Statistical And Non-statistical Quiz

To calculate the mean of the data set 4, 8, 6, 10, 2, add all the numbers together and divide by the number of items in the set. The sum is 4+8+6+10+2 = 30. There are 5 numbers in this data set. Therefore, the mean is 30 ÷ 5 = 6.

The range of a data set provides the difference between the maximum and minimum values, giving insight into the spread or dispersion of the data points. For example, if the smallest number is 2 and the largest is 8, the range would be 8 - 2 = 6. This calculation shows how spread out the values are in a data set.

Probability is the measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability helps in predicting the chance of various outcomes in processes or experiments where randomness or uncertainty is involved.

A non-statistical question does not involve numerical data or require data analysis to answer. "What is your favorite color?" is a non-statistical question because it asks for a personal preference, which is subjective and does not involve analyzing numerical data.

A histogram is ideal for showing the distribution of data because it visually represents the frequency of data points within specified ranges or bins. It helps in understanding the shape, spread, and central value of the data distribution, which are crucial for statistical analysis.

Categorical data refers to qualitative data that can be separated into different categories distinguished by non-numeric characteristics. This type of data is not numerical and often includes characteristics like names, labels, or other descriptors, such as "red" or "blue" for color.

The mean, or average, is most affected by outliers because it is calculated by dividing the sum of all values by the number of values. Outliers, which are significantly higher or lower than most of the data, can skew the mean much more than they affect the median or mode, which are more robust measures of central tendency.

The median is the middle value in a data set when the numbers are arranged in order. For the data set 3, 7, 9, 5, 12, first arrange the numbers in ascending order: 3, 5, 7, 9, 12. With five numbers, the third number is the median. Hence, the median is 7, which is the middle value in this ordered list.

Mean substitution is a common method for handling missing values in a data set. It involves replacing missing values with the mean (average) of the available data. This method is used because it preserves the mean of the data set and minimizes the impact on the distribution.

The 90th percentile is the value below which 90% of the data points fall. In the provided scenario, if 90% of values are below 50, then 50 is the 90th percentile. This statistic is commonly used to understand the distribution of data points in terms of thresholds and benchmarks.