I'll do the first two questions of each activity to get you started. The remaining unanswered questions will follow similar steps compared to the other questions in the same activity group.
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Activity 5, Problem 1
To find the mean, we first add up the values
4+8+2+8+5+9 = 36
Then we divide over n = 6 because there are 6 values in this data set.
36/n = 36/6 = 6
Answer: Mean = 6
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Activity 5, Problem 2
Follow the same idea as the previous problem.
Add the values: 9+8+8+13+12 = 50
Divide by the number of values: 50/n = 50/5 = 10
Answer: Mean = 10
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Activity 6, Problem 1
The median is the middle-most number. Think of a median of a highway or freeway.
In order to find the median, we first need to sort the data values from smallest to largest.
The original set {7,3,9,9,2,5,8} sorts to {2, 3, 5, 7, 8, 9, 9}
If we erased the first and last items, we get this smaller subset
{3, 5, 7, 8, 9}
repeat again to get
{5,7,8}
At this point its clear the middle most value is 7
But if you wanted, you could cross the first and last values from the list to end up with {7}
Answer: Median = 7
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Activity 6, Problem 2
We could do the same trick as the previous problem, but I'll use a slightly different route this time.
We'll need to sort {10,8,4,11,9} into {4, 8, 9, 10, 11}
There are n = 5 items in that set. The middle slot would be at slot n/2 = 5/2 = 2.5 = 3
The value 9 is in slot 3 of the sorted items.
Answer: Median = 9
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Activity 7, Problem 1
The mode is the most frequent value of a set. It repeats the most often.
The set {5,6,7,3,5,4} sorts to {3,4,5,5,6,7}
The value "5" shows up the most. It shows up twice when everything else shows up exactly once only.
Answer: Mode = 5
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Activity 7, Problem 2
Using the same idea in the previous problem, the set {7,4,11,9,7,3} has the mode 7 because it shows up the most of any other value.
Here's the sorted set: {3,4,7,7,9,11}
Sorting is optional with finding the mode in contrast to being mandatory when it comes to finding the median.
Answer: Mode = 7
