The Bell Curve

Hey everyone, I was learning about statistics, when I came across the bell curve - otherwise known as the normal curve. The curve is exactly what it sounds like, shaped like a bell with the highest point at the center. The curve shows how data from a sample - or a population - is distributed around the mean (average).

The bell curve can be used for many different types of samples, such as height, weight, rolling dice, IQs, etc. However, the bell curve cannot be used for some specific things, such as incomes, as these graphs don’t tend to follow the normal curve.

The image of the curve is shown below:

An important part of the normal curve is the standard deviation, which is used to calculate probabilities of certain things. To explain standard deviation in simple terms, it is basically the spread of the data. For example, a sample of numbers 45, 43, 44, 46, 45, 44, 47, 44 would have a much lower standard deviation than a sample of numbers 40, 54, 29, 38, 65, 52, 78.

The bell curve shows that 68% of the data stands between 1 standard deviation of the mean, and 95% of the data stands between 2 standard deviations of the mean. For example, if we collect some samples of many people’s heights, we can make some probability calculations.

Assuming that the mean height is 170 cm, and the standard deviation is 5 cm, we know that 68% of the people will be between height 165 cm and 175 cm inclusive, and 95% of the people will be between 160 cm and 180 cm.

What if you want to find the probability that a random person selected from the sample has a height between 160 cm and 175 cm. We know that 2 standard deviations around the mean is 95%, so it would be 95/2 = 47.5% for the range of 2 standard deviations below the mean till the mean. Using the same technique, it would be 68/2 = 34% from the mean till the first standard deviation above the mean. Next, add these percentages, 47.5+34 = 81.5%, which is the probability that a random person selected from the sample is between 160 cm and 175 cm.