Question 406695
Find the mean :

11 12 13 13 14 14 14........91
15 17 16 16 17 17 16..........114
15 15 18 19 16 16 18..........117
17 17 18 17 16 16 16..........117
15 9 10 18 14 11 9..................86

{{{(91+114+117+117+86)/35= 525/35=15}}}......the mean is {{{15}}} 


The {{{interval }}}is


Find the standard deviation of  using this formula first:

subtract the mean individually from each of the numbers in the question and square the result.
x               11       12        13       13       14       14        14        
(x - x)²     16         9           4       4           1         1           1..........36

x               15       17        16       16       17       17        16        
(15 - x)²     0         4           1        4         4         4          1.............18

 x   	    15 	15	18	 19	 16	 16 	18
(15 - x)²     0	 0  	  9	   16        1          1         9.............36


x   	    17 	17	18	 17	 16	 16 	16
(15 - x)²     4	 4  	  9	  4          1          1         1..................24

x   	    15 	 9	10	 18	 14	 11 	9
(15 - x)²     0	 36  	  25	  9          1          16      36............123
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                                                                                                     237
                                                                                                                    
Now add up these results (this is the 'sigma' in the formula): 237

{{{lower_case_sigma = sqrt(uper_case_sigma(x - x)^2/(n-1)) 

{{{n=35}}}, 

{{{lower_case_sigma = sqrt(237/34)}}} 

{{{lower_case_sigma = sqrt(6.9705882352941176470588235294118)}}} 


{{{lower_case_sigma = (2.6401871591412071041056987587526)}}}

the standard deviation is {{{(2.6401871591412071041056987587526)}}}
	 		


{{{x +-zs/sqrt(n)}}}

= 15 +-(1.96(2.6401871591412071041056987587526))/sqrt(35)

= 15 +-( 5.1747668319167659240471695671539)=15+-5.18


{{{15 +5.18 =20.17}}}

{{{15 -5.18 = 9.82}}}

So the interval is {{{9.82<the_ interval<20.17}}}....in average:14.995