The mean of a numerical data set is the sum of the data divided by the number of data values. The number of data values is 12. Therefore, we will divide the sum of the data by 12.
The median of a numerical data set is the middle number when the values are written in numerical order. If the data set has an even number of values, the mean of the two middle values will be the median. Let's write the given values in numerical order.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02
Since we have an even number of data values, we have to calculate the mean of the two middle values.
Median&=0.67+ 1.05/2
&⇓
Median&=0.86
Therefore, the median is $0.86.
Mode
The mode of a data set is the value or values that occur most often. Again, let's look at the values in numerical order.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02
Note that all of the values occur only once. Therefore, there is no mode.
b In this part we are asked to find which measure of center best represents the data. Let's first recall the given data.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02
First, the mean -$0.40 is less than most of the data. Second, we have no mode. Finally, since the median $0.86 splits the data evenly, it bests represent the data.
c We are told that on the 13^(th) day, the value of the stock increases by $4.28. We will find how this additional value affects the mean, median, and mode. Let's analyze one at a time.
Mean
Let's first write our data with the new value.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02, 4.28
Since we have 13 data values the mean will be the sum of the values divided by 13.
The mean is about -$0.04. Comparing this mean with the mean -$0.40 we found in Part A, we can see that the mean increases. Let's find the difference of these means to find how much it increased.
- $0.04-(- $ 0.40)=$0.36
Therefore, the additional value increases the mean by about $0.36.
Median
To find the mean after the value is added, let's first write our data in numerical order.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02, 4.28
In this case the median is $1.05. Comparing it with the original median $0.86, we can see that the new median is greater. Let's find the difference of these medians.
$1.05-$0.86=$0.19
Therefore, the additional value increases the median by $0.19.
Mode
Again, let's take a look at the given values after the new value is added.
-13.78, -3.01, -2.41, -0.28, 0.66, 0.67,
1.05, 1.39, 2.03, 2.20, 2.64, 4.02, 4.28
Note that all of the values occur once. Therefore, the additional value does not affect the mean.
