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Statistics: Mean
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To find out the mean height of members of one school class, you need to...?
If it's hard to keep up with this video, watch these videos first. Then go back to this one. Here's Mikhail's diagram about how tall the teachers at his school are, And Leena's diagram about how many municipalities with different populations there are in Sweden. Both of them found the mode and the median for their surveys, but Leena is missing something. She wants to know what would happen if the population were spread out equally, so that all municipalities would have the same number of inhabitants.
All together, there are about 9,7 million people in Sweden. Leena takes 9,7 million and divides it by the number of municipalities, 290, and she gets 33,448. This way, Leena calculated the mean value. If the population of Sweden were distributed evenly between municipalities, there would be around 33-and-a-half thousand people in each municipality. Like in Varno or Strangnas.
33,448 is the mean value of the number of inhabitants of Sweden's municipalities. The mode and median values are close to each other, while the mean value is significantly larger. This is because the mean value is affected by the presence of a small number of municipalities with very large populations, while the mode and the median are not. Should we take a look at Mikhail's teachers too? What is the mean value?
Mikhail adds all 39 teachers' heights and get 6,773 centimeters. This means that if all the teachers were stacked on top of each other, you would get a tower almost 68 meters high. Mikhail divides 6,773 centimeters by the number of teachers, 39. The mean value is 173,7 centimeters. In Mikhail's survey, the mean value is close to both the mode and the median.
The bars are tallest in the middle and shortest at the sides. The diagram is almost completely symmetrical. Moreover, if your data is distributed completely symmetrically, the mean, the median, and the mode are the same. Let's summarize it. The mode is the most common observation, one with the greatest frequency.
The median is the middle-most value that you find when you sort the data in increasing order. The mean value is the sum of all values divided by the number of observations. Each of the three measures presents a lot of data as a single value. The more symmetrically the data is spread out, the smaller the difference between the three values.