How To Find Median Of Even Set Of Numbers

Problem: The Doran family has 5 children, aged 9, 12, 7, 16 and 13. What is the age of the center child?

Solution: Ordering the childrens' ages from to the lowest degree to greatest, we go:

seven,  9,  12,  13,  16

Answer: The age of the middle child is the middlemost number in the data set, which is 12.

In the problem above, we found the median of a set of 5 numbers.

Definition:Themedian of a set of information is the middlemost number in the fix. The median is also the number that is halfway into the prepare. To detect the median, the data should commencement be arranged in guild from least to greatest.

To call back the definition of a median, just think of the median of a road, which is the middlemost function of the route. In the trouble above, 12 is the median: information technology is the number that is halfway into the prepare. There are two children older than 12 and two children younger than 12. Let's look at some more than examples.

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Case 1: The Jameson family unit drove through 7 states on their summertime vacation. Gasoline prices varied from land to country. What is the median gasoline toll?

$1.79,  $i.61,  $1.96,  $2.09,  $1.84,  $1,75,  $2.11

Solution: Ordering the data from least to greatest, nosotros become:

$1.61,  $1.75,  $1.79,$1.84,  $1.96,  $2.09,  $two.eleven

Answer: The median gasoline price is $one.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)

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Case ii: During the first marker flow, Nicole'south math quiz scores were 90, 92, 93, 88, 95, 88, 97, 87, and 98. What was the median quiz score?

Solution: Ordering the data from least to greatest, we get:

87,  88,  88,  90,92,  93,  95,  96,  98

Answer: The median quiz score was 92. (Four quiz scores were college than 92 and four were lower.)

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In each of the examples above, there is an odd number of items in each data set. In Example 1, there are seven numbers in the data gear up; in Example two there are 9 numbers. Let'south look at some examples in which in that location is an fifty-fifty number of items in the data set.

Instance 3: A marathon race was completed by iv participants. What was the median race fourth dimension?

2.7 hr,  8.3 hr,  three.v 60 minutes,  5.one 60 minutes

Solution: Ordering the information from least to greatest, we get:

2.7,3.5,5.1,  eight.3

Since there is an fifty-fifty number of items in the data set, nosotros compute the median by taking the mean of the two middlemost numbers.

three.5 + 5.ane = 8.6

Answer: The median race time was 4.3 hr.

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Example 4: The salaries of 8 employees who work for a small visitor are listed beneath. What is the median bacon?

$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000

Solution: Ordering the data from least to greatest, we get:

$27,000,  $29,000,  $30,000,$31,000,$32,000,  $35,500,  $twoscore,000,  $43,000

Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.

$31,000 + $32,000 = $63,000

Reply: The median bacon is $31,500.

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Summary:Themedian of a ready of information is the middlemost number in the set up. The median is also the number that is halfway into the set. To find the median, the information should exist arranged in gild from to the lowest degree to greatest. If there is an even number of items in the data set, then the median is establish by taking the hateful (boilerplate) of the two middlemost numbers.

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Exercises

Directions: Find the median of each set of information. Click once in an ANSWER BOX and blazon in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your respond is correct or incorrect. To start over, click Articulate.

1.	Find the median weight of five 7th grade students whose weights in pounds are listed beneath. 82 lb,  102 lb,  75 lb,  91 lb,  89 lb

two.	The ages of ten college students are listed below. Detect the median. 18,  24,  20,  35,  xix,  23,  26,  23,  19,  twenty

3.	Seven teenagers receive the allowances listed below. What is the median allowance? $15,  $10,  $12,  $18,  $14,  $fifteen,  $eight

iv.	Find the median number of magazines purchased in a store by half-dozen customers. ane,  7,  4,  2,  iii,  4.

5.	The almanac snow in inches for New York City for the last 9 years is listed below. Detect the median snowfall. 20.5 in,  26.ane in,  32.5 in,  18.9 in,  33.4 in,  29.vii in,  19.8 in,  25.6 in,  34.3 in

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Source: https://www.mathgoodies.com/lessons/vol8/median

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