Consider the following line plot.
1 dot over 1|1 dot over 2| 1 dot over 3| 2 dots over 4| 3 dots over 5| 3 dots over 6| 2 dots over seven
Would the mean or median be affected more with a data point of 20? Explain.
Thank you
Extreme deviant scores always effect the mean more than the median.
TYSM, this helped me a lot! Have a wonderful day
Welcome, or should I say W?
To determine whether the mean or median would be affected more with the addition of a data point of 20, we need to calculate these statistical measures both before and after adding the data point.
Let's start by determining the mean and median without the additional data point:
Mean: The mean is determined by adding up all the values and dividing by the total number of values. In this case, we have the following values: 1, 2, 3, 4, 5, 6, 7. So, the mean can be calculated as:
(1 + 2 + 3 + 4 + 5 + 6 + 7) / 7 = 28 / 7 = 4
Median: The median is determined by finding the middle value when the data is arranged in ascending order. In this case, the data set would be arranged as: 1, 2, 3, 4, 5, 6, 7. Since we have an odd number of values, the median would be the value in the middle, which is 4.
So, without the additional data point, the mean is 4 and the median is also 4.
Now let's calculate the mean and median after adding the data point of 20:
Mean: If we add the value of 20 to the existing data set, the new sum would be:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 20 = 48
The total number of values is now 8, so the new mean would be:
48 / 8 = 6
Median: Again, we need to arrange the data set in ascending order, including the additional data point: 1, 2, 3, 4, 5, 6, 7, 20. Since we have an even number of values, the median would be the average of the two middle values: (4 + 5) / 2 = 4.5.
After adding the data point of 20, the mean is 6 and the median is 4.5.
Therefore, in this case, the median would be affected more by the addition of the data point 20.