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Median

The median is used when locating the middle value in a numerical data set. To illustrate how to find the median, consider the following example. Data Set: 23, 8, 11, 10, 31 The first step in trying to locate the median value is to re-order the data set from the smallest value to the greatest value. Therefore, the new order of this data set is: 8, 10, 11, 23, 31. The median value is simply the middle number of this set of values, which in this case is 11. This case provides a simple example of how to find the median since the data set consists of an odd number of points. However, if the data set consisted of an even number of values, there would be an extra step in distinguishing the median value. For example, consider this new data set consisting of 8 values: 4, 7, 3, 9, 12, 3, 8, 5. So the first step again is to order the values from smallest to largest. Therefore, the new order is: 3, 3, 4, 5, 7, 8, 9, 12. Now in this case, there is no one single middle value. Instead, you need to take the fourth and fifth largest values and find the mean of these two numbers. The fourth and fifth numbers in this data set represent the two middle values in this set of 8 data points. Therefore, the mean of 5 and 7 = (5+7)/2 = 6. Thus, the median value is 6.

Measures of Central Tendency: Example Problems

1. The number of cardiograms performed each day for 10 days in an outpatient testing center is listed below. Find the mean, median and mode. 29 83 36 52 25 62 54 36 84 49 2. Mean of five numbers is 60. When a sixth number is included the mean of the six numbers is 95. What is the sixth number? 3. The hourly wag

Determining Mean, Median, Mode, and Binomial Probability

1) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the 2006 Winter Olympics. Find the mean, median, and mode of the numbers of medals won by these countries. 1 2 3 3 4 9 9 11 11 11 14 14

Mean, median and standard deviation

1. Scores on the LSAT are approximately normally distributed. In fact, published reports indicate that approximately 40 percent of all test takers score at or between 145 and 155, and about 70 percent score at or between 140 and 160. The full range of scores is 60 pts. (120-180). Use your knowledge of normal distributions to es

Difference in the Median Performance

Dan Thompson, the president of CEO Airlines, recently noted an increase in the number of no-shows for flights out of Atlanta. He is particularly interested in determining whether there are a different number of no-shows for flights that originate from Atlanta compared with flights leaving Chicago. Below are the numbers of no-sho

What will happen to the mean and the median scores of the class? Explain.

4) The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score of 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class? Explain.

Find the median salary.

The salaries of ten randomly selected physicians are shown below. Find the median salary. $105,000 $149,000 $163,000 $214,000 $225,000 $116,000 $111,000 $791,000 $240,000 $178,000

Statistic Questions: sample property crime and median income relationship

1. William used a sample of 68 U.S. cities to estimate the relationship between Crime (annual property crimes per 100,000 persons) and Income (median income per capita). His estimated regression equation was Crime = 428 + .050 Income. Assuming that b1 is significant, if Income decreases by 1000 we would predict that Crime will

Problem Set

12. In ten trips to Las Vegas, a person had the following net gains: $1492 $1439 $4136 $6111 $1963 $2516 $6961 $7109 $6936 $4105 Find the median net gain. a. $4752.94 b. $4136 c. $4277.20 d. $4120.50 e. None of these 13. The following figures represent Jennifer's mon

Median median line Scatterplot

Tree growth scatterplot. age 5, 14, 29, 16, 16, 26, 6, 25, 7 diameter 8, 23, 34, 24, 24, 10, 30, 14, 13 summary points for first middle and last group based on median-median.(show cords) equation of the line passing through the summary points. calculate distance from line through the outer summary points to the middle pnt.