Chapter 4, Problem 26E

(a)

To determine

To Explain: the mean and median.

Answer to Problem 26E

Median would be affected marginally.

The mean would be skewed download.

Explanation of Solution

Median would be affected marginally.

The mean would be skewed download.

The median would not be change. The lowest temperature was the lowest temperature already, and it simply got lower. Its placement in the data was always 1^st, when ordered, so the median does not change. The mean, however, is the average of all values. Replacing one value with a much smaller value will cause the mean to decrease.

(b)

To determine

To Explain: the range, IQR and standard deviation.

Answer to Problem 26E

The range will increase significantly

The IQR will not change.

The standard deviation will increase significantly.

Explanation of Solution

The range will increase significantly (by 34, to be exact).

The IQR will not change.

The standard deviation will increase significantly.

The range is the highest number minus the lowest. If the lowest number decreases significantly, the range would increase by the change. The IQR only counts the first and third quartile values, which are found similarly to the median (by discounting endpoints and only counting the middle data point). The value was already the smallest; making it smaller will not affect the IQR. The standard deviation will increase significantly, as the decreasing the value of the lowest data point will increase the overall spread.