Ages A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years. a. Are these numbers statistics or parameters? Explain. b. Label both numbers with their appropriate symbol (such as x ¯ , μ , s , or σ ).
Ages A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years. a. Are these numbers statistics or parameters? Explain. b. Label both numbers with their appropriate symbol (such as x ¯ , μ , s , or σ ).
Ages A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years.
a. Are these numbers statistics or parameters? Explain.
b. Label both numbers with their appropriate symbol (such as
x
¯
,
μ
,
s
,
or
σ
).
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 + ...
a .
Expert Solution
To determine
Identify if the given numbers are statistics or parameters.
Answer to Problem 1SE
The given numbers are parameters.
Explanation of Solution
It is given that the study of all students in the small college showed mean age of 20.7 years and standard deviation of 2.5 years.
The numerical characteristic of the population and sample are called parameter and statistic, respectively.
The study considered all the students, which can be referred to as the population. Thus, 20.7 years is the population mean and 2.5 years is the population standard deviation. So, the given numbers are characteristics of the population.
Therefore, the given numbers are parameters.
b .
Expert Solution
To determine
Identify the appropriate symbols for the given numbers.
Answer to Problem 1SE
The numbers can be labelled as "$
" μ=20.7 yearsMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaH8oqBcqGH9aqpcaaIYaGaaGimaiaac6cacaaI3aGaaeiiaiaabMhacaqGLbGaaeyyaiaabkhacaqGZbaaaa@407B@ and "$
" σ=2.5 yearsMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaHdpWCcqGH9aqpcaaIYaGaaiOlaiaaiwdacaqGGaGaaeyEaiaabwgacaqGHbGaaeOCaiaabohaaaa@3FCC@ .
Explanation of Solution
The given numbers 20.7 years and 2.5 years are population mean and population standard deviation of the ages of students in a small college, respectively.
The population mean is denoted by "$
" μMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaH8oqBaaa@3736@ and the population standard deviation is denoted by "$
" σMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaHdpWCaaa@3743@ . Thus, the given numbers can be labelled as "$
" μ=20.7 yearsMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaH8oqBcqGH9aqpcaaIYaGaaGimaiaac6cacaaI3aGaaeiiaiaabMhacaqGLbGaaeyyaiaabkhacaqGZbaaaa@407B@ and "$
" σ=2.5 yearsMathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciaaciGaaeqabaWaaeaaeaaakeaacqaHdpWCcqGH9aqpcaaIYaGaaiOlaiaaiwdacaqGGaGaaeyEaiaabwgacaqGHbGaaeOCaiaabohaaaa@3FCC@ .
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