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Measures of Central Location

Measures of Central Location

ANSWERS

  1. a. \mathrm{9}.
    b. \mathrm{41}.
    c. \mathrm{0}.
    d. \mathrm{14}.


  1. \bar{x}=2.5, \widetilde{x}=2.5, mode =\{1,2,3,4\}


  1. \bar{x}=3, \widetilde{x}=2, mode =2


  1. \bar{x}=3, \widetilde{x}=2, mode =2


  1. \{0,0,3\}.


  1. \{0,1,1,2\}.


  1. \bar{x}=146.9, \widetilde{x}=147.5


  1. \bar{x}=2.6, \widetilde{x}=2, mode =2


  1. \bar{x}=48.96, \widetilde{x}=49, mode =49


  1. a. No, the survival times of the fourth and fifth mice are unknown.
    b. Yes, \widetilde{x}=421


  1. \bar{x}=48.96, \widetilde{x}=49, mode =49


  1. \bar{x}=2.05, \widetilde{x}=2, mode =1


  1. Mean: n x_{\min } \leq \sum x so dividing by n yields x_{\min } \leq \bar{x}, so the minimum value is not above average. Median: the middle measurement, or average of the two middle measurements, \widetilde{x}, is at least as large as x_{\min }, so the minimum value is not above average. Mode: the mode is one of the measurements, and is not greater than itself.


  1. a. \bar{x}=3. \overline{18}, \widetilde{x}=3, mode =5.
    b. \bar{x}=6. \overline{18}, \widetilde{x}=6, mode =8
    c. \bar{x}=-2. \overline{81}, \tilde{x}=-3, \operatorname{mode}=-1
    d. If a number is added to every measurement in a data set, then the mean, median, and mode all change by that number.


  1. a. \mu=1528.74
    b. \bar{x}=1502.8
    c. \bar{x}=1535.2


  1. a. \bar{x}=553.4286 and \widetilde{x}=552.5
    b. \bar{x}=665.9692 and \widetilde{x}=667
    c. \bar{x}=455.8933 and \widetilde{x}=448