Posted: February 19th, 2023

Deduce an appropriate situation for the use of each of these statistical measures: mean, median mode. Construct examples to support each situation.

SOLUTION

- Mean: The mean is a useful measure of central tendency when dealing with data that is normally distributed or follows a symmetrical distribution. It is also appropriate for data that does not have extreme values or outliers that could skew the results. The mean is calculated by adding up all the values in a dataset and dividing by the total number of values.

Example: Suppose you are calculating the average height of a group of people. You measure the height of 10 people in centimeters and get the following values: 170, 172, 168, 174, 172, 169, 171, 173, 168, 175. To find the mean height, you add up all the heights and divide by 10: (170+172+168+174+172+169+171+173+168+175)/10 = 171.2 cm. Therefore, the mean height of the group is 171.2 cm.

- Median: The median is a useful measure of central tendency when dealing with data that is skewed or has outliers that could significantly affect the mean. The median is calculated by finding the middle value in a dataset after ordering the values.

Example: Suppose you are calculating the median income of a group of people. You have the following income data (in thousands of dollars): 15, 17, 18, 20, 25, 30, 35, 50, 100. To find the median income, you first order the values from lowest to highest: 15, 17, 18, 20, 25, 30, 35, 50, 100. The middle value is 25, so the median income is $25,000.

- Mode: The mode is a useful measure of central tendency when dealing with data that has distinct peaks or modes. It is also useful for data that has a large number of repeated values. The mode is the value that appears most frequently in a dataset.

Example: Suppose you are calculating the mode of a group of numbers. You have the following data: 5, 6, 5, 3, 2, 5, 7, 5, 8. The mode of this dataset is 5 because it appears most frequently.

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