Let’s imagine you have the following seed counts from eleven different apples:<\/p>\n
15 9 8 10 8 10 8 5 7 14 12<\/p>\n
We wish to find the mean, median, and mode of the seed counts.<\/p>\n
When I was a kid, people said “average” instead of mean. To find the mean, we add all the numbers together, then divide by how many there are (in this case, 11):<\/p>\n
mean=(15+9+8+10+…..+14+12)\/11=9.6363…<\/p>\n
So, the mean number of seeds in the apples is 9.6363…<\/p>\n
To find the median, you line up the numbers from least to greatest. The median is the middle one.<\/p>\n
We rewrite the numbers in ascending order:<\/p>\n
5 7 8 8 8 9 10 10 12 14 15<\/p>\n
The middle number is 9. Therefore, the median number of seeds in the apples is 9.<\/p>\n
The mode is simply the count that occurs most often. In this case, it’s 8. At three times, 8 happens more than any other count.<\/p>\n
Some points to note:<\/p>\n
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\nConsider the following list of six entries:<\/p>\n
5 6 7 10 13 14<\/p>\n
Here, the median is (7+10)\/2=8.5. To find the median of an even list, you take the two middle values, add them, then divide by two.<\/p>\n
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\nFor the six-membered list just above, you can see it in two ways: either there’s no mode, or else there are six different modes. However, consider the following list:<\/p>\n
1 1 2 3 5 6 7 7 9<\/p>\n
For this list, we would say there are two modes: 1 and 7.<\/ol>\n
The mean, median, and mode are all called measures of central tendency: they all estimate what the “next” value would be. I’ll be saying more about them in future posts:)<\/p>\n