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Mean, Median, Mode and Range
Statistic is a very important concept of math which deals with collection, organization, analysis and interpretation of small to large number of data. For these very reasons mean, median, mode, range and standard deviation becomes the building blocks of statistic. Below is a short description of mean, median, mode and range
- Mean – Average value
- Mode – Most frequently occurring value
- Median – Midpoint between lowest and highest value of a set
- Range – Difference between largest and smallest value within a set
Below are more detailed version of Mean, Median, Mode and Range.
Mean:
What is mean? Mean has various synonyms such as statistical mean and arithmetic mean, which is simply the average of a set or sample of numbers. For a set of number, the mean is the sum of all the values divided by number of values. The mean of set of numbers usually denoted by “x bar” or x .
Example:
Q1: What is the mean for the set 34, 28, 50, 25, 8.
Ans: The formula for mean is
Mean = (34+28+50+25+8)/5
Mean = 145/5 = 29
Median:
What is median? Median is described as the numeric value separating the lower half of a sample from higher half. In another word, median is the middlemost number in a set of number. The median is also halfway into the set. In order to find median we need to first arrange the set from least to greatest. For an odd set finding median is rather easy. It is the middlemost most number in ascending order. However, for an even set, the median is the average or mean of the two middlemost numbers. Use the Mean, Median, Mode, Range calculator above to calculate the median. Steps to calculate median is below.
Q1: During a summer class there 7 students. Their test scores are below. What is the median test
score? Show all steps.
95, 76, 88, 94, 67, 38, 90
Ans: Need to order the set from least to greatest
38, 67, 76, 88, 90, 94, 95
The Median score is 88. It separates the three highest scores to three lowest scores.
Remember in this case the set it odd. Thus, we just take the middle value .
Q2: James went to grocery shopping and listed all the prices from his receipt for 6 items. What is
the median price he paid? Show all steps.
$3.46, $5.14, $7.16, $2, $9, $10.15
Ans: We need to first sort the set in ascending order.
$2, $3.46, $5.14, $7.16, $9, $10.15
Since this an even set we need calculate the median by calculating the average or mean of two
middle most numbers.
($5.14 + $7.16)/2 = 6.15.
So the median is $6.15
Mode:
Mode is simply the most frequent number in a data set or a probability distribution. Mode allows us to capture important information about a random variable or a population. Mode is different from mean and median and can be very different in a large skewed dataset. Unlike mean or median, mode isn’t unique since the maximum frequency can be repeated for different numbers.
Q1: What is the mode for the set below?
12, 15, 13, 18, 15, 10, 13, 19, 13
Ans: The mode is 13 since it is most frequent.
12 is repeated 1 time
15 is repeated 2 times
13 is repeated 3 times
18 is repeated 1 time
15 is repeated 1 time
10 is repeated 1 time
19 is repeated 1 time
Range:
What is Range? Range is the interval between the largest value (sample max) and smallest value (sample min). To calculate range, we first need to order a set from least to greatest. Then we need to take the difference between the two numbers. Use the Mean, Median, Mode, Range Calculator above to calculate range. Below is the method to calculate range manually.
Q1: What is the range for the set below?
7, 14, 9, 6, 3, 4
Ans: First sort the set from least to greatest.
3, 4, 6, 9, 7, 14
Find the difference between the least (3) and greatest (14)
Range = 14 – 3 = 11
Suggested Calculators:
Mean, Median, Standard Deviation and Population Deviation Calculator
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