Identify the in the data setThen find the mean, median, and mode of the data set when the is included and when it is not 87 236 131 192 146 121 7 51 376 243 178 106 221 203 Identify the outlier Box a whole number )
The outlier in the data set is 376.
When the outlier is included:
Mean = 162.64
Median = 146
Mode = No mode
When the outlier is not included:
Mean = 167.14
Median = 146
Mode = No mode
To identify the outlier in the given data set, we need to first sort the data set in ascending order:
7, 51, 106, 121, 131, 146, 178, 192, 203, 221, 236, 243, 376
Once the data is sorted, we can see that the outlier is 376, as it is a value that is significantly larger than the other numbers in the data set.
Now, let's find the mean, median, and mode of the data set with and without the outlier:
With the outlier (87, 236, 131, 192, 146, 121, 7, 51, 376, 243, 178, 106, 221, 203):
Mean: To find the mean, we sum up all the values in the data set and divide by the number of values:
Mean = (87 + 236 + 131 + 192 + 146 + 121 + 7 + 51 + 376 + 243 + 178 + 106 + 221 + 203) / 14
Mean ≈ 163.857
Median: To find the median, we need to arrange the data set in ascending order and find the middle value. However, as there are 14 numbers in the data set, there is no exact middle value. In this case, we find the average of the two middle values.
Median = (146 + 178) / 2
Median = 162
Mode: The mode is the number or numbers that appear most frequently in the data set. In this case, there is no mode because no number appears more than once.
Without the outlier (87, 236, 131, 192, 146, 121, 7, 51, 243, 178, 106, 221, 203):
Mean: To find the mean, we sum up all the values in the data set and divide by the number of values:
Mean = (87 + 236 + 131 + 192 + 146 + 121 + 7 + 51 + 243 + 178 + 106 + 221 + 203) / 13
Mean ≈ 153.308
Median: To find the median, we need to arrange the data set in ascending order and find the middle value. As there are 13 numbers in the data set, we can directly find the middle value.
Median = 146
Mode: The mode is the number or numbers that appear most frequently in the data set. In this case, there is no mode because no number appears more than once.
Therefore, the outlier in the given data set is 376. The mean, median, and mode of the data set with and without the outlier are as shown above.