Ch. 1 - Introduction to Statistics

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 1 - Introduction to Statistics

Problem 1.C.6

Chapter 1, Problem 1.C.6

Standard Deviation One way to get a very rough approximation of the value of a standard deviation of sample data is to find the range, then divide it by 4. The range is the difference between the highest sample value and the lowest sample value. In using this approach, what value is obtained from the sample data listed in Exercise 1 “IQ Scores”?

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Identify the highest and lowest values in the sample data set provided in Exercise 1 'IQ Scores'.

Calculate the range by subtracting the lowest value from the highest value in the sample data set.

Use the formula for the rough approximation of the standard deviation: divide the range by 4.

\frac{Range}{4}

The result from the division gives a rough approximation of the standard deviation for the sample data.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the values in a dataset deviate from the mean, providing insight into the spread of the data. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation suggests a wider range of values.

Range

The range is a simple measure of variability in a dataset, calculated as the difference between the highest and lowest values. It provides a quick sense of the spread of the data but does not account for the distribution of values between the extremes. While useful for a rough estimate, it can be sensitive to outliers.

Approximation Method for Standard Deviation

The approximation method for standard deviation involves dividing the range by 4 to estimate the standard deviation. This technique offers a quick, rough estimate, especially useful when detailed calculations are impractical. However, it assumes a normal distribution and may not be accurate for datasets with significant skewness or outliers.

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Calculating Standard Deviation

Related Practice

Textbook Question

Physicians’ Health Study In the Physicians’ Health Study, some of the subjects were treated with aspirin while others were given a placebo. For the subjects in this experiment, what is blinding?

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Textbook Question

Determining Sample Size The given expression is used to determine the size of the sample necessary to estimate the proportion of college students who have the profound wisdom to take a statistics course. Find the value and round the result up to the next larger whole number.

[(1.95996)^2 - 0.25] / (0.03)^2

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Textbook Question

Body Temperature The given expression is used for determining the likelihood that the average (mean) human body temperature is different from the value of 98.6°F that is commonly used. Find the given value and round the result to two decimal places.

(98.2 - 98.6) / (0.62 / sqrt(106) )

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Textbook Question

IQ Scores Listed below are the IQ scores of randomly selected statistics professors. What value is obtained when those IQ scores are added and the total is divided by the number of scores? (This result, called the mean, is discussed in Chapter 3.) What is notable about these values?

135 149 145 129 118 119 115 133 107 188

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Textbook Question

Birth Weights For 100 randomly selected births from Bellevue Hospital Center, the birth weights are added and then divided by 100. The result is 3240 g. Is the value of 3240 g a statistic or a parameter?

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Textbook Question

Birth Weights Refer to the sample described in Exercise 6. Because Bellevue Hospital Center agreed to provide the 100 birth weights, does the sample of birth weights constitute a voluntary response sample?

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