The following data was collected from 10 visitors to disneyland. a researcher stood at the entrance gate and interviewed the first 10 families that agreed to participate. each family was asked, “how many times have you been to disneyland? ” the data values were: 1, 1, 2, 2, 2, 2, 3, 3, 4, 7. the average number of visits was calculated and reported.
calculate the standard deviation of the data values.

The standard deviation for the sample of 10 families is 1.68 (Rounding to two decimal places)

Step-by-step explanation:

1. The first step to calculate the standard deviation is to find out the mean, this way:

Mean = (1 + 1 + 2 + 2 + 2 + 2 + 3 + 3 + 4 + 7)/10

Mean = 27/10 = 2.7

2. Now we calculate the variance, this way:

Variance = [(1 - 2.7)²+(1 - 2.7)²+(2 - 2.7)²+(2- 2.7)²+(2 - 2.7)²+(2 - 2.7)²+(3- 2.7)²+(3 - 2.7)²+(4 - 2.7)²+(7- 2.7)²]/10

Variance = [2.89  + 2.89 + 0.49 + 0.49 + 0.49  + 0.49 + 0.09 + 0.09 + 1.69 + 18.49]/10

Variance = 28.1/10 = 2.81

3. Finally we calculate the standard deviation, this way:

Variance = Standard deviation²

√Variance = Standard deviation

√2.81 =  Standard deviation

Standard deviation = 1.68 (Rounding to two decimal places)

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3