Question

Data set the data that follows is from a local school district and represents the salaries of various employees. 10,000 11,000 11,000 12,500 14,300 17,500 18,000 16,600 19,200 21,000 16,500 108,500 instructions in the text box, please answer the following questions: compute the mean, median, and mode for the sample data above. assume you work for the school district and do not wish to raise property taxes to give employees a raise. decide which one of these measures supports your position. assume you work for the union and want teachers to receive raises. which one of these measures supports your position? is there an outlier in this data set? if so, which is it? explain how the outlier helps support one of the two positions (for raises, do not want to give raises) if the salaries above represented the entire school district, would the averages be statistics or parameters? which measures of central tendency can be misleading when when a data set contains an outlier? suppose the last data point (108,500) was a typo and should have been 18,500. recalculate the mean, median, and mode of the data. which of these measures were affected the most?

Answer 1

The mean, median, and mode of the data set are $30,000, $16,600, and $11,000 respectively. The mean supports the position of not raising property taxes, while the median would support giving raises to teachers. There is an outlier of $108,500 in the data set, which significantly affects the mean. If the outlier is corrected, the mean, median, and mode change to $21,000, $16,600, and $11,000 respectively.

Step-by-step explanation:

The mean, median, and mode of the data set are:

Mean: $30,000

Median: $16,600

Mode: $11,000

The mean supports the position of not raising property taxes, as it takes into account the outlier of $108,500. This outlier significantly affects the mean and makes it higher than the other measures. On the other hand, if you want teachers to receive raises, the median would be a better measure to support this position. The median is less affected by outliers and represents a more accurate middle value of the data set.

Yes, there is an outlier in this data set, which is $108,500. This outlier supports the position of not giving raises as it significantly affects the mean, making it higher and potentially skewing the data in favor of not giving raises.

If the salaries represented the entire school district, the averages would be parameters as they would be calculated using the entire population of employees in the district.

The mean can be misleading when a data set contains an outlier, as in this case. The outlier significantly affects the mean, making it higher and potentially misleading as a measure of central tendency. The median and mode, on the other hand, are less affected by outliers and provide a better representation of the middle value and the most frequently occurring value, respectively.

If the last data point of $108,500 was a typo and should have been $18,500, the mean, median, and mode would be affected as follows:

Mean: $21,000

Median: $16,600

Mode: $11,000

The mean is affected the most by the correction of the typo, as it is the measure that takes into account all the values in the data set. The median and mode are less affected as they represent the middle value and the most frequently occurring value, respectively.