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Find the mean, median, mode, and range for each data set given.

a. $7,12,1,7,6,5,11$

b. $85,105,95,90,115$

c. $10,14,16,16,8,9,11,12,3$

d. $8,7,5,9,10,7$

e. $45,50,40,35,75$

f. $15,11,11,16,16,9$

a. Range $=11$

b. Range $=30$

c. Range $=13$

d. Range $=5$

e. Range $=40$

f. Range $=7$

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all right for this one. There are a lot of answers, and so I'm gonna try my best to go about how to do it. But if I were to do every single calculation, we'd be here for 20 minutes. So I'm not gonna do that. Um, the mean happens when you add every single number up and then divide by the number of numbers. For instance, I would add all these up and then divide by seven. Because there are seven numbers. Just happens. The mean is seven for this one. And this one, Adama in divide by five for five numbers. And so I'm gonna write the means that I have calculated beforehand who this one's a decimal 10.375 all to 10.4 toe around. Sorry that it highlights. The text is I go there, but it will look good in a bit. Adam up. Divide by the number of numbers. And these air the means if I continue that process. Okay. Now, median. On the other hand, median says, Hey, put these in order from least greatest would be like one. Ah, I'll do this one. I'll do one out for you. guys. And if it happens twice, you gotta put both numbers there, and then you find the middle of the numbers, so it would be like crossing out on each side until you find the middle number. So the median is also seven for this Again, put him in the least a greatest find the middle number. I've done that for hand. It's 95 which you can see is an actual value. Um oh, and by the way, if there's two middle numbers, you find the mean of them like you would Adam up and divide by two. So that may happen every now and then. Like for this one, Meaning is 10.5, which happens because the middle number there's two. It's 10 and 11 if you put him in order from least greatest. And if you add 10 and 11 up and divide by two, you get 10.5. All right, then this median is eight. This medium's 45 in this medians, 13 again put him in order from least a greatest find. The middle number mode modes number that comes up the most. For instance, CEO of seven comes up twice, so seven is the mean median and vote for the 1st 1 Um, this next one. You see how no number comes up more than once. That means there is no mode, so put in a or you can put none or no mode. But if every single number comes up once you could say every numbers the mode, I think it's a much more accurate to say that there is no mode exact. Same thing happens for C. In fact, let's just get the ones out of the way where that happens. You see how all these numbers are different? It happens for E is well, all right. There is a mode for this one. It's 10 because it comes up twice and there is a mode for this one. It's 11 which comes up twice. Okay, now range Ranger, take the highest number and subtract the lowest number. So this one, I will calculate out for every single one So arranges 12 minus one because the house is 12. The lotions one, that's 11. This the highest number is 115. The lowest number is 85. And if you subtract those rangers 30 uh, the highest number is 16. The lowest number is three and 60 ministries 13 Highest number. Here's 10 most numbers. Five. Subtract those we get five. Last number is 75. Louis number is 35. Track those. We get 40. Last woman, highest number 16 and lowest number is nine. Subtract those and we get seven There it ISS all the means medians, modes and ranges.

University of Denver

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