Question 1

The difference between the largest and smallest observations in an ordered data set is called the range.

Accepted Answer

This statement is true. The range is calculated by subtracting the smallest observation from the largest observation in an ordered data set.

Question 2

In a negatively skewed distribution, the mean is smaller than the median and the median is smaller than the mode.

Accepted Answer

This is the correct definition of a negatively skewed distribution.

Question 3

The value of the mean times the number of observations equals the sum of the observations.

Accepted Answer

This statement is true and is known as the property of the arithmetic mean.

Question 4

In a histogram, the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.

Accepted Answer

This statement is true for a symmetric and unimodal distribution. The mean divides the histogram into two equal halves, so 50% of the area will be to the left of the mean and 50% to the right.

Question 5

Lily has been keeping track of what she spends to eat out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53, and $7.66. The mean amount Lily spends on meals is $8.35.

Accepted Answer

The answer of Lily has been keeping track of what...

Question 6

The Empirical Rule states that the percentage of observations in a data set (providing that the data set is bell shaped)that fall within one standard deviation of their mean is approximately 75%.

Accepted Answer

The Empirical Rule actually states that approximately 68% of observations in a bell-shaped distribution fall within one standard deviation of the mean.

Question 7

The mean is affected by extreme values but the median is not.

Accepted Answer

The mean is calculated by adding up all the values and dividing by the number of values. If there are extreme values, they can greatly affect the total value and therefore affect the mean. The median, on the other hand, is the middle value of a set of data when it is arranged in order. Extreme values do not affect this value as much.

Question 8

If the median, median and mode are all equal, the histogram must be symmetric and bell shaped.

Accepted Answer

A distribution where the mean, median, and mode are all equal does not necessarily have to be symmetric or bell-shaped. It could be a uniform distribution or any other shape where these measures of central tendency coincide.

Question 9

In a histogram, the proportion of the total area which must be to the left of the median is less than 0.50 if the distribution is negatively skewed.

Accepted Answer

In a histogram, regardless of whether the distribution is negatively skewed or not, the median divides the data into two halves, with approximately 50% of the area under the curve to the left of the median and 50% to the right, assuming continuous data and a large sample size. Skewness affects the shape and spread of the distribution, not the proportion of data on either side of the median.

Question 10

The mean is a measure of variability.

Accepted Answer

The mean is actually a measure of central tendency, representing the average value in a set of data. Measures of variability include standard deviation, variance, and range.

Question 11

A data sample has a mean of 107, a median of 122, and a mode of 134. The distribution of the data is positively skewed.

Accepted Answer

The mean is less than the median, which indicates that there are more values on the higher end of the distribution, resulting in positive skewness. The mode being greater than both the mean and median also supports this conclusion.

Question 12

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive.

Accepted Answer

The variance is always non-negative (i.e. it can be zero, but it cannot be negative), while the standard deviation can be positive or negative. However, in practice, the standard deviation is always reported as a non-negative value by taking the absolute value of it.

Question 13

In a histogram, the proportion of the total area which must be to the left of the median is more than 0.50 if the distribution is positively skewed.

Accepted Answer

In a positively skewed distribution, the median is closer to the left of the distribution, meaning that less than 50% of the total area of the histogram is to the left of the median.

Question 14

The median of an ordered data set with 30 items would be the average of the 15^th and the 16^th observations.

Accepted Answer

The median of an ordered data set is defined as the middle value when the data set is arranged in order. If the data set has an even number of observations, then the median is the average of the two middle values. In this case, there are 30 items in the ordered data set, so the middle values are the 15th and 16th observations. Therefore, the median is the average of those two values.

Question 15

The data set 10, 20, 30 has the same variance as the data set 100, 200, 300.

Accepted Answer

The answer of The data set 10, 20, 30 has...

Question 16

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

Accepted Answer

The standard deviation is the square root of the variance and is expressed in the original units of measurement, while the variance is expressed in the units squared.

Question 17

m is a population parameter and  is a sample statistic.

Accepted Answer

The answer of m is a population parameter and ...

Question 18

In a bell shaped distribution, there is no difference in the values of the mean, median, and mode.

Accepted Answer

In a bell shaped distribution, the mean, median, and mode are all located at the center of the distribution. Therefore, they have the same value.

Question 19

The median of a set of data is more representative than the mean when the mean is larger than most of the observations.

Accepted Answer

When the mean is larger than most of the observations, it indicates the presence of outliers or extreme values that can greatly affect the value of the mean. In such cases, the median, which is the middle value in the data set, can be a more representative measure of central tendency. This is because the median is not affected by extreme values and only depends on the position of the values in the data set.

Question 20

Suppose a sample of size 50 has a sample mean of 20. In this case, the sum of all observations in the sample is 1,000.

Accepted Answer

The sample mean is calculated by dividing the sum of all observations by the sample size. Therefore, if the sample mean is 20 and the sample size is 50, the sum of all observations would be 20 x 50 = 1,000.

Quiz 3: Numerical Descriptive Techniques