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Suppose the speed limits in thirteen countries in miles per hour are as follows: Country Highway Miles per Hour Italy 87 France 82 Hungary 75 Belgium 75 Portugal 75 Great Britain 70 Spain 62 Denmark 62 Netherlands 62 Greece 62 Japan 62 Norway 56 Turkey 56 What is the mean, median, and mode for these data? Feel free to use your computer (statistical software or spreadsheet) to get the answer. Which is the best measure of central tendency for this data?

Answer :

Answer and explanation:

Given : Suppose the speed limits in 13 countries in miles per hour are as follows:

Italy - 87 mph ,  France - 82 mph ,  Hungary - 75 mph ,  Belgium - 75 mph , Portugal - 75 mph ,  Great Britain - 70 mph ,  Spain - 62 mph  , Denmark - 62 mph  , Netherlands - 62 mph  , Greece - 62 mph , Japan - 62 mph ,  Norway - 56 mph ,  Turkey - 56 mph.

To find : What is the mean, median, and mode for these data? Which is the best measure of central tendency for this data?

Solution :  

The mean of the data is the summation of the speed divided by number of countries.

i.e. [tex]\mu =\frac{\sum s_n}{n}[/tex]

[tex]\mu =\frac{87+82+75+75+75+70+62+62+62+62+62+56+56}{13}[/tex]

[tex]\mu =\frac{886}{13}[/tex]

[tex]\mu =68.15[/tex]

The mean of the data is 68.15.

The median of the data is the middle term of the data.

Arrange data from least to greatest,

56,56,62,62,62,62,62,70,75,75,75,82,87

Median of the odd number is [tex]\frac{n+1}{2}[/tex]th term.

[tex]M=\frac{13+1}{2}[/tex]th term

[tex]M=\frac{14}{2}[/tex]th term

[tex]M=7th[/tex] term

[tex]M=62[/tex]

The median of the data is 62.

The mode of the data is the greatest times the number repeats.

    Number      Repeat

        56                 2

        62                 5

        70                 1

        75                 3

        82                 1

        87                 1

The mode of the data is 62.

Since it has no outlier so the best measure of central tendency for this data is mean.

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