DATA ANALYSIS & PROBABILITY M7D1.c – Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.

Words to Know  Mean – average found by using division (items of a set added together and the sum is then divided by the total number of items)  Median – the middle number in an ordered data set  Mode – the number that occurs most often in a data set  Mean, median and mode are called measures of central tendency.  Outlier – a number much greater or much less than the rest of the numbers in the data set

Practice One The students in Eagle River, Alaska missed 13 consecutive days of school due to heavy snow. The snowfall for each day is listed below in inches. What are the mode, median and mean of the snowfall in inches during the days the students missed? 5”, 2”, 3”, 10”, 3”, 1”, 7”, 3”, 2”, 0”, 3”, 1”, 0” RREMEMBER: When given a list of numbers, it is best to put them in order; either least to greatest or greatest to least. If we put ours least to greatest, what will it look like? 0”, 0”, 1”, 2”, 2”, 3”, 3”, 3”, 3”, 5”, 7”, 10”, 13” Now that it is in order least to greatest, it is much easier to see the mode and median and it will be easier to add up the total in order to find the mean. Mode: Median: Mean: 3” 4”

Practice Two This table shows the number of students who received a certain score on an assignment. Find the mean, median and mode for this frequency distribution. Mean: Median: Mode: ScoreFrequency Use the frequency column to find the total number of students. You must add all of the scores together, but remember, 31 students scored 10. Use multiplication and addition. The median will be the 48 th score. (There are 47 scores above and 47 scores below the 48 th score.) ≈

Practice Three There are 5 deckhands on the fishing vessel. For their most recent trip, Jake made $38,000, John made $41,000, Jesse made $38,000, Jimmy made $71,000 and Jordan made $42,000. Identify the outlier in the data set. How will it affect the mean, median or mode? RRemember to put the salaries in order… least to greatest would work well in this situation. Outlier: Jimmy with $71,000. The other four salaries are similar but Jimmy’s is nearly twice as much as them. Mode and median are not affected by the outlier because it is not an average of all five salaries combined. The mean will be greatly affected because we have to add in the much higher salary to get an average. The average will be much higher than the other four men’s salaries. Mean with the outlier: $46, 000Mean without the outlier: $39, 750