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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

Savings Bank Life Insurance: mean, median, range, variance, deviation

26. In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and

Median, mean, standard deviation & interquartile range

Two hundred candidates took each of two examination papers. The diagram shows the cumulative frequency graphs for their marks. i) Estimate the median marks for each of the papers. ii) State, with a reason, which of the two papers was the easier one. iii) It is suggested that the marks on Paper 2 were less varies than those

Mean and Median Analysis

The following data represents the weight lifted (in lbs) by a sample of 14 cyclists: 244 191 160 187 180 176 174 205 211 183 211 180 194 200 A. Calculate the mean and median of this sample. B. If the first sample should have been read as 204 instead of 244 how will that impact the mean and median?

Calculate Mean, Median, and Standard Deviation

Complaints have reached the City Manager of Normal that it is taking too long to pay bills submitted to the City. You are assigned to check how long it takes by looking at a few bills. Following are the lengths of time in days that it has taken the City to pay seven bills. Calculate the mean, median, and standard deviation.

Household Income: Mean, Median, Variance and Deviation

Just need help with a and c. A survey on household income in Northeast NJ area gave the following numbers in thousands of dollars 33,45,12,36,87,95,46,12,44,46,78,13,55,89,78,46,78,65,54,52,53,46,44,89,92,63,46,55,67,55,49,44,99,123,25, 36, 58,55,66,49,69,36,22,32,36,56,48,46,52,54,63,17 a- Find the mean, median, mode,

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

Distribution of a Data Set

James Johnson, manager of quality control at Creative Auto Corp., just received a report from the assembly plant. The latest shipment of 200 lug bolts used to attach the wheels showed a mean diameter of 18.01 mm and a median of 17.92 mm. Therefore, James can conclude that the distribution of the diameters of the lug bolts a

Mean and Median (See attached file xr03014)

A personnel administrator has collected data on 100 employees, including gender, age, and number of days absent during the previous year. Compare the mean and median number of days absent of female (coded as gender = 1) versus male ( coded as gender = 2) within the company. The data are in file XR03014.

Central Airlines claims that the median price of a round-trip ticket to Jackson Hole, Wyoming, is $503. This claim is being challenged by the Association of Travel Agents, who believe the median price is less than $503. To resolve the issue, a random sample of 400 round-trip tickets was selected. Of these, 160 tickets were below $503. None of the tickets were exactly $503.

Central Airlines claims that the median price of a round-trip ticket to Jackson Hole, Wyoming, is $503. This claim is being challenged by the Association of Travel Agents, who believe the median price is less than $503. To resolve the issue, a random sample of 400 round-trip tickets was selected. Of these, 160 tickets were below

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

Determine the median number of calls, and other questions

1) Wendy Hagel is the national sales manager for National Textbooks, Inc. She has a sales staff of 40 who visit college professors all over the United States. Each Saturday morning she requires her sales staff to send her a report. This report includes, among other things, the number of professors visited during the previous wee