Question 1

The measure of location which is the most likely to be influenced by extreme values in the data set is the

Accepted Answer

The mean is most likely to be influenced by extreme values in the data set because it takes into account all the values in the data set in its calculation. Extreme values can significantly affect the mean, skewing it towards the direction of the extreme value. The range, median, and mode are not affected by extreme values to the same extent as the mean.

Question 2

The 75th percentile is referred to as the

Accepted Answer

The 75th percentile is the point at which 75% of the data falls below, meaning that only 25% of the data is above it. This puts it in the third quartile of the data distribution, making option C the correct choice.

Question 3

When a percentage of the smallest and largest values are deleted from a data set, the mean of the remaining data values is the

Accepted Answer

When a percentage of the smallest and largest values are deleted from a data set, the resulting mean is called the trimmed mean. The trimmed mean is a type of average that is less affected by extreme values (outliers) in the data set. The percentage of values that are trimmed can vary depending on the situation, but common choices include trimming 5%, 10%, or 20% of the extreme values. The trimmed mean is a useful statistic for data sets that may contain outliers or other extreme values that could skew the results if included in the calculation of the mean.

Question 4

Geometric mean is a measure of

Accepted Answer

Geometric mean is a measure of location as it gives the central tendency of a set of values by taking the nth root of the product of the values, where n is the number of values in the set.

Question 5

Growth factors for the population of Atlanta in the past five years have been 1, 2, 3, 4 , and 5.The geometric mean is

Accepted Answer

The geometric mean of n numbers is the nth root of their product. The product of the growth factors is 1 * 2 * 3 * 4 * 5 = 120. Therefore, the geometric mean is the fifth root of 120, which is $\sqrt[5]{120}$.

Question 6

μ is an example of a​

Accepted Answer

μ (pronounced mu) is a population parameter, which is a numeric measurement that describes a characteristic of a population. Typically, a population parameter is unknown, so it must be estimated using sample statistics.

Question 7

The median is a measure of

Accepted Answer

The median is a measure of central location as it represents the midpoint in a dataset, with half of the values below and half of the values above. It is not a measure of dispersion, either absolute or relative, or relative location.

Question 8

The pth percentile is a value such that approximately

Accepted Answer

The pth percentile is defined as a value below which approximately p percent of the observations in a data set fall, and (100 - p) percent of the observations are above this value.

Question 9

The mean of the sample

Accepted Answer

The mean of a sample can indeed assume any value between the highest and the lowest value in the sample, depending on the specific values within that sample. It is not necessarily always smaller than the population mean (A), can be zero if the sum of the sample values is zero (B), and can be negative if the sample contains negative values that result in a negative average (C).

Question 10

The nth root of the product of the n observations is the

Accepted Answer

The definition of geometric mean involves taking the nth root of the product of n observations, making it the correct choice. Weighted mean involves multiplying each observation by a weight and then taking the sum, product deviation involves finding the difference between each observation and the product of all observations, and product variance involves taking the product of the differences between each observation and the geometric mean.

Question 11

Growth factors for the population of Chattanooga in the past two years have been 8 and 12.The geometric mean has a value of

Accepted Answer

The geometric mean of two numbers is the square root of their product. So, the geometric mean of 8 and 12 is $\sqrt{8 \times 12} = \sqrt{96}$.

Question 12

In computing the mean of a sample, the value of ∑x_i is divided by

Accepted Answer

The mean of a sample is calculated by dividing the sum of the sample values (∑xi) by the number of observations in the sample (n).

Question 13

The mean of a sample

Accepted Answer

The mean of a sample is computed by summing all the data values and dividing the sum by the number of items in the sample, which is represented by 'n'. Therefore, option D is correct. Option A is incorrect because the mean of a sample may not be equal to the mean of the population. Option B is incorrect because the mean of a sample may be smaller, larger or equal to the mean of the population. Option C is incorrect because the divisor should be 'n' and not (n-1).

Question 14

The geometric mean of five observations is the

Accepted Answer

The geometric mean of a set of numbers is defined as the nth root of the product of n numbers. In this case, we have 5 observations, so the geometric mean is the fifth root of the product of the 5 observations. Therefore, the correct answer is D. The weighted mean is a different type of average that takes into account the weights assigned to each observation, so A is incorrect. The mean is simply the sum of the observations divided by the number of observations, which is not the same as the geometric mean, so B is incorrect. The square root of the product of the 5 observations is the square root of 5 numbers multiplied together, which is not the same as the definition of the geometric mean, so C is also incorrect.

Question 15

The difference between the largest and the smallest data values is the

Accepted Answer

The range is the difference between the largest and smallest data values. Variance and coefficient of variation are measures of dispersion, but they are calculated differently. The interquartile range measures the range of the middle 50% of the data and is not necessarily related to the largest and smallest data values.

Question 16

If two groups of numbers have the same mean, then

Accepted Answer

The mean is just one measure of location and does not necessarily determine the values of other measures such as median, mode, quartiles etc. Therefore, two groups of numbers having the same mean need not have the same values for other measures of location. However, it is possible for two groups with the same mean to have the same standard deviation, but this is not always the case.

Question 17

Which of the following provides a measure of central location for the data?

Accepted Answer

The mean is a measure of central location that represents the average value of the data. The standard deviation measures the degree of dispersion or spread of the data around the mean. The variance is the average of the squared differences from the mean and also measures the degree of dispersion. The range is the difference between the highest and lowest values in the data set and does not provide information about central location.

Question 18

The variance of a sample of 169 observations equals 576.The standard deviation of the sample equals

Accepted Answer

The formula for the standard deviation is the square root of the variance. Thus, we take the square root of 576 to get:

sqrt(576) = 24

Therefore, the standard deviation of the sample is 24. The correct answer is B).

Question 19

A numerical value used as a summary measure for a sample, such as sample mean, is known as a

Accepted Answer

A sample statistic is a numerical value used as a summary measure for a sample. The other answer choices are either population parameters (A and D) or a mix of population and sample terms (B).

Question 20

The median of a sample will always equal the

Accepted Answer

The median is defined as the middle value in a set of data, which means that 50% of the data is below the median and 50% is above it. Therefore, the median will always be equal to the 50th percentile. Choices A, B, and D rely on specific quartiles or values, which may not always be representative of the middle value in a set of data.

Quiz 3: Descriptive Statistics: Numerical