long as the sample size is larger than 30.
To go more into depth to explain this theorem, we could take Grey’s Anatomy fans across the United States track their episode watching habits. They could write down how many episodes they watched a week from the beginning of January to the end June. Below is a graph(taken from the internet, not real data) showing the weeks from January to June as the x axis and showing the number of episodes on the y axis of the data provided by these Grey’s Anatomy fans.
The graph is clearly not normal, yet it*…show more content…*

Let’s say if I were to keep track of how long I walk my dog if I always take a longer path when I walk the dog during the morning compared to the late afternoon. Putting this data on a graph, it would look binomial like the graph I provided below. Yet just like the Grey’s Anatomy example, if we take the means of multiple random samples from the data and plot it on a graph, it would become normal. Another example where the Central Limit Theorem takes place is if I were to record the pitches that my two dogs bark at. My first dog, Oreo, has a deep, hearty bark where as my second dog, Mya, has a high pitched bark. Considering this, if we graphed their barks, there would be a dip in between which would look similar to the graph right above this paragraph. Yet just like the others, if I was to take multiple random samples from the data and figured out the means of each, it would look much more normal and the dip would be gone. Whether it be using Grey’s Anatomy watching habits, dog walking habits, or the pitch of a dog bark, the Central Limit Theorem can turn a binomial graph into a normal graph. This can be easily done by taking a random sample of over 30 from the data given, taking the means from each sample, and then plotting them on a graph will give us an approximately normal

Let’s say if I were to keep track of how long I walk my dog if I always take a longer path when I walk the dog during the morning compared to the late afternoon. Putting this data on a graph, it would look binomial like the graph I provided below. Yet just like the Grey’s Anatomy example, if we take the means of multiple random samples from the data and plot it on a graph, it would become normal. Another example where the Central Limit Theorem takes place is if I were to record the pitches that my two dogs bark at. My first dog, Oreo, has a deep, hearty bark where as my second dog, Mya, has a high pitched bark. Considering this, if we graphed their barks, there would be a dip in between which would look similar to the graph right above this paragraph. Yet just like the others, if I was to take multiple random samples from the data and figured out the means of each, it would look much more normal and the dip would be gone. Whether it be using Grey’s Anatomy watching habits, dog walking habits, or the pitch of a dog bark, the Central Limit Theorem can turn a binomial graph into a normal graph. This can be easily done by taking a random sample of over 30 from the data given, taking the means from each sample, and then plotting them on a graph will give us an approximately normal

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