Respuesta :
Answer:
[tex] \bar X = 31.09[/tex]
[tex] Midrange = \frac{50+8}{2}= 29.00[/tex]
[tex] \bar G = (x_1 *x_2*...*X_{32})^{\frac{1}{32}} = 28.33[/tex]
If we Trim the top and bottom 14% from the data we need to eliminate 32*0.14 =4.48 so we need to eliminate approximately 5 values from each tail and we got:
16 20 20 22 25 27 29 31 32 32 32 34 34 35 36 36 37 38 39 41 42 43
And the mean calculated from this data is :
[tex] \bar X_{T}= 31.86[/tex]
Step-by-step explanation:
For this case we have the following data:
27 11 36 22 36 12 35 37 50 16 31 45 48 14 20 34 46 15 25 41 34 39 42 29 32 32 8 32 20 38 43 45
And we can calculate the mean with this formula:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X = 31.09[/tex]
The mid range is calculated with this formula:
[tex]Midrange = \frac{High +Low}{2}[/tex]
And replacing we got:
[tex] Midrange = \frac{50+8}{2}= 29[/tex]
Since the sample size is n =32 we can calculate the geometric mean with this formula:
[tex] \bar G = (x_1 *x_2*...*X_{32})^{\frac{1}{32}} = 28.33[/tex]
For the trimmed mean we need to sort the dats on increasing order and we got:
8 11 12 14 15 16 20 20 22 25 27 29 31 32 32 32 34 34 35 36 36 37 38 39 41 42 43 45 45 46 48 50
If we Trim the top and bottom 14% from the data we need to eliminate 32*0.14 =4.48 so we need to eliminate approximately 5 values from each tail and we got:
16 20 20 22 25 27 29 31 32 32 32 34 34 35 36 36 37 38 39 41 42 43
And the mean calculated from this data is :
[tex] \bar X_{T}= 31.86[/tex]
