12.3 Measures of Central Tendency and Position 785 Now we will discuss the procedure for determining the mean of a set of data. Profile in Mathematics Florence Nightingale (1820–1910) While Florence Nightingale is known as the founder of modern nursing, she was also a passionate statistician and a pioneer in statistical graphs. During the Crimean War, Nightingale systematized medical records and collected data for analysis. Partially due to her analysis of data, the death rate at her hospital dropped from 42% to 2%. After returning to Britain, she asked Queen Victoria to appoint a Royal Commission on the Health of the Army so that the data she had collected, and other medical data, could be analyzed for medical reform. To support the case for reform, she created a clever graphical representation of the data as shown above. Nightingale continued to use statistics to reform medical record-keeping in Britain and to reform sanitary living conditions in rural India. In 1858, she became the first woman elected as a fellow of the Royal Statistical Society. She was also elected an honorary member of the American Statistical Association in 1874. Definition: Mean The mean , x is the sum of the data divided by the number of pieces of data. The formula for calculating the mean is x x n = Σ where xΣ represents the sum of all the data and n represents the number of pieces of data. The most common use of the word average is the mean. Example 1 Determine the Mean Determine the mean age of a group of nurses if the ages of the individuals are 30, 21, 51, 37, and 51. Solution x x n 30 21 51 37 51 5 190 5 38 = Σ = + + + + = = Therefore, the mean, x is 38 years. 7 Now try Exercise 11. The mean represents “the balancing point” of a set of data. For example, if a seesaw were pivoted at the mean and uniform weights were placed at points corresponding to the ages in Example 1, the seesaw would balance. Fig. 12.13 shows the five ages given in Example 1 and the calculated mean. 20 30 40 50 Mean 38 Figure 12.13 Traveler1116/DigitalVision Vectors/Getty Images 914 collection/Alamy Stock Photo
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