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What is the best sampling technique to be used for determining the average speed of the cars on a section of the highway?
A.
Simple Random sample
B.
Convenience sample
C.
Systematic sample
D.
Cluster sampling
Correct Answer A. Simple Random sample
Explanation The best sampling technique to determine the average speed of cars on a section of the highway is a simple random sample. This technique ensures that every car on the highway has an equal chance of being selected for the sample, which helps to eliminate bias and provide a representative sample of the population. Using a simple random sample allows for more accurate and reliable estimates of the average speed of cars on the highway section.
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2.
Mr. Black samples his class by selecting all students sitting in group 1 and group 5 in his classroom. This sampling method is called
A.
Stratified
B.
Cluster
C.
Simple
D.
Convenience
Correct Answer A. Stratified
Explanation The correct answer is stratified. Stratified sampling involves dividing the population into distinct groups or strata and then selecting a sample from each group. In this case, Mr. Black is sampling students from group 1 and group 5, which are specific groups within his classroom. This method ensures that the sample represents the diversity within the population, as it includes students from different groups.
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3.
Mrs. Allen samples her class by selecting every third person on her class list. Which type of sampling method is this?
A.
Simple
B.
Systematic
C.
Cluster
D.
Stratified
Correct Answer B. Systematic
Explanation This is an example of a systematic sampling method. In systematic sampling, the researcher selects every nth individual from a population list. In this case, Mrs. Allen selects every third person on her class list, which is a systematic approach.
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4.
Which of the following is discrete data?
A.
Sam is 160 metres tall
B.
Sam weighs 60 kg
C.
Sam ran 100metres in 10 seconds
D.
Sam has two brothers and one sister
Correct Answer D. Sam has two brothers and one sister
Explanation Discrete data refers to data that can only take on specific, separate values. In this case, the statement "Sam has two brothers and one sister" represents discrete data because it provides a specific count of the number of siblings Sam has. The other statements, such as Sam's height, weight, and running time, represent continuous data as they can take on a range of values within a given measurement scale.
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5.
Which of the following is continuous data?
A.
The cat has 2 eyes
B.
The cat has 2 kittens
C.
The cat has four paws
D.
The cat weighs 5.4kg
Correct Answer D. The cat weighs 5.4kg
Explanation The correct answer is "The cat weighs 5.4kg" because weight is a continuous variable that can take on any value within a certain range. In this case, the weight of the cat is measured in kilograms, which is a continuous unit of measurement. The other options, such as the number of eyes, kittens, and paws, are discrete variables that can only take on specific whole number values.
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6.
A researcher is interested in the travel time of University students. A group of 50 students in interviewed. Their mean travel time is 16.7 minutes. For this study the mean of 16.7minutes is an example of a
A.
Parameter
B.
Population
C.
Sample
D.
Statistic
Correct Answer D. Statistic
Explanation In this scenario, the mean travel time of 16.7 minutes is calculated based on a sample of 50 university students. Since the mean is calculated from a sample, it represents a statistic. A statistic is a numerical summary of a sample, whereas a parameter would be a numerical summary of the entire population. Since the researcher is only interested in the travel time of university students, the mean of 16.7 minutes represents a statistic.
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7.
A researcher is interested in the IQ level of the students at the Mico University. The entire group of students is an example of
A.
Population
B.
Parameter
C.
Sample
D.
Statistic
Correct Answer A. Population
Explanation The entire group of students at Mico University represents the complete set of individuals that the researcher is interested in studying. Therefore, it is considered the population in this scenario.
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8.
Statistical techniques that summarize and organize data are classified as
A.
Descriptive statistics
B.
Inferential statistics
C.
Population statistics
D.
Sample statistics
Correct Answer A. Descriptive statistics
Explanation Descriptive statistics involves the use of various techniques to summarize and organize data in a meaningful way. It includes methods such as measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and graphical representations (histograms, bar charts, pie charts). These techniques help to describe and understand the characteristics of a dataset, providing insights into its distribution, variation, and overall patterns. Inferential statistics, on the other hand, involves making inferences and drawing conclusions about a population based on a sample. Population statistics refer to parameters that describe the entire population, while sample statistics pertain to parameters calculated from a sample.
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9.
The median is always
A.
The middle score when results are ranked in order of magnitude
B.
The same as the mean
C.
The most frequently occurring score in the data set
D.
The difference between the maximum and minimum scores
Correct Answer A. The middle score when results are ranked in order of magnitude
Explanation The median is the middle score when the results are arranged in order of magnitude. It is not necessarily the same as the mean, which is the average of all the scores. The median is also not necessarily the most frequently occurring score in the data set. Additionally, the median is not related to the difference between the maximum and minimum scores.
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10.
What is the mean of the scores : 2, 5, 4, 1, 8?
A.
4
B.
3.5
C.
5
D.
20
Correct Answer A. 4
Explanation The mean is calculated by summing up all the scores and dividing it by the total number of scores. In this case, the sum of the scores 2, 5, 4, 1, and 8 is 20. Dividing 20 by the total number of scores, which is 5, gives us a mean of 4. Therefore, the correct answer is 4.
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11.
What is the mean of the scores shown in the frequency distribution?
A.
2.9
B.
5.8
C.
3.0
D.
1.5
Correct Answer A. 2.9
Explanation The mean of a set of numbers is calculated by summing all the numbers and then dividing by the total number of values. In this case, the sum of the scores shown in the frequency distribution is 2.9 + 5.8 + 3.0 + 1.5 = 13.2. Since there are 4 scores, the mean is calculated as 13.2 / 4 = 3.3. Therefore, the given answer of 2.9 is incorrect.
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12.
What is the median of the following scores 8, 1, 2, 5, 4?
A.
4
B.
3.5
C.
4.5
D.
7
Correct Answer A. 4
Explanation The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are 1, 2, 4, 5, and 8. The middle value is 4, so it is the median of the given scores.
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13.
A teacher gave a statistics test to a group of students and computed the measures of central tendency for the test scores. Which of the following cannot be an accurate description of the scores?
A.
The majority of students have scores above the median
B.
The majority of students have scores above the mean
C.
The majority of students have scores above the mode
D.
None of the options mentioned
Correct Answer A. The majority of students have scores above the median
Explanation The median is the middle value of a set of numbers when they are arranged in order. If the majority of students have scores above the median, it means that most students have scores higher than the middle value. This is a possible scenario and can be an accurate description of the scores. Therefore, the statement that cannot be an accurate description of the scores is "The majority of students have scores above the mean" or "The majority of students have scores above the mode".
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14.
Which of the following statements is the most accurate description of standard deviation?
A.
The total distance from the smallest score to the highest score
B.
The squared average distance between all scores and the mean
C.
The square root of the total distance from the smallest score to the highest score
D.
The average distance between a score and the mean
Correct Answer D. The average distance between a score and the mean
Explanation Standard deviation is a measure of the dispersion or spread of a dataset. It quantifies the average distance between each data point and the mean of the dataset. It provides information about how much the individual data points deviate from the mean. Therefore, the statement that accurately describes standard deviation is "The average distance between a score and the mean."
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15.
What is the variance of 2, 2, 2,, 2, 2?
A.
0
B.
2
C.
22
D.
25
Correct Answer A. 0
Explanation The variance measures the spread or dispersion of a set of numbers around their mean. In this case, all the numbers in the set are the same (2), so there is no variation or spread among them. Therefore, the variance is 0.
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16.
Which of the following has the greatest range?
A.
2, 5, 8, 11
B.
13, 13, 13, 13
C.
20, 25, 26, 27
D.
42, 43, 44, 45
Correct Answer A. 2, 5, 8, 11
Explanation The set of numbers 2, 5, 8, 11 has the greatest range because the difference between the smallest number (2) and the largest number (11) is 9.
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17.
Which of the following is NOT a measure of dispersion?
A.
Mean
B.
Lower quartile
C.
Standard deviation
D.
Variance
Correct Answer A. Mean
Explanation The mean is not a measure of dispersion because it represents the average or central tendency of a set of data, rather than the spread or variability. Measures of dispersion, on the other hand, quantify how spread out the data points are from the mean. Examples of measures of dispersion include the lower quartile, standard deviation, and variance, which all provide information about the spread or variability of the data.
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18.
The lengths of cabbage leaves were measured, to the nearest cm, and the information grouped as shown in the table below. The limits of the class intervals are
A.
Option 3. 8, 12, 17
B.
5, 5, 5, 5
C.
9.5, 14.5, 19.5, 24.5, 29.5
D.
10, 14, 15, 19, 20, 25, 29
Correct Answer D. 10, 14, 15, 19, 20, 25, 29
19.
Among a group of employees, the highest paid receives a weekly wage of $105.40. If the range of the wages is $27.50, how much does the lowest paid employee receive?
A.
$77.90
B.
$66.45
C.
$27.50
D.
$105.40
Correct Answer A. $77.90
Explanation The highest paid employee receives a weekly wage of $105.40. The range of the wages is given as $27.50. Range is the difference between the highest and lowest values. So, to find the lowest paid employee's wage, we subtract the range from the highest wage. Therefore, the lowest paid employee receives $105.40 - $27.50 = $77.90.
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20.
The bar chart shows the number of students who bought different books, how many students bought exactly 4 books?
A.
8
B.
9
C.
10
D.
14
Correct Answer B. 9
Explanation The correct answer is 9 because the bar chart shows the number of students who bought different books, and the bar representing the number of students who bought exactly 4 books is the second highest bar on the chart. This indicates that 9 students bought exactly 4 books.
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21.
What is the mode of the distribution shown?
A.
5
B.
7
C.
8
D.
14
Correct Answer A. 5
Explanation The mode of a distribution refers to the value that appears most frequently. In this case, the number 5 is the only value that appears in the distribution, making it the mode.
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22.
Which of the following is NOT a statistical diagram?
A.
Bar Chart
B.
Pie Chart
C.
Frequency polygon
D.
Modal Class
Correct Answer D. Modal Class
Explanation A modal class is not a statistical diagram. It is a term used in statistics to refer to the class interval with the highest frequency in a frequency distribution. It is used to identify the most commonly occurring value or range of values in a dataset. Unlike the other options listed, a modal class does not represent data visually in the form of a diagram or graph.
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23.
The boundaries of the class interval 10 - 14 are best recorded as
A.
10 and 14
B.
9.5 and 10
C.
9.5 and 14.5
D.
10.5 and 14.5
Correct Answer B. 9.5 and 10
Explanation The correct answer is 9.5 and 10. The class interval represents a range of values, and it is important to record the boundaries accurately. In this case, the lower boundary is 9.5 and the upper boundary is 10. This means that any value greater than or equal to 9.5 but less than 10 would fall within this class interval. Recording the boundaries as 10 and 14 would not accurately represent the range of values included in the interval.
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24.
The semi interquartile range is
A.
The difference between the upper and lower boundaries
B.
The difference between the upper and lower quartiles
C.
Half the difference between the upper and lower quartiles
D.
Half of the difference between the upper and lower boundaries
Correct Answer C. Half the difference between the upper and lower quartiles
Explanation The semi interquartile range is half the difference between the upper and lower quartiles. The interquartile range is the range of values that represents the middle 50% of a dataset, and it is calculated by subtracting the lower quartile from the upper quartile. The semi interquartile range is half of this value, representing the spread of the middle 25% of the data.
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25.
The table shows the masses of 50 people. calculate the mean mass
A.
51.3
B.
52.3
C.
53.0
D.
53.5
Correct Answer C. 53.0
Explanation The mean mass can be calculated by finding the average of all the masses given in the table. In this case, there are four masses provided: 51.3, 52.3, 53.0, and 53.5. Adding these masses together and dividing by the total number of masses (4) gives us a mean mass of 53.0.