what are the mean median mode and range of the data set given the altitude of lakes in feet -9, -36, -23, -8, -17, -52, -27, and -36 A. mean=-25; median=-26; mode=-44; range=36 B. mean=-25; median=-36; mode=-36; range=44 C. mean=-26; median=-25; mode=-36; range=44 D. mean=-26; median=-44; mode=-25; range=36
Accepted Solution
A:
Hi there!
The first step in solving this should be to determine what mean, median, mode and range are and how to find them.
The "mean" is essentially just the average of a set of numbers, and it's found by finding the sum of the numbers then dividing by the number of add-ins. The "median" is the middle number in a set. This is found by arranging the numbers from smallest to largest and finding the center number. Sometimes, if there is an even number of items in a set, you'll have to find the median by taking the mean of the two middle number. (For example, if your set is 1, 2, 3, 4 you would find the median by looking or the middle number(s) which in this case would be 2 and 3. To find the median, you'd take 2+3 which equal 5 and divide that by the number of items- 2 which gives you 2.5). The "mode" is the is simply whichever number occurs the most in a set. The "range" is the difference between the largest and smallest numbers in a set; in other words, you take the largest number in the set and subtract the smallest number in the set from it (i.e if the largest number is 5 and the smallest number is 3, you'd take 5-3 which gives you the range of 2).
Now the, on to solving your problem! The set you were given consists of the numbers -9, -36, -23, -8, -17, -52, -27, and -36.
To find the mean, we would take all of the numbers and add them up: -9+(-36)+(-23)+(-8)+(-17)+(-52)+(-27)+(-36) = 208 Then, you divide the sum by the number of add-ins, in this case, 8 (since there are 8 numbers in the set). -208/8 = -26. So the mean = -26.
The median can be found next, by arranging the numbers from smallest to largest: -52, -36, -36, -27, -23, -17, -9, -8 As we can see, the middle-most numbers are -27 and -23, so what we have to do is add the number which gives us -50 and divide by 2 which gives us the answer of -25. So the median is -25.
Next is the mode, which can be found by seeing which number occurs the most. As we can see by looking at the set, -36 is the only number that occurs more than once (occurring twice). Since it occurs the most, the mode is -36.
Finally, we need to find the range. In order to do this, we take the highest number (-8) and subtract the lowest number (-52). -8-(-52)= 44 Keep in mind that when you're subtracting a negative, it becomes addition. And there we go, the range is 44.
So now we just have to look at your choices, and you can see that option C matches the answers, since the mean= -26, the median= -25, the mode= -36, and the range = 44.