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AleksandrR [38]
2 years ago
9

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the -score for each of the five observations (to 2 decimal

s). Enter negative values as negative numbers. Observed value -score
Mathematics
1 answer:
dybincka [34]2 years ago
4 0

Answer:

Hence, the score for each of the five observations are -1.25,1.25,-0.75,0.50,0.25

Given :

Sample with data values of x_i  10,20,12,17 and 16

Sample sizen=5

To find:

Compute the score for each of the five observations.

Explanation :

\because Sample mean \bar{x}=\frac{\sum x_i}{n}

                     \Rightarrow \bar{x}=\frac{10+20+12+17+16}{5}=\frac{75}{5}

                    \Rightarrow \bar{x}=15

Standard deviation \sigma=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}

                             \Rightarrow \sigma=\sqrt{\frac{(10-15)^2+(20-15)^2+(12-15)^2+(17-15)^2+(16-15)^2}{5-1}}

                            \Rightarrow \sigma=\sqrt{\frac{(-5)^2+(5)^2+(-3)^2+(2)^2+(1)^2}{4}}

                           \Rightarrow \sigma=\sqrt{\frac{25+25+9+4+1}{4}}

                          \Rightarrow \sigma=\sqrt{\frac{64}{4}} =\sqrt{16}

                         \Rightarrow \sigma=4

\because The score of the observations Z is \frac{x-\bar{x}}{\sigma}.

So, when (x=10),       Z=\frac{10-15}{4}=-1.25

     when (x=20),       Z=\frac{20-15}{4}=1.25

     when (x=12),      Z=\frac{12-15}{4}=-0.75

    when  (x=17},       Z=\frac{17-15}{4}=0.50

    when (x=16)       Z=\frac{16-15}{4}=0.25

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