1.
(401) A natural number is stated as a positive number that
Correct Answer
A. A. has any actual value from zero to infinity.
Explanation
A natural number is defined as a positive integer that includes all values from zero to infinity. This means that it can take on any actual value within this range. The other options, such as having unique properties, being able to be added or subtracted, or being able to be summed, do not accurately describe what a natural number is.
2.
Correct Answer
C. C. 15.0.
3.
(401) When using natural numbers, a number placed directly behind brackets, with no sign of
operation between, indicates that
Correct Answer
D. D. the quantity within the brackets must be multiplied by that number.
Explanation
When using natural numbers, a number placed directly behind brackets, with no sign of operation between, indicates that the quantity within the brackets must be multiplied by that number.
4.
(401) Which phrase is true regarding signed numbers?
Correct Answer
D. D. Both positive and negative numbers have values.
Explanation
This phrase is true because both positive and negative numbers have values. In mathematics, signed numbers are used to represent both positive and negative quantities. They are essential for representing quantities such as gains and losses, temperatures above and below zero, and directions in coordinate systems. Therefore, option d is the correct answer.
5.
(401) Compute the difference of the signed numbers –17 – (–10).
Correct Answer
C. C. â€“7.0.
Explanation
The expression -17 - (-10) can be simplified by changing the subtraction of a negative number to addition. Therefore, -17 - (-10) becomes -17 + 10. When we add -17 and 10, we get -7. Therefore, the correct answer is c. â€“7.0.
6.
(401) How do you write: “The square root of 25 is 5.” as a mathematical expression?
Correct Answer
D.
Explanation
The mathematical expression for "The square root of 25 is 5" can be written as âˆš25 = 5.
7.
(402) What is 22 percent of 12?
Correct Answer
B. B. 2.64.
Explanation
To find 22 percent of 12, we can multiply 12 by 0.22. This calculation gives us 2.64, which is the correct answer.
8.
(403) Which statistical technique is an example of descriptive statistics?
Correct Answer
B. B. Extrapolation.
Explanation
Extrapolation is a statistical technique that involves estimating values beyond the range of observed data. It is used to make predictions or projections based on existing data. Descriptive statistics, on the other hand, involve summarizing and describing the main features of a dataset, such as measures of central tendency and dispersion. Probability, trend analysis, and measurement scales are not examples of descriptive statistics.
9.
(404) In the equation Y=X+2, what does the symbol “Y” represent?
Correct Answer
D. D. Variable.
Explanation
In the equation Y=X+2, the symbol "Y" represents a variable. In mathematical equations, variables are used to represent unknown values or quantities that can vary. In this equation, "Y" is the variable that represents the value that is equal to "X" plus 2. Therefore, "d. Variable" is the correct answer.
10.
Correct Answer
A. A. 64.
11.
(405) A sample of a population that is taken in such a manner that each value has an equal chance
of being selected is referred to as a
Correct Answer
B. B. random sample.
Explanation
A random sample is a sample taken from a population in such a way that every individual in the population has an equal chance of being selected. This ensures that the sample is representative of the entire population and reduces the risk of bias. The other options, biased sample, sampling theory, and sampling application, do not accurately describe the specific method of sampling where each value has an equal chance of being selected.
12.
(405) If you construct a QLP retrieval to select every 8th record, you are using which sampling
technique?
Correct Answer
C. C. Systematic.
Explanation
A systematic sampling technique involves selecting every nth item from a population, where n is a fixed interval or "skip" value. In this case, selecting every 8th record fits this definition, as it follows a systematic pattern. Selective sampling involves intentionally choosing certain items based on specific criteria, stratified sampling involves dividing the population into subgroups and selecting from each subgroup, and purposeful sampling involves selecting specific individuals or cases that are of particular interest.
13.
(406) Which measurement scale consists of equal intervals between scale values and an arbitrary
zero point?
Correct Answer
D. D. Interval.
Explanation
The interval measurement scale consists of equal intervals between scale values and an arbitrary zero point. This means that the differences between the values on the scale are meaningful and can be compared. However, the zero point is arbitrary and does not indicate the absence of the measured attribute.
14.
(406) You are given two pieces of test equipment that must be loaded on a pallet. One piece
weighs 125 pounds and the other piece weighs 3.5 times as much. Using the ratio measurement
scale, how much does the second piece of equipment weigh?
Correct Answer
C. C. 437.5 pounds.
Explanation
The second piece of equipment weighs 3.5 times as much as the first piece, which weighs 125 pounds. To find the weight of the second piece, we multiply 125 by 3.5, which equals 437.5 pounds. Therefore, the correct answer is c. 437.5 pounds.
15.
(406) Given measurements of 5.0 hours, 10.0 hours, 15.0 hours, and 20.0 hours, what type of data
and measurement scale would you use to classify these data items?
Correct Answer
C. C. Continuous; ratio.
Explanation
The given measurements of hours can take on any value within a range, making it continuous data. Additionally, the measurements are on a ratio scale because there is a meaningful zero point (0 hours) and the ratios between the measurements are meaningful (e.g. 10 hours is twice as long as 5 hours). Therefore, the correct classification for these data items is continuous and ratio.
16.
(407) The second step in making a frequency distribution is to
Correct Answer
B. B. determine the class interval size.
Explanation
The second step in making a frequency distribution is to determine the class interval size. This is important because it helps to organize the data into manageable groups or intervals. The class interval size should be chosen in a way that captures the range of values in the data set while also allowing for a sufficient number of intervals to accurately represent the data. By determining the class interval size, we can then proceed to group the data into these intervals and count the frequency of values within each interval.
17.
(407) With a noncumulative frequency distribution range of 3.6, which class interval will give
you 18 classes?
Correct Answer
B. B. 0.2.
18.
(407) One way of comparing class frequencies to the total frequency is by
Correct Answer
D. D. percentage.
Explanation
One way of comparing class frequencies to the total frequency is by using percentages. By calculating the percentage of each class frequency in relation to the total frequency, we can easily compare the relative sizes of different class frequencies. This allows us to understand the distribution of the data and identify any significant patterns or trends.
19.
(408) What does each rectangle in a histogram represent?
Correct Answer
B. B. One class of data.
Explanation
Each rectangle in a histogram represents one class of data. A histogram is a graphical representation of a frequency distribution, where the data is divided into intervals or classes. The height of each rectangle corresponds to the frequency or number of observations that fall within that class. Therefore, each rectangle represents a specific range or class of data values.
20.
(408) When constructing a frequency polygon, what are plotted against the corresponding
midpoints?
Correct Answer
D. D. Frequencies of the various class intervals.
Explanation
When constructing a frequency polygon, the frequencies of the various class intervals are plotted against the corresponding midpoints. This allows for the visualization of the distribution of data and the identification of any patterns or trends. The frequency of each class interval represents the number of data points that fall within that interval, and plotting these frequencies against the midpoints helps to create a visual representation of the data's distribution. The frequency polygon is a useful tool for summarizing and analyzing data sets.
21.
(409) What measure of central tendency is the most typical value in a distribution?
Correct Answer
B. B. Mode.
Explanation
The mode is the measure of central tendency that represents the most frequently occurring value in a distribution. It is the value that appears the highest number of times, making it the most typical value. The mean represents the average value of the distribution, the median represents the middle value when the data is arranged in order, and the weighted mean is a variation of the mean that takes into account the weights assigned to different values. However, in terms of representing the most typical value, the mode is the correct answer.
22.
(409) The mode is the only measure of central tendency that can be used with what measurement
scale?
Correct Answer
D. D. Nominal.
Explanation
The mode is the most appropriate measure of central tendency to use with nominal measurement scales. Nominal scales categorize data into distinct categories or groups, such as colors or categories of a variable. The mode represents the category that occurs most frequently in the data, making it the only measure of central tendency that can be applied to nominal data. The other measures of central tendency (mean and median) require numerical values and cannot be used with nominal scales.
23.
(410) Analysts frequently use the median because it is easy to compute and gives a better picture
of data than the mean and mode when data are
Correct Answer
B. B. skewed.
Explanation
Analysts frequently use the median because it is easy to compute and gives a better picture of data than the mean and mode when data are skewed. Skewed data means that the distribution of values is not symmetrical, with a longer tail on one side. In such cases, the mean can be heavily influenced by extreme values, while the mode may not accurately represent the central tendency. The median, on the other hand, is less affected by extreme values and provides a more robust measure of the central value in skewed distributions.
24.
(410) The median cannot be used with data from which measurement scale?
Correct Answer
A. A. Nominal.
Explanation
The median is a measure of central tendency that is used to find the middle value in a set of data. It is calculated by arranging the data in ascending or descending order and finding the value that separates the higher half from the lower half. However, the median cannot be used with data from a nominal measurement scale. Nominal data consists of categories or labels that do not have any inherent order or numerical value. Therefore, it is not possible to determine a meaningful middle value or calculate a median for nominal data.
25.
(410) What must you do first to determine the median from ungrouped data?
Correct Answer
D. D. Arrange the data in ascending order.
Explanation
To determine the median from ungrouped data, the first step is to arrange the data in ascending order. This is because the median is the middle value of the data set when it is arranged in order. By arranging the data in ascending order, it becomes easier to identify the middle value and calculate the median accurately.
26.
(411) The harmonic mean is used primarily for averaging
Correct Answer
D. D. rates.
Explanation
The harmonic mean is used primarily for averaging rates. This is because the harmonic mean gives more weight to smaller values, making it useful for calculating average rates or ratios. It is commonly used in fields such as finance, economics, and physics to calculate average rates of return, average speed, or average efficiency.
27.
(411) Compute a weighted mean for a distribution containing two values of 3 each, four values of
2 each, and four values of 5 each.
Correct Answer
B. B. 3.4.
Explanation
The weighted mean is calculated by multiplying each value by its corresponding weight, summing up these products, and then dividing by the total sum of the weights. In this case, we have two values of 3 with a weight of 2 each, four values of 2 with a weight of 4 each, and four values of 5 with a weight of 4 each. Therefore, the calculation would be (2*3 + 4*2 + 4*5) / (2+4+4) = 3.4.
28.
(411) The arithmetic mean should be weighted when
Correct Answer
C. C. a mean of means is desired.
Explanation
When a mean of means is desired, the arithmetic mean should be weighted. This means that instead of treating all values equally, certain values are given more importance or weight in the calculation of the mean. This is useful when there are multiple subgroups or categories within a data series, and we want to calculate the mean of each subgroup and then take the mean of those subgroup means. Weighting allows us to give more importance to larger subgroups or subgroups with more variability, resulting in a more accurate representation of the overall data.
29.
(411) Three workers perform a similar task. Worker A takes 30 minutes to complete the task and
can finish 2 jobs per hour. Worker B takes 20 minutes to complete the task and can complete 3
jobs per hour. Worker C takes 40 minutes to complete the task, and completes 1.5 jobs per hour.
Which calculation method will you use to find the average time it takes to complete the job?
Correct Answer
B. B. Arithmetic mean.
Explanation
The arithmetic mean is the most appropriate calculation method to find the average time it takes to complete the job. This is because the arithmetic mean takes into account the total time taken by each worker and divides it by the number of workers. In this case, the arithmetic mean will give an accurate representation of the average time taken by the three workers to complete the task.
30.
(411) A unique feature of the harmonic mean is it
Correct Answer
B. B. will always be less than the arithmetic mean.
Explanation
The harmonic mean is a type of average that is used to calculate the average of rates or ratios. It is calculated by dividing the number of observations by the sum of the reciprocals of the observations. One unique feature of the harmonic mean is that it will always be less than the arithmetic mean. This is because the harmonic mean gives more weight to smaller values, which pulls the average down. In contrast, the arithmetic mean gives equal weight to all values. Therefore, the harmonic mean will always be lower than the arithmetic mean.
31.
(412) For any distribution, the sum of the deviations is
Correct Answer
B. B. zero.
Explanation
For any distribution, the sum of the deviations is zero. This is because the deviations from the mean can be positive or negative, but they cancel each other out when summed together. Some values will be above the mean and have positive deviations, while others will be below the mean and have negative deviations. The sum of these deviations will always equal zero, indicating that on average, the values in the distribution are evenly distributed around the mean.
32.
Correct Answer
A. A. 5.7.
33.
Correct Answer
A. A. 0.
34.
(412) As the number of values in a normal distribution sample decreases, the standard deviation
Correct Answer
B. B. becomes less representative of the population.
Explanation
As the number of values in a normal distribution sample decreases, the standard deviation becomes less representative of the population. This is because with a smaller sample size, there is a higher chance of sampling error and less precision in estimating the true population standard deviation. Therefore, the standard deviation calculated from a smaller sample may not accurately reflect the variability of the entire population.
35.
(413) Given a large number of random samples, the mean of all the sample means related to the
population mean is
Correct Answer
A. A. the same.
Explanation
The mean of all the sample means related to the population mean is expected to be the same. This is because the sample means are calculated from random samples, which are expected to be representative of the population. Therefore, the average of all these sample means should converge to the population mean, resulting in the mean of all the sample means being the same as the population mean.
36.
(413) In estimating the standard error of the mean, for what sample size do you use n–1 in the
formula?
Correct Answer
D. D. Less than 30.
Explanation
The correct answer is d. Less than 30. In estimating the standard error of the mean, the formula typically uses n-1 for sample sizes less than 30. This adjustment is made to account for the fact that with smaller sample sizes, the sample mean is less likely to accurately represent the population mean. By using n-1 instead of n in the formula, it provides a more conservative estimate of the standard error.
37.
Correct Answer
C. C. 1.0.
38.
(414) A normal distribution contains what two parameters?
Correct Answer
C. C. Mean and standard deviation.
Explanation
A normal distribution is characterized by its mean and standard deviation. The mean represents the average or central tendency of the distribution, while the standard deviation measures the spread or variability of the data around the mean. These two parameters are essential in fully describing the shape and characteristics of a normal distribution. The mode, which represents the most frequently occurring value, is not necessary to define a normal distribution. Standard error, on the other hand, is a measure of the uncertainty or variability of sample estimates and is not directly related to the parameters of a normal distribution.
39.
(414) In a normal distribution, how many standard deviations on each side of the mean contain
over 99 percent of the area under the normal area curve within?
Correct Answer
C. C. 3.
Explanation
In a normal distribution, approximately 99.7% of the area under the curve falls within three standard deviations on each side of the mean. This means that the range from three standard deviations below the mean to three standard deviations above the mean contains the vast majority of the data. Therefore, the correct answer is c. 3.
40.
(414) When plotted on normal probability graph paper, data from a normal distribution shows up
as a
Correct Answer
C. C. straight line.
Explanation
When plotted on normal probability graph paper, data from a normal distribution shows up as a straight line. This is because normal probability graph paper is specifically designed to represent a normal distribution, with the x-axis representing the z-scores (standard deviations from the mean) and the y-axis representing the cumulative probability. When the data points are plotted on this graph paper, they form a straight line because the data is evenly distributed around the mean and follows a symmetrical pattern.
41.
(415) If X equals 24 and s equals 6, what are the values of X ± 2s?
Correct Answer
C. C. 12 and 36.
Explanation
If X equals 24 and s equals 6, X + 2s would be 24 + 2(6) = 24 + 12 = 36. Similarly, X - 2s would be 24 - 2(6) = 24 - 12 = 12. Therefore, the values of X Â± 2s are 12 and 36.
42.
Correct Answer
C. C. 1.6.
43.
(416) Where does the most frequent value of a normal curve occur?
Correct Answer
A. A. At the center of the distribution.
Explanation
The most frequent value of a normal curve occurs at the center of the distribution because the normal curve is symmetric and bell-shaped. The center of the distribution represents the mean, which is the average value of the data. Since the normal curve is symmetrical, the highest point of the curve is at the mean, making it the most frequent value.
44.
(417) The causes of variation that can be identified on a control chart, regulated, and possibly
eliminated are
Correct Answer
C. C. assignable.
Explanation
The correct answer is c. assignable. Assignable causes of variation are those that can be identified and controlled, leading to possible elimination. These causes are not random or due to chance, but rather can be attributed to specific factors or events. By identifying and addressing these assignable causes, organizations can improve their processes and reduce variation in their outputs.
45.
(417) The purpose of a control chart in statistics is to
Correct Answer
D. D. detect the presence of assignable causes for variation.
Explanation
A control chart in statistics is a graphical tool used to monitor a process over time and detect any variations or changes in the process. It helps identify whether the variations are due to common or chance causes, which are inherent to the process and expected, or assignable causes, which are abnormal and need to be investigated and eliminated. Therefore, the purpose of a control chart is to detect the presence of assignable causes for variation, as stated in option d.
46.
(418) When identifying processes out of control and using a control chart, what action should you
take if you have set your control limits at three standard deviations and later find not enough time
is spent looking for assignable causes?
Correct Answer
A. A. Switch to tighter limits.
Explanation
If not enough time is spent looking for assignable causes, switching to tighter limits can help in identifying any potential issues or variations in the process. Tighter limits would make it easier to detect any deviations from the expected performance and take appropriate corrective actions. This ensures that the process remains in control and any potential problems are addressed promptly. Recalculating the standard deviation or discarding the current data would not address the issue of not enough time being spent on investigating assignable causes.
47.
(419) In statistical terms, what does the control chart for plotting individual X values use for the
centerline?
Correct Answer
A. A. Mean.
Explanation
The control chart for plotting individual X values uses the mean as the centerline. This means that the average value of the data points is used as a reference point on the control chart. The control chart helps to monitor and control the process by showing any variations or trends in the data, and having the mean as the centerline allows for easy comparison and identification of any deviations from the expected average.
48.
(419) The statistical interpretation of a control chart for individuals
Correct Answer
B. B. distribution is extremely skewed.
Explanation
The correct answer is b. distribution is extremely skewed. A control chart for individuals is used to monitor the variation in a process over time. In a control chart, the data points are plotted on a chart and compared to control limits. If the distribution of the data points is extremely skewed, it means that the data is not normally distributed and there may be issues with the process. This can indicate that there are outliers or other non-random patterns in the data, which may need to be investigated and addressed.
49.
(420) A statistical chart for averages is used to plot
Correct Answer
D. D. means of small samples.
Explanation
A statistical chart for averages is used to plot the means of small samples. This type of chart is commonly used in quality control to monitor the process and identify any variations or deviations from the desired average. By plotting the means of small samples over time, it becomes easier to detect any trends or patterns that may indicate a need for adjustment or intervention. Control limits, individual values, and standard deviations are not typically plotted on this type of chart.
50.
(420) What characteristic of the distribution used in a control chart for averages gives it an
advantage over a chart for individuals?
Correct Answer
A. A. The distribution of means tends to be normal.
Explanation
The correct answer is a. The distribution of means tends to be normal. In a control chart for averages, the data is collected and plotted using sample means. The Central Limit Theorem states that when independent random variables are added, their sum tends toward a normal distribution. Therefore, the distribution of means tends to be normal, which makes it advantageous for constructing a control chart. This allows for better understanding and interpretation of the data, as the normal distribution provides a predictable pattern for identifying process variation and detecting any potential issues or outliers.