Question 1

The range rule of thumb is only an approximation and should only be used when the distribution of data
values is unimodal and roughly symmetric.

Accepted Answer

The range rule of thumb assumes a normal distribution, which is unimodal and symmetric. Therefore, it should only be used when the distribution of data values is unimodal and roughly symmetric.

Question 2

For a set of data with mean 12 and variance 36, approximately 68% of the values will fall between 0 and 24.

Accepted Answer

False

Question 3

The interquartile range or IQR is found by subtracting the mean from the maximum value of a data
set.

Accepted Answer

The interquartile range is calculated by subtracting the first quartile (25th percentile) from the third quartile (75th percentile) of a data set. It is not related to the mean or the maximum value.

Question 4

For the sample 1, 8, 7, 2, 9, 15, and 18, the mean is 7.6.

Accepted Answer

To find the mean, you add up all the numbers and divide by the total number of numbers. 
(1+8+7+2+9+15+18)/7 = 60/7 = 8.57 (rounded to two decimal places).
Therefore, the statement "For the sample 1, 8, 7, 2, 9, 15, and 18, the mean is 7.6" is false.

Question 5

The following data set could also be referred to as a data array:
3, 4, 2, 7.

Accepted Answer

The answer of The following data set could also be...

Question 6

Chebyshev's theorem can be used to find the minimum percentage of data values that will fall between
any two given values.

Accepted Answer

Chebyshev's theorem is a statistical rule that gives a minimum percentage of observations that lie within a certain number of standard deviations from the mean, regardless of the shape of the distribution, which can be used to estimate the proportion of data between any two points.

Question 7

The percentile corresponding to a given value X is computed by adding the 0.5 to number of values below
X and dividing this value by the total number of values within the data set.

Accepted Answer

This is the correct formula for calculating the percentile rank of a value within a data set.

Question 8

If the range is divided by 6, an approximate value for the standard deviation is obtained.

Accepted Answer

Dividing the range by 6 does not give an accurate approximation of the standard deviation. The standard deviation takes into account the variability of all data points, not just the range.

Question 9

To find the mean for grouped data, we take the sum of all the frequencies, multiply this by the midpoint
of each class and then divide boor the sample size.

Accepted Answer

To find the mean of grouped data, we need to calculate the sum of midpoints multiplied by their respective frequencies. We then divide this by the sum of frequencies, not the sample size.

Question 10

The coefficient of variation is the mean divided by the standard deviation expressed as a percentage.

Accepted Answer

The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage.

Question 11

The unbiased estimator is included in the formula for calculating the variance of a sample because
without it, the computed variance usually underestimates the population variance.

Accepted Answer

The unbiased estimator corrects for any bias in the sample variance caused by using the sample mean as an estimate of the population mean, and as a result, the computed variance with unbiased estimator tends to be closer to the population variance.

Question 12

The median can be a more appropriate measure of central tendency if the distribution of the data is
extremely skewed.

Accepted Answer

When the distribution is extremely skewed, the mean can be heavily influenced by outliers or extreme values while the median is resistant to such outliers, making it a more appropriate measure of central tendency in such cases.

Question 13

John, who was a business student, received a grade corresponding to a z-score of 1 whereas his girl friend
who was studying engineering, received a grade corresponding to a z-score of 2.John's grade score was
necessarily below his girl friend's grade

Accepted Answer

Z-scores measure how many standard deviations an element is from the mean. A higher z-score indicates a score further above the mean, but because John and his girlfriend are in different classes (or even different subjects), their z-scores are relative to their respective class distributions, not directly comparable in terms of raw scores.

Question 14

The variance is the square root of the standard deviation of a set of data.

Accepted Answer

The variance is the square of the standard deviation, not the square root. Therefore, the statement is false.

Question 15

The procedure for finding the mean for grouped data assumes that the mean of all the raw data values in
each class is equal to the midpoint of the class.

Accepted Answer

In the calculation of the mean for grouped data, it is assumed that all values within a class interval are concentrated at the class midpoint, simplifying the computation by using these midpoints to represent the data.

Question 16

Methods commonly called traditional statistics include using measures of position, Chebyshev's theorem,
and the coefficient of variation.

Accepted Answer

These are indeed methods commonly used in traditional statistics.

Question 17

If a distribution is negatively skewed as shown in the figure below, the mean will fall to the right of the
median and the mode will be on the left of the median.

Accepted Answer

If a distribution is negatively skewed, the mean will fall to the left of the median and the mode will be on the right of the median. If a distribution is negatively skewed, the mean will fall to the left of the median and the mode will be on the right of the median.

Question 18

A five-number summary of a data set consists of the minimum,  , the mean,  , and the
maximum.

Accepted Answer

A five-number summary consists of the minimum, first quartile, median, third quartile, and maximum. A five-number summary consists of minimum, first quartile, median, third quartile, and maximum.

Question 19

The range of a data set is the distance between the highest value and the lowest value.

Accepted Answer

The definition of range is correct, and it is indeed the distance between the highest value and the lowest value in a data set. Therefore, option A is correct.

Question 20

A weighted mean is used when the values of the data set are not all equally represented.

Accepted Answer

A weighted mean takes into account the importance or weight assigned to each data value, meaning that not all values are equally represented.

Quiz 3: Data Description

The range rule of thumb is only an approximation and should only be used when the distribution of data values is unimodal and roughly symmetric.

For a set of data with mean 12 and variance 36, approximately 68% of the values will fall between 0 and 24.

The interquartile range or IQR is found by subtracting the mean from the maximum value of a data set.

For the sample 1, 8, 7, 2, 9, 15, and 18, the mean is 7.6.

The following data set could also be referred to as a data array: 3, 4, 2, 7.

Chebyshev's theorem can be used to find the minimum percentage of data values that will fall between any two given values.

The percentile corresponding to a given value X is computed by adding the 0.5 to number of values below X and dividing this value by the total number of values within the data set.

If the range is divided by 6, an approximate value for the standard deviation is obtained.

To find the mean for grouped data, we take the sum of all the frequencies, multiply this by the midpoint of each class and then divide boor the sample size.

The coefficient of variation is the mean divided by the standard deviation expressed as a percentage.

The unbiased estimator is included in the formula for calculating the variance of a sample because without it, the computed variance usually underestimates the population variance.

The median can be a more appropriate measure of central tendency if the distribution of the data is extremely skewed.

John, who was a business student, received a grade corresponding to a z-score of 1 whereas his girl friend who was studying engineering, received a grade corresponding to a z-score of 2.John's grade score was necessarily below his girl friend's grade

The variance is the square root of the standard deviation of a set of data.

The procedure for finding the mean for grouped data assumes that the mean of all the raw data values in each class is equal to the midpoint of the class.

Methods commonly called traditional statistics include using measures of position, Chebyshev's theorem, and the coefficient of variation.

If a distribution is negatively skewed as shown in the figure below, the mean will fall to the right of the median and the mode will be on the left of the median.

A five-number summary of a data set consists of the minimum, , the mean, , and the maximum.

The range of a data set is the distance between the highest value and the lowest value.

A weighted mean is used when the values of the data set are not all equally represented.