Step-by-step explanation: Here, we want to find the mean, median, and mode for the data set. Let's begin by finding the mean.
The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set. So to find the mean of the data set shown here, let's begin by adding the numbers.
So we have
120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155.
This will be divided by how many numbers are in the set which is 12.
[tex]So[/tex] [tex]we[/tex] [tex]have[/tex] [tex]\frac{120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155}{12}[/tex].
Adding the numbers, we get 1,912.
1,912 is divided by the number of numbers in the set or 12.
1,912 divided by 12 is about 159.3333.
So the mean of the set of data shown here is about 159.3333.
Next, let's find the median.
The median is the middle number in the data set when the data set is written from least to greatest. So let's write our data set from least to greatest.
So we have 120, 127, 128, 140, 145, 155, 158, 159, 161, 163, 164, 292.
In this data set however, notice that there is no one middle number. When there is no middle number in a data set, we take the two numbers that are in the middle and we take the average of those numbers.
In this set, the two middle numbers are 155 and 158 because if we group these numbers together, there are five numbers on either side of them.
Now, to find the average of 155 and 158, we simply add them together and divide by 2. So we have 155 + 158 which is 313. Now, 313 ÷ 2 is 156.5.
So the median of the data set is 156.5.
Finally, let's find the mode.
The mode is the number that appears most frequently in a data set.
Notice that each number in our data set appears only once so there is no mode.
