Question

The normal distribution is a special distribution of quantitative data that has a symmetric Bell-shape. Data, such as the average temperature in a region or over time, often have a normal distribution. Why?

The graph that we were looking at in class in on the nytimes website. It’s title is “It’s not your Imagination. Summers are getting hotter.”( This is only if you’ve wanted context to the question, although I do not think you need the graph to answer). I believe I have an idea as to what the reasoning is, but I do not know if it is correct. Plus I’m a little confused. Can someone explain and help answer? Thanks!

Answer 1

Yes!

the graph we looked at in nytimes website titled as "It’s not your Imagination. Summers are getting hotter" is following the Normal Distribution (Overall).

As you we can see that the time interval is 10 years, which is long time.

Concept: As per the central limit theorem (CLT) - states that the sampling distribution of the any sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30. All this is saying is that as you take more samples, especially large ones, your graph of the sample means will look more like a normal distribution.

Now see the nytimes plot

1) 1951-1980 it follows normal distribution as we have sample great sample size is there. so CLT suggest this has normal distribution.

2) 1983 - 1993 it has less time duration but it also has the normal distribution.

3) 1994 - 2004 Now the thing has change as we can notice here that the temprature is consistently increasing. So you have one diection data alwys in that case and the direction is positive or right. Overall it has a normal disribution features but its not perfectly symmetric Bell-shaped.

4) 2005 - 2015 This is time duration when there is a bit sharp increase in temperature so again its not in both direction. this part is perfectly normal. you can say its a negatively skewed, or skewed to the left.

Overall data from 1951 - 2015 is following normall distribution. and there is shift after a time intervals can be seen in the figure.

So Average temperature in a region or over a time often has normal distribution,reason is Cenral Limit Theoram. But  Average temperature in a region or over a time always has normal distribution is not true all the time.

Cheers!!