Question

The numbers of runs scored by a baseball team in a sample of five games were:Fill in the blanks

Answer 1

a) The mean can be calculated by adding all values and then divide by the total number of values:

`\text{Mean}=(3+1+0+0+6)/(5)=2`

b) The median is the middle value in the list of numbers, then you have to order the numbers as follows: 0, 0, 1, 3, 6.

`\text{Median}=\text{ 1}`

c) The mode is the value that occurs most often, as you have a 0 value twice, then

`\text{Mode}=\text{ 0}`

d) To calculate the sample variance you can use this formula

`\begin{gathered} s^2=\frac{\sum^{}_{}(x-\bar{x})^2}{n-1}\text{ where x is each value, }\bar{x}\text{ is the mean, and n the number of values} \\ s^2=((0-2)^2+(0-2)^2+(1-2)^2+(3-2)^2+(6-2)^2)/(5-1) \\ s^2=((-2)^2+(-2)^2+(-1)^2+(1)^2+(4)^2)/(4) \\ s^2=(4+4+1+1+16)/(4) \\ s^2=(26)/(4)=6.5 \end{gathered}`

The sample standard deviation is the square root of sample variance, then

`\begin{gathered} s=\sqrt[]{s^2}=\sqrt[]{6.5} \\ s=2.55 \end{gathered}`