Statistics & Probability 1 Incourse Test 2020

The median is the middle value of a set of numbers when they are arranged in order. In this case, the numbers are 1, 2, 4, 5, and 8. Since there are an odd number of numbers, the median is the middle number, which is 4.

The cat weighs 5.4kg is an example of continuous data because weight is a quantitative measurement that can take on any value within a certain range (e.g., 5.4kg, 5.5kg, 5.6kg, etc.). In contrast, the other statements provide discrete data because they represent specific counts or quantities (e.g., 2 eyes, 2 kittens, 4 paws). Continuous data is typically measured on a scale and can have decimal values, while discrete data is counted and can only take on whole number values.

The correct answer is "The middle score when results are ranked in order of magnitude." The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in ascending or descending order. It is not necessarily the most frequently occurring score, the same as the mean, or the difference between the maximum and minimum scores.

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 helps in identifying the mode, which is the value that appears most frequently in a dataset. Unlike bar graphs, pie charts, and frequency polygons, which are visual representations of data, the modal class is a concept used in statistical analysis.

In this scenario, the entire group of students at the Mico University represents the total number of individuals that the researcher is interested in studying. This group is referred to as the population because it includes every student at the university, which is the target population for the researcher's investigation.

The mean is calculated by adding up all the scores and dividing the sum by the total number of scores. In this case, the sum of the scores 2, 5, 4, 1, and 8 is 20. Since there are 5 scores, dividing the sum by 5 gives us the mean of 4.

The answer is "Sam has two brothers and one sister." This is discrete data because it represents a countable number of distinct objects (siblings). The other options involve continuous measurements (height, weight, distance, time) which can take on any value within a range.

The range of a set of numbers is determined by subtracting the smallest number from the largest number. In this case, the set with the greatest range is 2, 5, 8, 11. The smallest number is 2 and the largest number is 11, so the range is 11 - 2 = 9. The other sets have smaller ranges: 13 - 13 = 0, 27 - 20 = 7, and 45 - 42 = 3. Therefore, the set 2, 5, 8, 11 has the greatest range.

Descriptive statistics refers to the statistical techniques used to summarize and organize data. It involves methods such as measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation). These techniques are used to describe the basic features of the data, such as the distribution, patterns, and relationships. Descriptive statistics do not involve making inferences or generalizations about a population, which is the domain of inferential statistics. Population statistics and sample statistics are subsets of descriptive statistics, as they specifically focus on summarizing data from a population or a sample, respectively.

The bar chart represents the number of students who purchased different books. To determine how many students bought exactly 4 books, we look at the corresponding bar on the chart. In this case, the bar indicating 9 represents the number of students who bought exactly 4 books.

The range of the wages is the difference between the highest and lowest paid employees. Since the highest paid employee receives $105.40, and the range is $27.50, the lowest paid employee must receive $105.40 - $27.50 = $77.90.

This is a systematic sampling method because Mrs. Allen is selecting every third person on her class list. Systematic sampling involves selecting every nth element from a population list to create a sample.

The mode of a distribution refers to the value that appears most frequently. In this case, the number 5 appears only once, while all the other numbers appear only once as well. Therefore, there is no number that appears more frequently than others, making it impossible to determine a mode.

The variance measures the spread or dispersion of a set of numbers. In this case, all the numbers are the same (2), so there is no variation or spread. Therefore, the variance is 0.

The mean travel time of 16.7 minutes is an example of a statistic because it is calculated from a sample of 50 students, rather than the entire population of University students. A statistic is a numerical measure that describes a characteristic of a sample, whereas a parameter describes a characteristic of a population.

The semi interquartile range is a measure of the spread of data that focuses on the middle 50% of the data. It is calculated by taking half of the difference between the upper quartile (Q3) and the lower quartile (Q1). This means that it represents the range within which the middle 50% of the data falls. By dividing the difference between the upper and lower quartiles in half, we can determine the spread of the data around the median.

The mean is not a measure of dispersion because it represents the average value of a dataset and does not provide information about the spread or variability of the data points. Measures of dispersion, such as the lower quartile, standard deviation, and variance, quantify how spread out the data is from the mean.

The mean of a set of numbers is found by adding up all the numbers in the set and then dividing the sum by the total number of values. In this case, the given scores are 5.8, 3.0, 2.9, and 1.5. Adding these scores together gives a sum of 13.2. Since there are a total of 4 scores, dividing the sum by 4 gives an average of 3.3. Therefore, the mean of the scores shown in the frequency distribution is 3.3.

A simple random sample is the best sampling technique to use for determining the average speed of cars on a section of highway because it ensures that every car on the highway has an equal chance of being included in the sample. This helps to eliminate bias and provides a representative sample of the population. Convenience sampling may introduce bias as it relies on selecting cars that are readily available. Systematic sampling may introduce bias if there is a pattern in the speed of the cars. Cluster sampling may introduce bias if the cars within each cluster are not representative of the overall population.

The boundaries of the class interval 10 – 14 are best recorded as 9.5 and 14.5 because class intervals are usually recorded as half units below and half units above the given range. In this case, 9.5 is half a unit below 10, and 14.5 is half a unit above 14. Therefore, 9.5 and 14.5 are the most appropriate boundaries for the class interval.

The mean mass can be calculated by summing up all the masses and dividing it by the total number of people. In this case, the given masses are 51.5, 52.3, 53.0, and 53.5. Adding these masses together gives a sum of 210.3. Since there are 4 people, dividing the sum by 4 gives the mean mass of 52.575. However, since the masses are given to only one decimal place, rounding up to the nearest whole number gives a mean mass of 53.0.

The given answer, 10, 14, 15, 19, 20, 25, 29, represents the limits of the class intervals for the lengths of cabbage leaves. These intervals are used to group the measured lengths of the cabbage leaves. Each interval represents a range of values, and the limits indicate the minimum and maximum values within each interval. In this case, the intervals are 10-14, 14-15, 15-19, 19-20, 20-25, and 25-29, with the limits corresponding to the lower and upper bounds of each interval.

Stratified sampling is the correct answer because Mr. Black is selecting students from specific groups in his classroom. In stratified sampling, the population is divided into different subgroups or strata, and a random sample is taken from each stratum. In this case, group 1 and group 5 are the strata, and Mr. Black is selecting all students from these groups. This method ensures that each stratum is represented in the sample, allowing for a more accurate representation of the entire population.

The correct answer is "The average distance between a score and the mean." Standard deviation is a measure of the dispersion or spread of a set of data. It quantifies how much the individual data points deviate from the mean. By calculating the average distance between each data point and the mean, we can determine the standard deviation.

The statement "The majority of students have scores above the median" cannot be an accurate description of the scores because the median represents the middle value of a dataset when arranged in ascending or descending order. If the majority of students have scores above the median, it would imply that more than half of the students have scores that are higher than the middle value, which is not possible.