The histogram on the right does not, so the data is probably not normally distributed. The histogram on the left appears to follow the general shape of a bell curve (though not perfectly). Planet - around 7 billion people! - so it is much more realistic to take a smallerįigure 2 shows two examples of normal distributions with different means and standard deviations.Įxamples of two histograms compared to the same bell curve. ForĮxample, if your variable is "height of a person," the population would be every person on the The population), the mean is represented by x̄ and the standard deviation by s. Measurement you can make), the mean and standard deviation are represented by the Greek When referring to an entire population (every possible The mean is the location of the middle of the curve, and the standard deviation measures So the mean, median, and mode are all different in this case - but any one of them can be called an "average" for this set of numbers. The mode is 9, because it occurs the most (twice, while all the other numbers appear only once).The median when the numbers are listed in order from lowest to highest (3,5,8,9,9) is 8.Mode: take the number that occurs most often.įor example, say we have five numbers: 9, 5, 8, 9, and 3.Median: list the numbers in order from smallest to largest and take the middle number.Mean: add up all the numbers and divide by how many numbers there are.These are calculated three different ways: " Average" can refer to one of three things - the mean, median, or mode. Sometimes the words "mean" and "average" are used interchangeably, but technically that is not correct. The values of the mean and standard deviation, which you can calculate for your data, help describe the distribution. A normal distribution follows a "bell-shaped" curve, so you may frequently hear it referred to as a bell curve (less commonly it can also be referred to as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss). The bar graph shows how many people fall into a (non-numeric) category - for example, Mexico was named as home country by 27 people.Ĭonstructing a histogram will also help you tell if your data follows a normal distribution. The histogram shows how many people fall into a weight range - for example, 15 people weighed between 126 and 150 pounds. The bar graph is arranged from largest to smallest populations: USA, Mexico and Canada.Īn example of a histogram (left) and a bar graph (right) with data collected from 100 people who reported their weight and country of birth. The histogram has 6 ranges of weights that account for all weights between 100 and 250 pounds and resembles a normal distribution. Histogram of weight in pounds (left) and a bar chart showing country of origin (right) for 100 people who reported their weight in pounds. The histogram you make for this project will be similar to the one in Figure 1, except you will use the distance the ball travels instead of the weight of a person. Figure 1 shows an example histogram and bar graph displaying weight and country of birth for 100 people. You will try to find different settings that can launch a ball the same distance, and then construct a histogram of your results to see which settings are more reliable.Ī histogram is a graphical way to display how many things in a set of data fall into a certain numerical range (similar to a bar graph, but not quite the same). The catapult makes it easy to launch balls repeatedly with the same intended settings for the catapult (we will explain those settings later) - but, due to small, random changes in these settings, the ball will not travel exactly the same distance every single time. Similarly, in this project you will use a toy catapult to launch a ping pong ball and measure the distance it travels.
Imagine that you were commanding an army in the Middle Ages and needed to use your catapult to hit a castle wall from a certain distance away - you would definitely need to know the most reliable way to launch the ball into the wall.
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