Answer :
Okay, let's analyze how including the new value of 19 in the data set will affect the median and mode.
Original data set: 10, 14, 14, 18
Adding the new value of 19:
New data set: 10, 14, 14, 18, 19
Effect on the Median:
The median is the middle value when the data is arranged in numerical order.
For the original data set (10, 14, 14, 18):
The median is 14, as there are two middle values (14 and 14), and the average of these two values is 14.
For the new data set (10, 14, 14, 18, 19):
The median will change to 14, as there are now five values, and the middle value is 14.
So, including the new value of 19 will not change the median, which will remain at 14.
Effect on the Mode:
The mode is the value that appears most frequently in the data set.
For the original data set (10, 14, 14, 18):
The mode is 14, as it appears twice, which is the most frequent occurrence.
For the new data set (10, 14, 14, 18, 19):
The mode will still be 14, as it appears twice, which is the most frequent occurrence.
So, including the new value of 19 will not change the mode, which will remain at 14.
In summary, adding the new value of 19 to the data set will not affect the median or the mode. The median will remain at 14, and the mode will also remain at 14.
Original data set: 10, 14, 14, 18
Adding the new value of 19:
New data set: 10, 14, 14, 18, 19
Effect on the Median:
The median is the middle value when the data is arranged in numerical order.
For the original data set (10, 14, 14, 18):
The median is 14, as there are two middle values (14 and 14), and the average of these two values is 14.
For the new data set (10, 14, 14, 18, 19):
The median will change to 14, as there are now five values, and the middle value is 14.
So, including the new value of 19 will not change the median, which will remain at 14.
Effect on the Mode:
The mode is the value that appears most frequently in the data set.
For the original data set (10, 14, 14, 18):
The mode is 14, as it appears twice, which is the most frequent occurrence.
For the new data set (10, 14, 14, 18, 19):
The mode will still be 14, as it appears twice, which is the most frequent occurrence.
So, including the new value of 19 will not change the mode, which will remain at 14.
In summary, adding the new value of 19 to the data set will not affect the median or the mode. The median will remain at 14, and the mode will also remain at 14.
