The data set shown below has an outlier. Determine the outlier and then fill out the chart.
Data: 5, 10, 12, 14, 18, 24, 60
If the outlier is excluded, what happens to:
Increase
Decrease
No effect
A
the median?
B
the mean?
C
the mode?
D
the range?
To determine the outlier in the given data set, we can calculate the values for the median, mean, mode, and range and identify the value that stands out from the rest.
A) Median: The median is the middle value of a data set when arranged in ascending order. In this case, the data set is already in ascending order, and there are 7 data points. Since there is an odd number of data points, the median would be the middle value, which is 14.
B) Mean: The mean is the average of all the data points. To calculate the mean, we sum up all the values and divide by the number of data points. In this case, the sum of the values is 143. Dividing this by 7 (the number of data points), we get a mean of approximately 20.43.
C) Mode: The mode is the value that appears most frequently in a data set. In this case, there is no value that appears more than once, so there is no mode.
D) Range: The range is the difference between the largest and smallest values in a data set. In this case, the largest value is 60 and the smallest value is 5. Therefore, the range is 60 - 5 = 55.
Now, let's identify the outlier in the data set. Based on the calculations, we can see that the value 60 stands out compared to the rest of the data points. Hence, 60 is the outlier.
If the outlier is excluded, the following changes would occur:
A) The median: The median would change as the outlier, 60, is excluded. The new median would be the middle value of the remaining data points, which is 14.
B) The mean: The mean would decrease as the outlier, 60, which is a larger value compared to the rest, is excluded from the calculation.
C) The mode: The mode would remain the same as there are no values that repeat in the data set.
D) The range: The range would decrease as the largest value, 60, is excluded from the data set. The new range would be 24 - 5 = 19.
Chart:
Before excluding the outlier:
Data: 5, 10, 12, 14, 18, 24, 60
Median: 14
Mean: 20.43 (approximately)
Mode: No mode
Range: 55
After excluding the outlier:
Data: 5, 10, 12, 14, 18, 24
Median: 14 (changes)
Mean: decreases
Mode: No mode (remains the same)
Range: 19 (decreases)
you sure
Apologies for any confusion. Can you please specify which part you are questioning?
the whole thing :]
Apologies for the confusion earlier. Let's reassess the data set and determine the outlier.
Data: 5, 10, 12, 14, 18, 24, 60
To determine the outlier, we can examine the values in the data set and identify any that deviate significantly from the other values. In this case, the value 60 appears to be significantly larger than the other values.
Therefore, based on the given data set, the outlier is 60.
Now, let's analyze what happens to the measures of central tendency and range when the outlier is excluded:
A) Median: The median is not affected by outliers, so excluding the outlier would have no effect on the median.
B) Mean: The mean is greatly influenced by outliers. Excluding the outlier would decrease the mean.
C) Mode: The mode is not affected by outliers, so excluding the outlier would have no effect on the mode.
D) Range: The range represents the difference between the largest and smallest values. Excluding the outlier would decrease the range.
Revised chart:
Before excluding the outlier:
Data: 5, 10, 12, 14, 18, 24, 60
Median: 14
Mean: Approximately 20.43
Mode: No mode
Range: 55
After excluding the outlier:
Data: 5, 10, 12, 14, 18, 24
Median: 14 (no change)
Mean: Decreases
Mode: No mode (no change)
Range: Decreases
I apologize for the initial incorrect response and any confusion it may have caused.