Question 1

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

In a symmetric and unimodal distribution, the mean and median will be the same and exactly at the center of the distribution. Therefore, exactly 50% of the area under the histogram will be to the left and 50% to the right of the mean.

Question 2

$\mu$ is a population parameter and  is a sample statistic.

Accepted Answer

The answer of $\mu$ is a population parameter and ...

Question 3

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?
A) The mean, median, and mode are all equal.
B) Only the mean and median are equal.
C) Only the mean and mode are equal
D) Only the median and mode are equal.

Accepted Answer

The answer of Which of the following statements is true...

Question 4

Consider the following data:
  
a.
Calculate the covariance and the coefficient of correlation for the sample.
b.
What do these statistics tell you about the relationship between x and y?

Accepted Answer

The answer of Consider the following data:
  
a.
Calculate the...

Question 5

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 less than 50% of the total area is to the left of the median.

Question 6

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 7

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

The median is less affected by outliers than the mean, so when the mean is larger than most of the observations, the median will be a better representation of the central tendency of the data.

Question 8

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 the middle value. In this case, the data set has 30 items, so the middle value would be the 15th observation. However, if there are an even number of items in the data set, then the median is the average of the two middle values. In this case, the two middle values are the 15th and 16th observations. Therefore, the median would be the average of these two observations.

Question 9

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

Accepted Answer

In a negatively skewed distribution, the mean is pulled in the direction of the long tail and is therefore smaller than the median. The median, being the middle value, is less affected by extreme values and will be higher than the mean. The mode will be the highest point of the curve and may or may not be the same as the median.

Question 10

Which of the following statistics is a measure of central location?
A) The mean
B) The median
C) The mode
D) All of these choices are true.

Accepted Answer

All three statistics (mean, median, and mode) are measures of central location. The mean is the average value of a dataset, which represents the middle of the data spread. The median is the middle value of a dataset when the values are arranged in order, which is also a measure of central location. The mode is the most frequently occurring value in a dataset, which can also represent the center or typical value of the data. Therefore, all of these choices are valid measures of central location.

Question 11

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

Accepted Answer

When the mean, median, and mode are all equal, it indicates that the data is symmetric around the middle. And the most commonly observed value in the data set is also the middle value. Therefore, the histogram must be symmetric and bell-shaped.

Question 12

Which measure(s) of central location is/are meaningful when the data are ordinal?
A) The mean and median
B) The mean and mode
C) The median and mode
D) Only mean

Accepted Answer

The median and mode are the most appropriate measures of central location for ordinal data because they both take into account the order or ranking of the data. The mean, on the other hand, may not make sense for ordinal data as it involves adding and dividing by numbers, which may not be meaningful in terms of order. The mode can also be informative as it identifies the most frequently occurring value in the data set.

Question 13

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

Accepted Answer

This is the statement of the definition of the mean. It is also known as the "sum of the observations divided by the number of observations."

Question 14

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 found 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 in the sample must be 1,000 (20 x 50 = 1,000).

Question 15

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 50% of the data falling to the left of the median and 50% to the right, assuming continuous data and a perfectly representative histogram. Skewness affects the shape and spread of the data, not the proportion of data on either side of the median.

Question 16

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 17

The mean is a measure of variability.

Accepted Answer

The mean is a measure of central tendency, not variability. Measures of variability include the range, variance, and standard deviation.

Question 18

Which of the following statements about the mean is not always correct?
A) The sum of the deviations from the mean is zero.
B) Half of the observations are on either side of the mean.
C) The mean is a measure of the central location.
D) The value of the mean times the number of observations equals the sum of all observations.

Accepted Answer

While it is true that the mean is a measure of central location (C), that the sum of deviations from the mean is zero (A), and that the value of the mean times the number of observations equals the sum of all observations (D), it is not always the case that half of the observations are on either side of the mean (B). This would only be true if the data is symmetrically distributed around the mean, which is not always the case. In skewed distributions, for example, more observations may be clustered on one side of the mean than the other.

Question 19

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

Accepted Answer

The mean is calculated by taking the sum of all values and dividing it by the total number of values. Therefore, extreme values can heavily influence the mean, pulling it towards them. On the other hand, the median is the middle value when the data is arranged in order. Since it is only concerned with the middle value(s), extreme values do not have a significant impact on the median.

Question 20

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

Accepted Answer

In a perfectly symmetric bell shaped distribution, the mean, median, and mode will all be the same.

Quiz 4: Numerical Descriptive Techniques

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.

$\mu$ is a population parameter and $\mu is a population parameter and is a sample statistic.$ is a sample statistic.

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?

Consider the following data: a. Calculate the covariance and the coefficient of correlation for the sample. b. What do these statistics tell you about the relationship between x and y?

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.

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.

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

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

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

Which of the following statistics is a measure of central location?

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

Which measure(s) of central location is/are meaningful when the data are ordinal?

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

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.

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.

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.

The mean is a measure of variability.

Which of the following statements about the mean is not always correct?

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

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

Quiz 4: Numerical Descriptive Techniques

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.

μ\muμ is a population parameter and is a sample statistic.

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?

Consider the following data: a. Calculate the covariance and the coefficient of correlation for the sample. b. What do these statistics tell you about the relationship between x and y?

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.

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.

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

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

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

Which of the following statistics is a measure of central location?

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

Which measure(s) of central location is/are meaningful when the data are ordinal?

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

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.

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.

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.

The mean is a measure of variability.

Which of the following statements about the mean is not always correct?

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

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

$\mu$ is a population parameter and $\mu is a population parameter and is a sample statistic.$ is a sample statistic.

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