Understanding Point Estimators: Mean, Mode, and Median

Essentially, point estimators/measurement of central tendency gives us a "snap shot" of the sample population data which then can be used to estimate the population.

Point estimators are broken into 3 areas:

1. Mean
2. Median
3. Mode

These 3 tools are used to tell us the center or balance of the data...the average score You use average score when you are dealing with grouped data...data that is all based on one test and or phenomenon, such as taking a final exam with 10 students. Each student has an individual score. What is the average score of the class? This is inferred by 3 tools

Example

A History class with 10 students takes a final exam (10 scores). The test was out of a possible 40 points¿¿.. how well did the class do?

Score

27

28

29

29

29

30

30

31

31

32

For the mean.....add up all the scores and divide by number of scores/observations.                                                                                                             

27+28+29+29+29+30+30+31+31+32  = 296  = 29.6 is   The Sample Mean                  

10                             10                                                _

The Sample MEAN which is X with a line over it

The Population mean is symbolized by μ (mu) For the Median take the same numbers and find the middle that splits the lower 5 and the upper 5.

27    28    29    29    29    30    30    31    31    32

Since n=10 is even, the sample median is the average of the observations in positions 10/2 = 5 and 10/2+1 = 6 so we go to the 5th and 6th position: (29+ 30)/2 = 29.5 is the Median

If it is an odd number say 11 take the lower 5 and upper 5 and the Median is the number in the middle

27    28    29    29    29    30    30    31    31    32    34 In this case 30 is the MEDIAN

The MODE is the observation that appears the most: (no mathematics required)

27    28    29    29    29    30    30    31    31    32 In this case the MODE is 29 because it appears the most times. The MODE is the highest frequency, Team do you get this?

Now...You are to go into the classroom and tell me the Mean Mode and Median for the following data: You will post it under "Hermis Burger Joint". It is a real greasy joint but they make great fried chicken and apple pie (mmmm.....Pie)!

The Hermis Burger Joint pays its 5 hourly employees $6, $3, $5, $7 and $6 per hour. What is the Mean Mode and Median of the data.