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 In statistics, mode refers to the value or values in a dataset that appears most frequently. It is a measure of central tendency, along with the mean and median. Here are examples of modes for ungrouped and grouped data: Ungrouped data : Consider the following set of numbers: 3, 4, 2, 1, 4, 5, 4, 6, 2. The mode is the value that appears most frequently, which in this case is 4. Therefore, the mode for this dataset is 4. Grouped data : Suppose we have a dataset that represents the number of hours spent watching TV per week for a group of people, and the data is grouped into the following frequency distribution: Hours per week Number of people 0-4 10 5-9 15 10-14 5 15-19 3 To find the mode for this dataset, we need to determine which group has the highest frequency. In this case, the group with the highest frequency is 5-9. N...

The median is another measure of central tendency that represents the middle value of a data set. To find the median, the data set is arranged in order from lowest to highest (or highest to lowest), and then the middle value is selected. If the data set has an even number of values, then the median is the average of the two middle values. For ungrouped data , the formula for finding the median is: If n is odd: Median = (n + 1) / 2 th value If n is even: Median = (n / 2) th value + ((n / 2) + 1) th value) / 2 where n represents the number of values in the data set. Example of median for ungrouped data: Consider the following set of data: 5, 6, 3, 8, 7 First, we arrange the data set in order: 3, 5, 6, 7, 8 Since the number of values in the data set is odd (n = 5), the median is the middle value, which is 6. For grouped data , the formula for finding the median is: Median = L + ((n/2 - F) / f) * h where L represents the lower limit of the median class interval, n represents the total n...

  The arithmetic mean, also known as the average, is a measure of central tendency that represents the typical or average value of a set of data. It is calculated by adding up all the values in a data set and dividing the total by the number of values. The formula for the arithmetic mean for a data set with n values is: x̄ = (x₁ + x₂ + ... + xn) / n where x̄ represents the arithmetic mean, and x₁, x₂, ..., xn represent the individual values in the data set. For ungrouped data , the formula for the arithmetic mean is simply the sum of all the values in the data set divided by the number of values. Example of arithmetic mean for ungrouped data: Consider the following set of data: 5, 6, 3, 8, 7 The arithmetic mean is: x̄ = (5 + 6 + 3 + 8 + 7) / 5 = 29 / 5 = 5.8 For grouped data , the formula for the arithmetic mean is: x̄ = ∑ (fi * xi) / ∑ fi where x̄ represents the arithmetic mean, fi represents the frequency of each class interval, and xi represents the midpoint of each class inter...