Q: Given the following frequency distribution for hours spent studying per week: 0-4 (2 students), 5-9 (6 students), 10-14 (8 students), 15-19 (4 students). What is the estimated mean number of hours spent studying per week?

$$\frac{(2 \times 2) + (6 \times 7) + (8 \times 12) + (4 \times 17)}{2+6+8+4} = \frac{4 + 42 + 96 + 68}{20} = \frac{210}{20} = 10.5$$

Q: A student receives the following grades: B in a 4-credit course, A in a 3-credit course, C in a 2-credit course, and D in a 1-credit course. Using the point system A=4, B=3, C=2, D=1, what is the student's weighted mean (GPA)?

$$\frac{(3 \times 4) + (4 \times 3) + (2 \times 2) + (1 \times 1)}{4+3+2+1} = \frac{12+12+4+1}{10} = \frac{29}{10} = 2.9$$

Q: A teacher wants to estimate the mean test score for a large class using grouped data. The midpoints and frequencies for the score intervals are: 60 (5 students), 70 (10 students), 80 (15 students), 90 (10 students). What is the estimated mean score?

$$\frac{(60 \times 5) + (70 \times 10) + (80 \times 15) + (90 \times 10)}{5+10+15+10} = \frac{300+700+1200+900}{40} = \frac{3100}{40} = 77.5$$

Q: A frequency distribution has class midpoints of 10, 20, 30, and 40 with frequencies 2, 3, 4, and 1, respectively. What is the estimated mean?

$$\frac{(10 \times 2) + (20 \times 3) + (30 \times 4) + (40 \times 1)}{2+3+4+1} = \frac{20+60+120+40}{10} = \frac{240}{10} = 24$$

Question 1

A sample of exam scores is: 72, 85, 90, 90, 95, 100. What is the mode of this data set?

Accepted Answer

$$90$$

Question 2

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is affected by outliers in the data set.

Question 3

Given the following frequency distribution for hours spent studying per week: 0-4 (2 students), 5-9 (6 students), 10-14 (8 students), 15-19 (4 students). What is the estimated mean number of hours spent studying per week?

Accepted Answer

$$\frac{(2 	imes 2) + (6 	imes 7) + (8 	imes 12) + (4 	imes 17)}{2+6+8+4} = \frac{4 + 42 + 96 + 68}{20} = \frac{210}{20} = 10.5$$

Question 4

A student receives the following grades: B in a 4-credit course, A in a 3-credit course, C in a 2-credit course, and D in a 1-credit course. Using the point system A=4, B=3, C=2, D=1, what is the student's weighted mean (GPA)?

Accepted Answer

$$\frac{(3 	imes 4) + (4 	imes 3) + (2 	imes 2) + (1 	imes 1)}{4+3+2+1} = \frac{12+12+4+1}{10} = \frac{29}{10} = 2.9$$

Question 5

Which measure of central tendency is most appropriate for summarizing the typical political party affiliation in a survey of voters?

Accepted Answer

Mode

Question 6

A data set has the following values: 10, 12, 13, 14, 15, 100. Which measure of central tendency is LEAST affected by the outlier?

Accepted Answer

Median

Question 7

In a left-skewed (negatively skewed) distribution, which of the following is true about the relationship between the mean and the median?

Accepted Answer

The mean is less than the median.

Question 8

A hospital administrator wants to summarize the number of days patients stay in the hospital. The data are: 2, 2, 3, 3, 3, 4, 5, 30. Which measure of central tendency best describes a typical stay?

Accepted Answer

Median

Question 9

Which of the following distributions is described as having all entries with approximately equal frequencies?

Accepted Answer

Uniform distribution

Question 10

Given the following data set: 5, 7, 7, 8, 10, 12, 15, what is the median?

Accepted Answer

$$8$$

Question 11

A teacher wants to estimate the mean test score for a large class using grouped data. The midpoints and frequencies for the score intervals are: 60 (5 students), 70 (10 students), 80 (15 students), 90 (10 students). What is the estimated mean score?

Accepted Answer

$$\frac{(60 	imes 5) + (70 	imes 10) + (80 	imes 15) + (90 	imes 10)}{5+10+15+10} = \frac{300+700+1200+900}{40} = \frac{3100}{40} = 77.5$$

Question 12

Which of the following is NOT a property of the mode?

Accepted Answer

It is always unique for any data set.

Question 13

A data set is perfectly symmetric. Which of the following statements is true?

Accepted Answer

The mean and median are equal.

Question 14

A company has 10 employees with the following ages: 22, 23, 23, 24, 24, 24, 25, 25, 26, 60. Which measure of central tendency is most affected by the 60-year-old employee?

Accepted Answer

Mean

Question 15

Which formula correctly represents the sample mean $$\bar{x}$$ for a data set with $$n$$ entries and values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum x}{n}$$

Question 16

A data set has two values that occur with the same highest frequency. What is this type of data set called?

Accepted Answer

Bimodal

Question 17

Which of the following best describes a positively skewed (right-skewed) distribution?

Accepted Answer

The mean is greater than the median.

Question 18

A researcher collects the following data on the number of pets owned by 8 families: 0, 1, 1, 2, 2, 2, 3, 10. Which measure of central tendency would best represent a typical family?

Accepted Answer

Median

Question 19

If a data set has no repeated values, which of the following is true?

Accepted Answer

The data set has no mode.

Question 20

A frequency distribution has class midpoints of 10, 20, 30, and 40 with frequencies 2, 3, 4, and 1, respectively. What is the estimated mean?

Accepted Answer

$$\frac{(10 	imes 2) + (20 	imes 3) + (30 	imes 4) + (40 	imes 1)}{2+3+4+1} = \frac{20+60+120+40}{10} = \frac{240}{10} = 24$$

Measures of Central Tendency in Descriptive Statistics

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