find the range and standard deviation for .

Question

49, 50, 60, 25, 35, 56, 6, 75, 140, 50, 42, 43, 94, 70, 39, 35, 50, 30, 15, 34, 25, 38, 38.5, 68, 8, 20, 26, and 40

Answer 1

 

The Range is the difference between the lowest and highest values.

 

The range is:   (140 - 6) = 136

 

The standard deviation is given by the Math expression:

https://www.mathsisfun.com/data/images/standard-deviation-formula.gif

 

1) Find the mean:

 

mean =(49+50+60+25+35+56+6+75+140+50+42+43+94+70+39+35+50+30+15+34+25+38+38.5+68+8+20+26+40}/28

 

2) Take each individual data point, subtract the mean and square the results:

For example,  

 

(49 - mean)^2

(50 - mean)^2

(60 - mean)^2, and so until get the final value  (40 - mean)^2

 

3) Add up these results and divide the sum by the number or data points – in this case, 28:

4) Finally, to find the standard deviation, take the square root of this sum as calculated in (3).

Answer 2

Depending on the instructions received from your teacher, you can either make a table of these values and conduct the manual calculations to get mean, and deviations, etc. OR you can use a calculator, entering the data and having it do 1-Var Stats.

 

If required to do it by hand, you can nevertheless check your work using the 1-Var-Stats.