Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average, so I'll add and then divide:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
The median is the middle value, so first I'll have to rewrite the list in numerical order:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:
So the median is 14.
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
mean: 15
median: 14
mode: 13
range: 8
Note: The formula for the place to find the median is "([the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. Either way will work.
Find the mean, median, mode, and range for the following list of values:
1, 2, 4, 7
The mean is the usual average:
(1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5
The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers. Because of this, the median of the list will be the mean (that is, the usual average) of the middle two values within the list. The middle two numbers are 2 and 4, so:
(2 + 4) ÷ 2 = 6 ÷ 2 = 3
So the median of this list is 3, a value that isn't in the list at all.
The mode is the number that is repeated most often, but all the numbers in this list appear only once, so there is no mode.
The largest value in the list is 7, the smallest is 1, and their difference is 6, so the range is 6.
mean: 3.5
median: 3
mode: none
range: 6
The values in the list above were all whole numbers, but the mean of the list was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.
8, 9, 10, 10, 10, 11, 11, 11, 12, 13
The mean is the usual average, so I'll add up and then divide:
(8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5
The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5-th value; the formula is reminding me, with that "point-five", that I'll need to average the fifth and sixth numbers to find the median. The fifth and sixth numbers are the last 10 and the first 11, so:
(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5
The mode is the number repeated most often. This list has two values that are repeated three times; namely, 10 and 11, each repeated three times.
The largest value is 13 and the smallest is 8, so the range is 13 – 8 = 5.
mean: 10.5
median: 10.5
modes: 10 and 11
range: 5
As you can see, it is possible for two of the averages (the mean and the median, in this case) to have the same value. But this is not usual, and you should not expect it.
A student has gotten the following grades on his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
The minimum grade is what I need to find. To find the average of all his grades (the known ones, plus the unknown one), I have to add up all the grades, and then divide by the number of grades. Since I don't have a score for the last test yet, I'll use a variable to stand for this unknown value: "x". Then computation to find the desired average is:
(87 + 95 + 76 + 88 + x) ÷ 5 = 85
Multiplying through by 5 and simplifying, I get:
87 + 95 + 76 + 88 + x = 425
346 + x = 425
x = 79
He needs to get at least a 79 on the last test.
No comments:
Post a Comment