An Error A dieter recorded the number of calories he consumed at lunch for one week. As you can see, a mistake was made on one entry. The calories are listed in increasing order: 331, 374, 387, 392, 405, 4200 When the error is corrected by removing the extra 0, will the median calories change? Will the mean ? Explain without doing any calculations.
An Error A dieter recorded the number of calories he consumed at lunch for one week. As you can see, a mistake was made on one entry. The calories are listed in increasing order: 331, 374, 387, 392, 405, 4200 When the error is corrected by removing the extra 0, will the median calories change? Will the mean ? Explain without doing any calculations.
Solution Summary: The author explains the difference between median and mean if the error is corrected by removing an extra 0 from the last observation.
An Error A dieter recorded the number of calories he consumed at lunch for one week. As you can see, a mistake was made on one entry. The calories are listed in increasing order:
331, 374, 387, 392, 405, 4200
When the error is corrected by removing the extra 0, will the median calories change? Will the mean? Explain without doing any calculations.
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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Part (b)
Draw a scatter plot of the ordered pairs.
N
Life
Expectancy
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Expectancy
80
70
600
50
40
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10
Year of
1950
1970 1990
2010 Birth
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Part (c)
800
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1950
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J7
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80
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1950 1970 1990
2010 Birth
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Expectancy
Ox
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Year of
1950 1970 1990 2010 Birth
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Chapter 3 Solutions
Pearson eText Introductory Statistics: Exploring the World Through Data -- Instant Access (Pearson+)
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