The frequency distribution shows the average number of pupils per teacher in the United States. Find the variance and standard deviation for the data. Round your answers to one decimal place. Class limits Frequency
9-11 1
12-14 17
15-17 13
18-20 8
21-23 2
24-26 1
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Variance =
Standard deviation =

Variance = 9.8

Standard deviation = 3.1

Step-by-step explanation:

Group    Midpoint X    Frequency f    f*x      x^2    f*(x^2)

9 to 11             10                    1              10      100     100

12 to 14           13                   17             221    169     2873

15 to 17           16                   13             208   256    3328

18 to 20          19                    8             152     361     2888

21 to 23          22                   2              44      484    968

24 to 26         25                    1              25      625    625

SUM                                      42             660   1995   10782

Mean (x) = ∑(f*x) / ∑f

Mean (x) = 660/42

Mean (x) = 15.7142857143

Variance = ∑(f*x^2) / ∑f - (Mean^2)

Variance =  [10782/42] - [15.71428571432 ]

Variance = 9.77551020408

Variance = 9.8

Standard deviation =

Standard deviation = 3.12658123261

Standard deviation = 3.1

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: