Question 1

When data are positively skewed, the mean will usually be

Accepted Answer

When data are positively skewed, there are more values on the lower end of the range and fewer values on the higher end. This will pull the mean towards the higher end, making it larger than the median.

Question 2

Which of the following is not a measure of dispersion?

Accepted Answer

The 50th percentile, also known as the median, is a measure of central tendency, not a measure of dispersion. The measures of dispersion are the range, standard deviation, and interquartile range.

Question 3

The interquartile range is

Accepted Answer

The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1). Therefore, option D is the correct answer. Option A is incorrect because the 50th percentile is the median, not the interquartile range. Option B is incorrect because the variance is a measure of variability calculated by taking the average of the squared deviations from the mean. Option C is incorrect because the difference between the largest and smallest values is the range, not the interquartile range.

Question 4

The first quartile

Accepted Answer

The first quartile is the same as the 25th percentile, meaning that 25% of the data falls below this value. Therefore, option B is correct. Option A is incorrect because the first quartile represents 25% of the data, not one-third. Option C is incorrect because the 50th percentile is the median, not the first quartile. Option D is incorrect because the third quartile is the same as the 75th percentile, not the first quartile.

Question 5

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

Accepted Answer

Skewness measures the degree of asymmetry in the distribution. When the distribution is skewed to the right, it means that the tail on the right-hand side is longer than the tail on the left-hand side. This results in a positive skewness value.

Question 6

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 7

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 8

Which of the following is a measure of dispersion?

Accepted Answer

Interquartile range is the only one of the options listed that is a measure of dispersion. Percentiles and quartiles are measures of position within a dataset, not measures of how spread out or varied the data is.

Question 9

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

Accepted Answer

Variance is a measure of spread or dispersion, not central location. The other three measures (mean, median, and mode) are all measures of central location.

Question 10

The interquartile range is used as a measure of variability to overcome what difficulty of the range?

Accepted Answer

The range is influenced too much by extreme values, which can cause it to not accurately reflect the spread of the data. The interquartile range is calculated using the middle 50% of the data, which makes it less sensitive to outliers and extreme values.

Question 11

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

Accepted Answer

The value which has half of the observations above it and half the observations below it is called the median. It is not affected by extreme values and hence provides a better measure of central tendency than the mean. The range is the difference between the largest and smallest observations in a data set, while the mode is the value that occurs most frequently in a data set.

Question 12

When computing the mean, the smallest value

Accepted Answer

The answer of When computing the mean, the smallest value
...

Question 13

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

Accepted Answer

The range is defined as the difference between the largest and smallest values in a dataset. The other options do not directly measure this difference.

Question 14

The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals

Accepted Answer

The standard deviation is the square root of the variance, so
standard deviation = √(64) = 8. Therefore, the correct answer is choice C.

Question 15

If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?

Accepted Answer

When computing the variance with n - 1 in the denominator, it means that the data set is a sample. Using n (without subtracting 1) is used when calculating variance in a population (known as population variance). Therefore, option A is the correct choice.

Question 16

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...

Question 17

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 (CV) is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. 
CV = (standard deviation/mean) x 100%
We are not given the standard deviation, but we can calculate it using the variance:
standard deviation = square root(variance) = square root(324) = 18
Therefore, 
CV = (18/160) x 100% = 11.25% 
So, the answer is B.

Question 18

In computing descriptive statistics from grouped data,

Accepted Answer

In grouped data, the frequency distribution is given in terms of class intervals instead of individual data points. Therefore, to compute descriptive statistics such as mean or median, data values are assumed to be occurring at the midpoint of each class interval. This assumption is made for convenience in computation, but it can lead to some loss of accuracy. Therefore, option B is incorrect. Grouped data computations can be used for both population and sample data, so option C is also incorrect. Finally, option D is incorrect because option A is correct.

Question 19

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

Accepted Answer

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

Question 20

If index i which is used to determine the location of the pth percentile) is not an integer, its value should be

Accepted Answer

The answer of If index i which is used to...

Quiz 3: Descriptive Statistics: Numerical Measures