Q: A camera is rated on three features: Image Quality (weight 0.5), Battery Life (weight 0.3), and Zoom Range (weight 0.2). Camera A scores 8, 6, and 7 respectively. What is the weighted mean score for Camera A?

$$\bar{x} = \frac{8 \times 0.5 + 6 \times 0.3 + 7 \times 0.2}{0.5 + 0.3 + 0.2} = 7.2$$

Question 1

Which of the following best describes the difference between a sample statistic and a population parameter?

Accepted Answer

A sample statistic is any measurement taken from a sample (uses Roman letters), while a population parameter is any measurement taken from a population (uses Greek letters).

Question 2

Given the following raw data set: 3.7, 4.8, 4.8, 4.0, 4.7, 5.1, 4.3, what is the mean $$\bar{x} of $$the data?

Accepted Answer

$$\bar{x} = \frac{3.7 + 4.8 + 4.8 + 4.0 + 4.7 + 5.1 + 4.3}{7} = 4.49$$

Question 3

A researcher collects the following frequency table for number of books read by students:

0 books: 2 students
1 book: 3 students
2 books: 3 students
3 books: 5 students
4 books: 6 students

What is the mode $$m_o$$?

Accepted Answer

$$m_o = 4$$

Question 4

Which formula is used to calculate the weighted mean $$\bar{x}$$ when data values $$x$$ have corresponding weights $$w$$?

Accepted Answer

$$\bar{x} = \frac{\sum xw}{\sum w}$$

Question 5

A data set is described as right-skewed. Which of the following is most likely true about the relationship between the mean, median, and mode?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 6

In a frequency table, what is the purpose of cumulative frequency?

Accepted Answer

To help locate the median by showing the running total of frequencies up to each data value.

Question 7

A student receives grades: A in one 4-credit class, B in three 3-credit classes, C in one 3-credit class, and D in one 4-credit class. If A=4, B=3, C=2, D=1, what is the weighted mean (GPA)?

Accepted Answer

$$\bar{x} = \frac{16 + 27 + 6 + 4}{20} = 2.65$$

Question 8

Which measure of central tendency is most affected by an outlier in a data set?

Accepted Answer

Mean

Question 9

Given a symmetric distribution, which statement is true?

Accepted Answer

Mean = Median = Mode

Question 10

A frequency table for test scores is given below:

Score: 31, Frequency: 112
Score: 32, Frequency: 97
Score: 37, Frequency: 520
Score: 53, Frequency: 866

What is the mode?

Accepted Answer

Mode = 37

Question 11

If a data set has two modes, what is the correct term for its modality?

Accepted Answer

Bimodal

Question 12

A researcher wants to mitigate the effect of outliers in a data set. Which method is most appropriate?

Accepted Answer

Use a trimmed mean, removing a set percentage of the lowest and highest values.

Question 13

Given the following class bounds and frequencies:

Class: 52.5–63.5, Frequency: 6, Midpoint: 58
Class: 63.5–74.5, Frequency: 12, Midpoint: 69
Class: 74.5–85.5, Frequency: 25, Midpoint: 80
Class: 85.5–96.5, Frequency: 18, Midpoint: 91
Class: 96.5–107.5, Frequency: 14, Midpoint: 102
Class: 107.5–118.5, Frequency: 5, Midpoint: 113

What is the formula to calculate the mean $$\bar{x}$$ for this grouped data?

Accepted Answer

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

Question 14

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 15

A data set has values: 2, 4, 6, 8, 10. What is the midrange $$m_r$$?

Accepted Answer

$$m_r = \frac{2 + 10}{2} = 6$$

Question 16

Which statement is true about the mean for nominal data?

Accepted Answer

The mean cannot be calculated for nominal data because it is qualitative.

Question 17

In a left-skewed distribution, which measure is typically the largest?

Accepted Answer

Mode

Question 18

A camera is rated on three features: Image Quality (weight 0.5), Battery Life (weight 0.3), and Zoom Range (weight 0.2). Camera A scores 8, 6, and 7 respectively. What is the weighted mean score for Camera A?

Accepted Answer

$$\bar{x} = \frac{8 	imes 0.5 + 6 	imes 0.3 + 7 	imes 0.2}{0.5 + 0.3 + 0.2} = 7.2$$

Question 19

If a data set is uniform, what can be said about its mode?

Accepted Answer

There is no mode because all values occur with the same frequency.

Measures of Central Tendency and Distribution Shapes in Statistics

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