ECON10 Chapter2
For any distribution, if the mean is equal to the standard deviation, you can infer that the distribution is symmetric.
False
For any distribution, the standard deviation is a measure of variability of the data around the median.
False
If the mean value of a set of data is 83.5 and the median is 72.8, then the third quartile will be at least 83.5.
False
If the variability of a set of data is very small, then the sample variance may be negative.
False
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 skewed to the right.
False
Measures of variability describe typical values in the data.
False
Tchebysheff's Theorem applies only to data sets that have a mound-shaped distribution.
False
Tchebysheff's Theorem provides us with a measure of shape that focuses on the difference between the mode and the mean and then relates it to the standard deviation.
False
The 10th percentile of a set of measurements is the value which exceeds 90% of the measurements and is less than the remaining 10% of the measurements.
False
Suppose that the distribution of actual weight of students in your university or college is thought to be symmetric. If the average weight is 168 pounds, what would the median weight be?
168 pounds
A sample of 25 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is:
384
The average score for a class of 35 students was 70. The 20 male students in the class averaged 73. The 15 female students in the class averaged:
66
Consider the data set: 5, 6, 7, 11, and 15. Its mean equals:
8.8
Which of the following statements about the median is correct?
All of the above.
A data sample has a mean of 87, and a median of 117. The distribution of the data is skewed to the right.
False
A parameter and statistic can be used interchangeably.
False
A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is 76.
False
A sample of 50 values produced the following summary statistics: Q1=10, Q2= 14.6, Q3= 16.7, and sample mean = 15.3. Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,
10 and 16.7
A sample of 600 values produced the following summary statistics: Q1=35.6, Q2=54.2, Q3=62.4, mean is 56.8. Based on this information, upper fence on a box and whisker plot is:
102.60
The following five-number summary for a sample of size 500 were obtained: Minimum = 250, Q1=1,200, Q2=3,600, Q3=4,800, and Maximum = 4,950. Based on this information, if you were to construct a box and whisker plot, the value 215 is considered an outlier.
False
The population mean, , is used to estimate the sample mean, .
False
The sample variance calculated with a divisor of n gives a better estimate of the population variance, S^2 , than does the sample variance, s^2 , with a divisor of n - 1.
False
The value (n + 1) / 2 indicates the value of the median in an ordered data set, where n is the number of data values.
False
The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive or zero.
False
The value of the standard deviation will always exceed that of the variance.
False
z-scores exceeding 3 in absolute value are likely to occur.
False
Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97th percentile. Therefore:
Lily scored as high or higher than 97% of the students who took the test
Whenever a statistical population can be described, at least roughly, by the perfectly symmetrical, mound-shaped normal curve, we can estimate the percentages of all population values that lie within specified numbers of standard deviations from the mean with the help of:
Tchebysheff's Theorem or the empirical rule
Which of the following represents a disadvantage of using the sample range to measure spread or dispersion?
The largest or smallest observation (or both) may be an outlier.
Which of the following statements is true for a symmetric distribution?
The mean and median are equal.
Which of the following statements is true for the following data values: 17, 15, 16, 14, 17, 18, and 22?
The mean, median and mode are all equal.
Which of the following statements is true?
The population mean and the mean of a sample selected from that population will usually be different values.
Which of the following best describes measures of center?
They are numbers around which observations tend to cluster and that describe the location of what in some sense might be called the center of a data set.
According to Tchebysheff's Theorem, at least 96% of observations should fall within 5 standard deviations of the mean.
True
Expressed in percentiles, the upper quartile is the 75th percentile.
True
For distributions of data that are skewed to the left or right, the median would likely be the best measure of center.
True
If the mean value of a distribution is 85 and the median is 67, the distribution must be skewed to the right.
True
In a mound-shaped distribution, there is no difference in the values of the mean, and median.
True
In all cases, the sum of the deviations of the measurements from their mean is 0.
True
Measures of center are values around which observations tend to cluster and that describe the location of what in some sense might be called the "center" of a data set.
True
Measures of relative standing indicate the position of one observation relative to other observations in a set of data.
True
Measures of variability are numbers that indicate the spread or scatter of observations; they show the extent to which individual values in a data set differ from one another and, hence, differ from their central location.
True
One advantage of using the median as a measure of center is that its value is not affected by extreme values.
True
One of the advantages of the standard deviation over the variance as a measure of variability is that the standard deviation is measured in the original units.
True
Tchebysheff's Theorem states that: Given a number k greater than or equal to 1, and a set of measurements, at least [1 - (1/k^2)] of the measurements in the data set will lie within k standard deviations of their mean.
True
The interquartile range is the difference between the upper and lower quartiles.
True
The larger the values of the sample variance and sample standard deviation s, the greater the variability in the data.
True
The left and right ends of the box in a box and whisker plot represent the 25th and 75th percentiles, respectively.
True
The mean of forty sales receipts is $69.75 and the standard deviation is $10.25. Using Tchebysheff's Theorem, at least 75% of the sales receipts were between $49.25 and $90.25.
True
The sample variance is approximately the average of the squared deviations of the measurements from their mean.
True
The sample z-score is a measure of relative standing defined by: . It measures the distance between an observation and the mean in units of the standard deviation.
True
The standard deviation is expressed in terms of the original units of measurement but the variance is not.
True
The value of the mean times the number of observations equals the sum of all of the observations.
True
While Tchebysheff's Theorem applies to any distribution, regardless of shape, the empirical rule applies only to distributions that are mound-shaped.
True
If a store manager selected a sample of customers and computed the mean income for this sample, he has computed:
a statistic
According to Tchebysheff's Theorem, provided only a number , regardless of the shape of a population's frequency distribution. The proportion of observations falling within k standard deviations of the mean is:
at least 1 - (1/k^2)
Tchebysheff's Theorem states that the percentage of measurements in a data set that fall within three standard deviations of their mean is:
at least 89%
A college placement office conducted a survey of 100 engineers who had graduated from Stanford University. For these engineers, the mean salary was computed to be $72,000 with a standard deviation of $8,000. The percentage of these engineers who earn more than $96,000 or less than $48,000 is:
at most 11.1% (1/9 of the engineers)
In a histogram, the proportion of the total area which must be to the left of the median is:
exactly 0.50
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
Data about qualitative variables can be summarized by:
proportions
If two data sets have the same range:
the distances from the smallest to largest observations in both sets will be the same
Which of the following is not a measure of variability?
the mean
Which of the following measures is not affected by extreme values in the data?
the median
The expression is recognizable as the formula for:
the sample variance, computed from grouped data
Which of the following is the most frequently used measure of variation?
the standard deviation
