A nationwide test taken by high school sophomores and juniors has 3 sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 48.7, with a standard deviation of 10.6. Based on the information, complete the following statements about the distribution of the scores on the writing section for the recent year. A nationwide test taken by high school sophomores and juniors has three sections,h scored on a scale of 20 to 80. Ina recent year, the national mean score for the writing section was 48.7, with a stanc deviation of 10.6. Based on thisinformation, complete the following statements about the distribution of the scores r+he writing section for the recentyear.(a) According to Chebyshev's theorem, at least ?v of the scores liebetween 27.5 and 69.9.(b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the scoreslie between and .(Round your answer to 1 decimal place.)

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Description: A nationwide test taken by high school sophomores and juniors has 3 sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 48.7, with a standard deviation of 10.6. Based on the information,

The Chebyshev's theorem states that 1. At least 75% of all the data values should fall within 2 standard deviations of the mean. 2. At least 89%, of all data values fall within 3 standard deviations of the mean(a) μ±σ=48.7±2×10.6=27.5,69.9 As the values 27.5 and 69.9 falls within 2 standard deviations of the mean, it can be said that At least 75% of scores fall between 27.5 and 69.9. (b) μ±σ=48.7±3×10.6=16.9,80.5 At least 89% of scores fall between 16.9 and 80.5.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A nationwide test taken by high school sophomores and juniors has 3 sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 48.7, with a standard deviation of 10.6. Based on the information, complete the following statements about the distribution of the scores on the writing section for the recent year.

A nationwide test taken by high school sophomores and juniors has three sections,
h scored on a scale of 20 to 80. In
a recent year, the national mean score for the writing section was 48.7, with a stanc deviation of 10.6. Based on this
information, complete the following statements about the distribution of the scores r
+he writing section for the recent
year.
(a) According to Chebyshev's theorem, at least ?
v of the scores lie
between 27.5 and 69.9.
(b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the scores
lie between and .(Round your answer to 1 decimal place.)

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 + ...

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