Question 1

When data are positively skewed, the mean will usually be

Accepted Answer

When data are positively skewed, it means that there are many values that are smaller than the median, but a few extreme values that are much larger than the median. Therefore, the mean will be pulled towards these extreme values, resulting in a larger value than the median.

Question 2

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. The other options are measures of variability, but do not specifically refer to the difference between the largest and smallest values.

Question 3

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 4

The most frequently occurring value of a data set is called the

Accepted Answer

The mode is the value that occurs most frequently in a data set.

Question 5

Which difficulty of range as a measure of variability is overcome by interquartile range?

Accepted Answer

Interquartile range is preferred over range because it is not affected much by extreme values. This makes it a better measure of variability when there are outliers or extreme values in the data set.

Question 6

Which of the following is not a measure of central location?

Accepted Answer

Standard deviation is a measure of dispersion, not central location. The other options (mean, median, mode) are all measures of central location.

Question 7

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated. mean = 160
Range = 60
Mode = 165
Variance = 324
Median = 170
The coefficient of variation equals

Accepted Answer

The coefficient of variation is calculated as the standard deviation divided by the mean, expressed as a percentage. Since the standard deviation is the square root of the variance, we first need to find the standard deviation:

Standard deviation = sqrt(Variance) = sqrt(324) = 18

Coefficient of variation = (standard deviation / mean) x 100%
Coefficient of variation = (18 / 160) x 100%
Coefficient of variation = 0.1125 x 100%
Coefficient of variation = 11.25%

Therefore, the answer is B.

Question 8

The value which has half of the observations above it and half the observations below it is called the

Accepted Answer

The value described is the median. The median is the middle value when the data is arranged in order from lowest to highest. It is not affected by extreme values and is therefore a better measure of central tendency than the mean in skewed distributions.

Question 9

If a data set has an even number of observations, the median

Accepted Answer

When a data set has an even number of observations, the median is calculated by taking the average of the two middle numbers after arranging all the observations in ascending order.

Question 10

The interquartile range is

Accepted Answer

The interquartile range (IQR) identifies the spread of the middle 50% of a dataset. It is the difference between the third quartile (the value at 75% of the ordered data) and the first quartile (the value at 25% of the ordered data), and it provides a measure of variability that is less sensitive to extreme values than the range or standard deviation.

Question 11

Which of the following is not a measure of variability?

Accepted Answer

The midrange is a measure of central tendency, not variability.

Question 12

When n - 1 is used in the denominator to compute variance, the data set

Accepted Answer

When n - 1 is used in the denominator to compute variance, it is called the sample variance formula. Therefore, the data set is a sample.

Question 13

When computing the mean, the smallest value

Accepted Answer

The mean is calculated as the sum of all values divided by the number of values, and there's no restriction on the values being positive, zero, or greater than the mean. Therefore, the smallest value in a dataset can indeed be any value, including negative numbers, zero, or a value less than the mean.

Question 14

The variance of a sample of 100 observations equals 64. The standard deviation of the sample equals

Accepted Answer

The standard deviation is the square root of the variance. Since the variance is 64, the standard deviation is the square root of 64, which equals 8.

Question 15

When the data are skewed to the right, the measure of Skewness will be

Accepted Answer

When we talk about skewness, we are examining the symmetry of a data set. If the data are skewed to the right, the tail of the distribution will be longer on the right side than on the left side. As a result, the mean will be greater than the median, resulting in a positive skewness value. Therefore, option C) positive is the correct answer.

Question 16

The first quartile is the same as the

Accepted Answer

The first quartile represents the 25th percentile, meaning 25% of the data falls below this value. It is not the same as the median or 50th percentile, which represent the middle value. It is also not the same as the 75th percentile, which represents the third quartile.

Question 17

Which of the following is a measure of variability?

Accepted Answer

Percentiles and quartiles are measures of position, not variability. Midrange is a measure of central tendency, not variability. Interquartile range is a measure of variability, specifically the range of the middle 50% of data.

Question 18

In computing descriptive statistics from grouped data,

Accepted Answer

In computing descriptive statistics from grouped data, data values are treated as if they occur at the midpoint of a class. This is known as the midpoint approximation method. The grouped data result may not always be more accurate than the ungrouped result, but it is often more manageable for large data sets. Grouped data computations can be used for both sample and population analysis.

Question 19

The standard deviation of a sample of 81 observations equals 49. The variance of the sample equals

Accepted Answer

The answer of The standard deviation of a sample of...

Question 20

The heights (in inches) of 25 individuals were recorded and the following statistics were calculated mean = 70
Range = 20
Mode = 73
Variance = 784
Median = 74
The coefficient of variation equals

Accepted Answer

The answer of The heights (in inches) of 25 individuals...

Quiz 3: Descriptive Statistics: Numerical Measures