Statistics - Measures of Central Tendency

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Questions and Answers

What is the formula for calculating the mean of a set of numbers?

Divide the largest number by the total count of numbers.
Find the middle number in a ranked list of data.
Multiply the average of the two middle numbers by the total number of entries.
Sum all the numbers and divide by the number of data values. (correct)

Which measure of central tendency is defined as the middle number of a ranked list?

Mean
Mode
Range
Median (correct)

In which area of statistics is the mean primarily used?

Descriptive statistics only
Inferential statistics only
Both descriptive and inferential statistics (correct)
Neither descriptive nor inferential statistics

What is the primary difference between a population and a sample in statistics?

A population includes all members, while a sample is a subset of the population. (D) Signup and view all the answers

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

Standard deviation (B) Signup and view all the answers

What is the correct term for the average of the two middle numbers in a dataset with an even number of entries?

Median (D) Signup and view all the answers

What is the role of inferential statistics?

To draw conclusions about a population based on a sample. (B) Signup and view all the answers

When calculating the mode of a dataset, what are you determining?

The most frequently occurring value. (C) Signup and view all the answers

What is the mode of the list 18, 15, 21, 16, 15, 14, 15, 21?

15 (C) Signup and view all the answers

Which of the following statements about the median is true?

The median is the middle number in a ranked list. (B) Signup and view all the answers

Which list contains no mode?

5, 6, 7, 8, 9, 10 (B) Signup and view all the answers

In a dataset, what does 'bimodal' mean?

There are two modes in the dataset. (B) Signup and view all the answers

What is the primary difference between the mean and the median?

The mean is sensitive to extreme values, while the median is not. (B) Signup and view all the answers

How is the weighted mean calculated?

By multiplying each number by its weight and dividing by the sum of the weights. (A) Signup and view all the answers

Which set of numbers represents an unimodal dataset?

2, 3, 4, 4, 4, 5, 6 (C) Signup and view all the answers

If a dataset has extreme high and low values, which measure of central tendency is the most appropriate to use?

Median (A) Signup and view all the answers

What does a decile divide a distribution into?

10 parts (A) Signup and view all the answers

What is the purpose of the least-squares regression line?

To minimize the sum of squares of vertical deviations (D) Signup and view all the answers

How many parts does a quartile divide a distribution into?

4 parts (A) Signup and view all the answers

Which of the following is a characteristic of bivariate data?

Pairs each value of one variable with a value of another (A) Signup and view all the answers

What geometric representation displays the relationship between two variables?

Scatter plot (C) Signup and view all the answers

What does the vertical deviation represent in the context of a least-squares regression line?

The difference between actual and predicted values (D) Signup and view all the answers

Which of the following statements is true regarding percentiles, deciles, and quartiles?

Percentiles divide the data into 100 equal parts (A) Signup and view all the answers

What is the main feature of a least-squares regression line?

It minimizes the sum of the squares of deviations from points (A) Signup and view all the answers

What is the formula for calculating the variance of a sample?

$s^2 = \frac{\sum (x - \bar{x})^2}{n-1}$ (C) Signup and view all the answers

Which of the following represents the standard deviation of a population?

$\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}$ (B) Signup and view all the answers

In the calculation of percentiles, what does P50 represent?

The 50th percentile, which is the median (A) Signup and view all the answers

What does the term 'measures of dispersion' refer to?

The spread or variability of a data set (D) Signup and view all the answers

When calculating the variance for a population, which symbol is used?

$\sigma^2$ (C) Signup and view all the answers

How do you compute the mean of the following dataset: 80, 82, 83, 90, 84, 88, 81, 85, 92, 82?

85 (A) Signup and view all the answers

If a dataset is divided into 100 equal parts, which measure is being represented?

Percentile (C) Signup and view all the answers

What is the main difference between sample variance and population variance?

Sample variance uses a smaller divisor, $n$ instead of $n-1$ (C) Signup and view all the answers

What does the least-squares regression line equation represent?

The relationship between independent variable x and dependent variable y. (D) Signup and view all the answers

Which of the following expressions correctly represents the slope 'a' of the least-squares line?

$rac{n extstyle igg( xy igg) - igg(xigg)igg(yigg)}{n extstyle igg( x^2igg) - igg(xigg)^2} (C) Signup and view all the answers

How is the linear correlation coefficient 'r' interpreted when it is negative?

As one variable increases, the other variable tends to decrease. (C) Signup and view all the answers

What is the impact of increasing 'n' on the linear correlation coefficient 'r' calculation?

It can result in a more stable and representative coefficient. (C) Signup and view all the answers

Which of the following statements is true about the least-squares regression line?

It minimizes the sum of squared differences between observed and predicted values. (D) Signup and view all the answers

In the least-squares regression formula, what does 'b' represent?

The y-intercept of the regression line. (B) Signup and view all the answers

What are the implications if the linear correlation coefficient 'r' is close to 1?

There is a strong positive linear relationship between the variables. (A) Signup and view all the answers

What is the purpose of computing the linear correlation coefficient 'r'?

To measure the strength and direction of a linear relationship. (B) Signup and view all the answers

Study Notes