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S_A_V [24]
3 years ago
8

In a statistics​ class, the standard deviation of the heights of all students was 3.8 inches. The standard deviation of the heig

hts of males was 3.3 inches and the standard deviation of females was 3.1 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered​ separately?
Mathematics
1 answer:
goblinko [34]3 years ago
4 0

Answer:

The reason why standard deviation of the entire class is greater than standard deviation of males and females considered separately, is that mean values for males and females are different from each other.

Step-by-step explanation:

The concept of mean is well represented by the following formula

mean = \frac{(x1 + x2 + x3 + ..... + xn)}{N}, where x1, x2, xn are the observations and N is the number of observations (population).

Standard deviation represents the distance between each observation and the mean of the population (all observations). The formula for this parameter is:

Standard deviation =√[((x1 - x)² + (x2-x)² + ....+ (xn-x)²)/N-1], where x1, x2,..., xn are the observations and x is the mean value.

In this case you have that each height registered is an observation and the number of observations represents the N value. As you can see if the mean for males is different from that of females their standard deviation will be different too. Usually males have heigths greater than that of females (1.77 vs 1.64, in USA for example), and heights inside each group will be more similar than between groups. Then, when you mix all observation there will be an increase in standard deviation, because you are mixing very different heigths

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pochemuha

The first step that we need to take before attempting to solve a problem is to understand what the problem is asking us to do and what is given to us to help accomplish that goal.  Looking at the problem statement they are asking for us to determine the value of the unknown variable h.  We are given one angle along with two sides.

Now that we have completed that step, we can move onto understanding what needs to be done to solve for the unknown.  We know that the best option is to use some trigonometry to help us determine the other side. Using Soh | Cah | Toa we are able to determine that we have the opposite side (h) and the hypotenuse (15.6 cm).

<u>Trigonometric functions</u>

  • sin(\theta) = \frac{opposite}{hypotenuse}
  • cos(\theta) = \frac{adjacent}{hypotenuse}
  • tan(\theta) = \frac{opposite}{adjacent}

<u>Plug in the values</u>

  • sin(\theta) = \frac{opposite}{hypotenuse}
  • sin(36) = \frac{h}{15.6\ cm}

We know have an expression which contains everything that we need to determine the value of the unknown.  To help isolate h we need to multiply both sides by 15.6 cm which will isolate h.  After that we need to simplify the expression so we can get the value of h.

<u>Multiply both sides by 15.6 cm</u>

  • sin(36) * 15.6\ cm = \frac{h}{15.6\ cm}  * 15.6\ cm
  • sin(36) * 15.6\ cm = h

<u>Simplify the expression</u>

  • 0.5878 * 15.6\ cm = h
  • 9.169 = h

After simplifying the expression, we are able to eliminate options A and C because they state that h is equal to 8.4 cm.  We also know that with the given dimensions we would be able to create two triangles. Therefore, the option that best incapsulates the correct answer would be option B - 9.2, two possible triangles.

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Answer: The weight of the iceberg at the end of the day will be 449,100 lbs.

Step-by-step explanation: The question is solved by first calculating what the loss of weight is during the day. The question indicates that it will lose .2%. In order to calculate the loss you need to multiply 450,000 x .002, which equals 900. Next, we subtract the weight loss from the original weight to determine the end of day weight. 450,000 - 900 = 449,100 lbs.

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Answer:

A ∩ B = {1, 3, 5}

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Step-by-step explanation:

The given problem regards sets and set notation, a set can simply be defined as a collection of values. One is given the following information:

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1. Solving problem 1

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The symbol (∩) in set notation refers to the intersection between the two sets. It essentially asks one to find all of the terms that two sets have in common. The given sets (A) and (B) have the values ({1, 3, 5}) in common thus, the following statement can be made,

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