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katovenus [111]
3 years ago
5

What is the standard deviation of the following data? 52 61 31 44 47 45 25 48 47

Mathematics
1 answer:
Elena-2011 [213]3 years ago
3 0
Standard deviation is calculated by
1. calculate mean, m
2. calculate deviation of EACH entry of data set from the mean, i.e.
d=(x-m)
3. calculate mean of square of deviations (d^2)/n to get variance,v
4. take square-root of variance to get standard deviation.

For example,
To find the standard deviation of data set {3,7,8}
1. mean=(3+7+8)/3=6
2. deviations, di={3-6,7-6,8-6}={-3,1,2}
3. squares of deviations, di^2={9,1,4}
4. mean of squares of deviations=(9+1+4)/3=14/3
Standard deviation=sqrt(14/3)=2.16

For the given data set, if you follow the above steps, you would get
sum=400
mean=400/9
variance (mean square of deviations)=8246/81
standard deviation=sqrt(8246/81)=sqrt(8246)/9


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Charra [1.4K]

Answer:

=m2+6mn+9n2

Step-by-step explanation:

=(m+3n)(m+3n)

=(m)(m)+(m)(3n)+(3n)(m)+(3n)(3n)

=m2+3mn+3mn+9n2

7 0
3 years ago
When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elap
Mkey [24]

Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

<h3>Methods used to calculate speed and distance traveled</h3>

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, <em>t</em> = 10 s - 5 s = 5 s

Speed = \mathbf{\dfrac{Distance}{Time}}

Therefore;

  • Bill's \  maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance,<em> s</em> = Speed, <em>v</em> × Time, <em>t</em>

<em />

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

  • Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = <u>69 meters</u>

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

  • Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = <u>57 meters</u>

Learn more about distance, speed, time, relationship here:

https://brainly.in/question/49075584

6 0
2 years ago
the legs of a scalene triangle are represented by (x+4),(x+8), and (2x - 3) which polynomial expression best represents the peri
AVprozaik [17]

perimeter means add the side

(x+4) +( x+8)+(2x-3) =P

x+x+2x+4+8-3=P

4x-9 =P

8 0
3 years ago
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October 21st, 24 days later
3 0
3 years ago
A certain fraction is greater than 2. The denominator is 8. What must be true about the numerator?
Volgvan

Answer:

The numerator must be greater than 16

Step-by-step explanation:

We are told that a certain fraction is greater than 2. Thus, if the numerator and denominator are x and y respectively, then we have;

x/y > 2

We are further told that the denominator is 8.

Thus;

x/8 > 2

Multiply both sides by 8 to give;

x > 16

Thus,the numerator must be greater than 16.

5 0
2 years ago
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