Probs And Stats 1

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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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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.

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."

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".

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.