Q: Given the data set: $$42.1, 49.9, 42.9, 39.2, 40.6, 40.8$$, what is the range of the data?

$$\text{Range} = 49.9 - 39.2 = 10.7$$

Q: Given the following weights for a course: attendance (5%), quizzes (10%), exams (60%), final exam (25%), and Marissa's scores: 100% (attendance), 95% (quizzes), 86% (exams), 85% (final), what is her weighted course average?

$$0.05 \times 100 + 0.10 \times 95 + 0.60 \times 86 + 0.25 \times 85 = 87.15$$

Question 1

Which of the following statements best describes the difference between the three histograms shown in the first image, given that all have the same mean ($$\bar{x} = 5$$)?

Accepted Answer

The histograms have the same mean but different measures of dispersion (standard deviation).

Question 2

Given the data set: $$42.1, 49.9, 42.9, 39.2, 40.6, 40.8$$, what is the range of the data?

Accepted Answer

$$	ext{Range} = 49.9 - 39.2 = 10.7$$

Question 3

Which of the following is a disadvantage of using the range as a measure of dispersion?

Accepted Answer

It is affected by extreme values and only uses two data points.

Question 4

If a data set has a mean of $$31$$ and a standard deviation of $$6$$, how many standard deviations away from the mean is the value $$25$$?

Accepted Answer

$$\frac{31-25}{6} = 1$$ standard deviation

Question 5

According to the Empirical Rule, for a bell-shaped distribution, approximately what percentage of data falls within two standard deviations of the mean?

Accepted Answer

About 95%

Question 6

The weights (in grams) of kidney pairs in adult males are bell-shaped with mean $$325$$ grams and standard deviation $$30$$ grams. According to the Empirical Rule, about 95% of kidney pairs will be between what weights?

Accepted Answer

$$325 \pm 60$$ grams, or between $$265$$ and $$385$$ grams

Question 7

Which of the following is true about standard deviation and variance?

Accepted Answer

They measure the spread of data around the mean.

Question 8

Given the following weights for a course: attendance (5%), quizzes (10%), exams (60%), final exam (25%), and Marissa's scores: 100% (attendance), 95% (quizzes), 86% (exams), 85% (final), what is her weighted course average?

Accepted Answer

$$0.05 	imes 100 + 0.10 	imes 95 + 0.60 	imes 86 + 0.25 	imes 85 = 87.15$$

Question 9

If two data sets have the same mean but different standard deviations, what does this indicate about the data sets?

Accepted Answer

They have different spreads but the same center.

Question 10

A data set is symmetric and bell-shaped with mean $$50$$ and standard deviation $$5. $$According to the Empirical Rule, what percentage of data falls between $$45$$ and $$55$$?

Accepted Answer

About 68%

Question 11

Which of the following best describes why standard deviation is preferred over range as a measure of dispersion?

Accepted Answer

Standard deviation uses all data values, while range only uses the two extreme values.

Question 12

Given two mutual funds with the same mean return but different standard deviations, which fund is less risky?

Accepted Answer

The fund with the smaller standard deviation.

Question 13

If a data set has a mean of $$100$$ and a standard deviation of $$15$$, what is the interval that contains approximately 99.7% of the data according to the Empirical Rule?

Accepted Answer

$$100 \pm 45$$, or between $$55$$ and $$145$$

Question 14

Which of the following is the correct formula for the weighted mean $$\bar{x}_w of a $$data set with values $$x_1$$, $$x_2$$, ..., x_n$$ and corresponding weights w_1$, w_2$, ..., w_n$$?

Accepted Answer

$$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$$

Question 15

A bell-shaped distribution has mean $$70$$ and standard deviation $$8. $$What percentage of data is expected to fall between $$54$$ and $$86$$?

Accepted Answer

About 95%

Study Guide: Measures of Dispersion, Empirical Rule, and Weighted Mean in Introductory Statistics

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