Respuesta :
The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
What is a Range?
A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.
The range of the numbers of medals won by these countries is,
Range = Max - Min = 29 - 1 = 28
To find the standard deviation we need to know the following details,
- Sum of the number of medals = ∑x = 234
- Sum of the square of the number of medals = ∑x² = 4372
- Number of observations = n = 18
Now, the standard deviation of medals won by these countries is,
[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]
The variance of the numbers of medals won by these countries is,
v = σ²
v = 78.2353
Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
Learn more about Range:
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