Question

3. Find the standard deviation of the data set 1,2,3,4,5) using the formula from class/discussion section. Do not use a computer/program to skip all the work. Then, find the IQR. When breaking the data into two pieces, do not include the median in either piece. 4. Find the standard deviation of the data set f-2n, -2n+2,..,-2,0,2,..,2n-2,2n). Simplify your answer as much as possible. Recall that in calculus you learned simpleformulas for i Σ2 and Σί3. For example, you might remember that Σ rl 2

Please show all the step

Answer 1

3) The mean of the data 1,2,3,4,5 is

1+2 3 +45 5

The standard deviation is

2 σー 5

The quantiles of the data 1,2,3,4,5 are . Interquartile range (IQR) is

25% = 2375% 4

$IQR=Q_{75\%}-Q_{25\%}=4-2={\color{Blue} 2}$

4) The mean of the data set is

(-2n,-2n + 2, ,-2,0, 2, , 2n-2, 2n}

0 2n ± 1

Number of data points is .

2n + 1

Now,

(2n -2)2 + (2n)2 x7 = 8 (12+22 + +12) (2n +1) 6 x 4n(n +1)2n+1) 2

The standard deviation is

2n1 4n(n+11(2n+1) 2n 1 4n (n 1)