Identify the outlier in the data set, and determine how the outlier affects the mean, median, mode and range of the data set. 7,7,4,9,6,26,4,5,8,4
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To determine the outlier in the data set, you can follow these steps:
1. Sort the data set in ascending order: 4, 4, 4, 5, 6, 7, 7, 8, 9, 26.
2. Calculate the range of the data set by subtracting the smallest value from the largest value: 26 - 4 = 22.
3. Calculate the median by finding the middle value in the sorted data set. In this case, since we have an even number of values (10), we take the average of the two middle values: (6 + 7) / 2 = 6.5.
4. Calculate the mean by summing up all the values and dividing by the total number of values: (4 + 4 + 4 + 5 + 6 + 7 + 7 + 8 + 9 + 26) / 10 = 8.
5. Calculate the mode, which is the value that appears most frequently. In this case, the mode is 4, as it appears three times.
Now, we can determine the outlier. An outlier is a value that significantly deviates from the other values in the data set. In this case, the value 26 is the outlier since it is much larger than the rest of the values.
The outlier affects the measures of central tendency (mean, median, and mode) and the range differently:
1. Mean: The outlier (26) significantly increases the sum of the values in the data set. Consequently, the mean is affected and becomes larger than it would be without the outlier.
2. Median: The outlier (26) has less impact on the median since it only affects one value. In this case, the median remains relatively unaffected by the outlier.
3. Mode: The outlier (26) does not affect the mode, as it is still 4, which is the value that appears most frequently.
4. Range: The outlier (26) increases the difference between the smallest and largest values, thus increasing the range. In this case, the range becomes larger due to the presence of the outlier.
Which number is much larger than the other numbers?
Find the median and the mean with and without the outlier? What difference do you see?