Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10.(a) Does the mean change? Explain.No, the sum of the data does not change.Yes, the sum of the data changes.    Yes, the number of data values changes.Yes, changing the extreme data values affects the mean.No, the number of data values does not change.(b) Does the median change? Explain.Yes, the sum of the data changes.No, the sum of the data does not change.    No, the number of data values does not change.No, changing the extreme data values does not affect the median.Yes, the number of data values changes.(c) Is it possible for the mode to change? Explain.Yes, depending on the range of the data values.No, the only change is an increased frequency of 1 for the extreme values.    No, all values will still occur at the same frequency.Yes, depending on which data value occurs most frequently after the data are changed.Yes, depending on the number a data values.

If the mean of a dataset is 50 and one value is changed from 40 to 80, how does this affect the mean?a.The mean decreasesb.The mean increasesc.The mean remains the samed.Cannot be determined without additional information

2.Question 2The data shown above has one “extreme” observation relative to the others. In this case, which of the following is true? Select all that apply.1 pointThe Median of this data is a larger dollar amount than the Mean of this data.The Mean of this data is a larger dollar amount than the Median of this data.The Median more accurately reflects the typical data when the extreme observations are removed.The Mean more accurately reflects the typical data when the extreme observations are removed.

The numbers of students in the 10 schools in a district are given below.(Note that these are already ordered from least to greatest.)210, 216, 270, 307, 322, 324, 349, 371, 424, 437Suppose that the number 210 from this list changes to 340. Answer the following.(a)   What happens to the median? It decreases by.It increases by.It stays the same.(b)   What happens to the mean? It decreases by.It increases by.It stays the same.

35, 55, 40, 20, 24, 17, 22, 30, 12, 17, 4735, 55, 40, 20, 24, 17, 22, 30, 12, 17, 47a)Find the minimum value of the data set:b)Find the maximum value of the data set:c)Find the arithmetic mean of the data set:d)Find the median of the data set:Let's include one more data point in the data set. Suppose this new data value lies between the values 12 and 55, inclusively.e)Find the smallest possible value of the mean of the new data set:f)Find the largest possible value of the mean of the new data set:g)Find the smallest possible value of the median of the new data set:h)Find the largest possible value of the median of the new data set:

Given are the eight values, [10, 9, 5, 18, 12, 13, 5, 20]. Which data value when added to the data set does not change the median? A. 5     B. 10    C. 11    D. 12