the means and standard deviations for API and growth scores

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Answer 1

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 1CS

To determine

To find: the means and standard deviations for API and growth scores

Expert Solution & Answer

Answer to Problem 1CS

In Alvord district:

Statistic	Mean	Standard deviation
API	756.42	40.08
Growth	271	17.95

In Riverside unified district:

Statistic	Mean	Standard deviation
API	806.85	43.12
Growth	14.78	12.67

Explanation of Solution

Given:

API and the growth scores for each of the two districts

Calculation:

Let’s find out means and standard deviations for API and growth scores for each of the two districts

API (1= Alvord schools and 2= riverside unified schools)

The mean is the sum of all values divided by the number of values:

$x1¯=786+760+768+745+731+815+6907=756.4286x2¯= 891+778+827+789+805+762+798+ 796+731+818+769+815+841+87614=806.8571$

The sample standard deviation is the square root of the population sample

$s1= ( 786−756.4 ) 2 + ( 760−756.4 ) 2 + ( 768−756.4 ) 2 + ( 745−756.4 ) 2 + ( 731−756.4 ) 2 + ( 815−756.4 ) 2 + ( 690−756.4 ) 2 7−1=40.08$

$s2= ( 891−806.85 ) 2 + ( 778−806.85 ) 2 + ( 827−806.85 ) 2 + ( 789−806.85 ) 2 + ( 805−806.85 ) 2 + ( 762−806.85 ) 2 + ( 798−806.85 ) 2 + ( 796−806.85 ) 2 + ( 731−806.85 ) 2 + ( 818−806.85 ) 2 + ( 769−806.85 ) 2 + ( 815−806.85 ) 2 + ( 841−806.85 ) 2 + ( 876−806.85 ) 2 14−1=43.12$

Growth (1= Alvord schools and 2 = riverside unified schools)

$x1¯=−5−2+8+40−6+0−157=2.7143x2¯= 18+8+10+23+28+6+35+ 34−4+28+3+7+8+314=14.7857$

The sample standard deviation is the square root of the population sample

$s1= ( −5−2.71 ) 2 + ( −2−2.71 ) 2 + ( 8−2.71 ) 2 + ( 40−2.71 ) 2 + ( −6−2.71 ) 2 + ( 0−2.71 ) 2 + ( −16−2.71 ) 2 7−1=17.9510s2= ( 18−14.78 ) 2 + ( 8−14.78 ) 2 + ( 10−14.78 ) 2 + ( 23−14.78 ) 2 + ( 28−14.78 ) 2 + ( 6−14.78 ) 2 + ( 35−14.78 ) 2 + ( 34−14.78 ) 2 + ( −4−14.78 ) 2 + ( 28−14.78 ) 2 + ( 3−14.78 ) 2 + ( 7−14.78 ) 2 + ( 8−14.78 ) 2 + ( 3−14.78 ) 2 14−1=12.6745$

In Alvord district:

Statistic	Mean	Standard deviation
API	756.42	40.08
Growth	271	17.95

In Riverside unified district:

Statistic	Mean	Standard deviation
API	806.85	43.12
Growth	14.78	12.67

Conclusion:

Therefore, means and standard deviations for API and growth scoresare done

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 1CS

To determine

To find: the means and standard deviations for API and growth scores

Expert Solution & Answer

Answer to Problem 1CS

In Alvord district:

Statistic	Mean	Standard deviation
API	756.42	40.08
Growth	271	17.95

In Riverside unified district:

Statistic	Mean	Standard deviation
API	806.85	43.12
Growth	14.78	12.67