Identify the in the data setThen find the mean, median, and mode of the data set when the outlier is included and when it is not 219 203 133 178 232 144 55 11 121 235 190 106 380 87 Identify the Type a whole number )
The outlier in the data set is 380.
Mean (including outlier) = (219+203+133+178+232+144+55+11+121+235+190+106+380+87) / 14 = 171.36
Mean (excluding outlier) = (219+203+133+178+232+144+55+11+121+235+190+106+87) / 13 = 156.15
To find the median, we first need to order the data set from smallest to largest: 11, 55, 87, 106, 121, 133, 144, 178, 190, 203, 219, 232, 235, 380.
Median (including outlier) = (144+178) / 2 = 161
Median (excluding outlier) = (144+178) / 2 = 161
The mode is the value that appears most frequently in the data set. In this case, there is no mode as no value appears more than once in the data set.
The data set provided is: 219, 203, 133, 178, 232, 144, 55, 11, 121, 235, 190, 106, 380, 87.
To find the mean, median, and mode of the data set, including the outlier and excluding the outlier, we need to first identify the outlier.
An outlier is a value that differs significantly from other values in a data set. In this case, it seems like 380 may be the outlier based on its relatively high value compared to the rest of the data.
Now, let's calculate the mean, median, and mode of the data set including and excluding the outlier:
Data set including the outlier (380):
Mean: To find the mean, we add up all the numbers in the data set and divide the sum by the total number of values.
Mean = (219 + 203 + 133 + 178 + 232 + 144 + 55 + 11 + 121 + 235 + 190 + 106 + 380 + 87) / 14
Mean = 2362 / 14
Mean ≈ 168.71
Median: To find the median, we need to arrange the numbers in ascending order and then determine the middle value. If there is an even number of values, we take the average of the two middle values.
Arranging the numbers: 11, 55, 87, 106, 121, 133, 144, 178, 190, 203, 219, 232, 235, 380
Median = (144 + 178) / 2
Median = 322 / 2
Median = 161
Mode: The mode is the value that appears most frequently in the data set.
Mode = There is no value that appears more than once, so there is no mode.
Data set excluding the outlier (380):
Mean: To find the mean, we add up all the numbers in the data set (excluding the outlier) and divide the sum by the total number of values.
Mean = (219 + 203 + 133 + 178 + 232 + 144 + 55 + 11 + 121 + 235 + 190 + 106 + 87) / 13
Mean = 1984 / 13
Mean ≈ 152.62
Median: To find the median, we need to arrange the numbers in ascending order and then determine the middle value. If there is an even number of values, we take the average of the two middle values.
Arranging the numbers: 11, 55, 87, 106, 121, 133, 144, 178, 190, 203, 219, 232, 235
Median = (144 + 178) / 2
Median = 322 / 2
Median = 161
Mode: The mode is the value that appears most frequently in the data set.
Mode = There is no value that appears more than once, so there is no mode.
In summary:
Data set including outlier:
Mean ≈ 168.71
Median = 161
Mode = No mode
Data set excluding outlier:
Mean ≈ 152.62
Median = 161
Mode = No mode