Identify appropriate measure with outliers

2 Twenty children were asked to estimate the height of a particular tree. Their estimates, in metres, were as follows.

1. Find the mean of the estimated heights.
2. Find the median of the estimated heights.
3. Give a reason why the median is likely to be more suitable than the mean as a measure of the central tendency for this information.

1 The salaries, in thousands of dollars, of 11 people, chosen at random in a certain office, were found to be: $$40 , \quad 42 , \quad 45 , \quad 41 , \quad 352 , \quad 40 , \quad 50 , \quad 48 , \quad 51 , \quad 49 , \quad 47 .$$ Choose and calculate an appropriate measure of central tendency (mean, mode or median) to summarise these salaries. Explain briefly why the other measures are not suitable.

1 Twelve tourists were asked to estimate the height, in metres, of a new building. Their estimates were as follows. $$\begin{array} { l l l l l l l l l l l l } 50 & 45 & 62 & 30 & 40 & 55 & 110 & 38 & 52 & 60 & 55 & 40 \end{array}$$

1. Find the median and the interquartile range for the data.
2. Give a disadvantage of using the mean as a measure of the central tendency in this case.

7 A farmer has 200 apple trees. She is investigating the masses of the crops of apples from individual trees. She decides to select a sample of these trees and find the mass of the crop for each tree.

1. Explain how she can select a random sample of 10 different trees from the 200 trees. The masses of the crops from the 10 trees, measured in kg, are recorded as follows.
   \(\begin{array} { l l l l l l l l l l } 23.5 & 27.4 & 26.2 & 29.0 & 25.1 & 27.4 & 26.2 & 28.3 & 38.1 & 24.9 \end{array}\)
2. For these data find
   • the mean,
   • the sample standard deviation.
   • Show that there is one outlier at the upper end of the data. How should the farmer decide whether to use this outlier in any further analysis of the data?