Question

How do you find the mean, median, and mode of $ 4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6, 2 $ ?

Answer 1

Hint: Here in this question, to find, the Mean by add together all of your values and divide by the number of addends. The median is the middle number of a given data set when in order from least to greatest. The mode is the number that occurred the most often in the given set of data.

Complete step-by-step answer:
Consider the given set of data or values
4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6, 2
To find the mean, you need to add up all the data, and then divide this total by the number of values in the data.
First add up all the numbers together
$ \Rightarrow 4 + 5 + 3 + 3 + 1 + 2 + 3 + 2 + 4 + 8 + 2 + 4 + 4 + 5 + 2 + 3 + 6 + 2 = 63 $
Then divide the answer by the number of numbers in the data set, there are 18 numbers in the given data set.
 \[ \Rightarrow \,\,\dfrac{{63}}{{18}} = 3.5\]
3.5 is the average or mean of the given data set
To find the median, you need to put the values in order, then find the middle value. Just remember if it's an amount of odd numbers you will find a definite middle, if it's an amount of even numbers you will find two middle numbers. Take two those numbers and divide it by 2 and you'll get your middle number
 Arrange given data points from smallest to largest
 \[ \Rightarrow \,\,\,\,\,1,{\text{ }}2,{\text{ }}2,{\text{ }}2,{\text{ }}2,{\text{ }}2,{\text{ }}3,{\text{ }}3,{\text{ }}3,\,\,3,{\text{ }}4,{\text{ }}4,{\text{ }}4,{\text{ }}4,{\text{ }}5,{\text{ }}5,{\text{ }}6,{\text{ }}8.\]
Then locate the central number by crossing off the numbers from each end until you find the middle number. Here, there are even numbers of numbers, there are 2 middle numbers, i.e., 3, 3.
Hence the middle number or Median is
 \[ \Rightarrow \,\,\dfrac{{3 + 3}}{2}\]
 \[ \Rightarrow \,\,\dfrac{6}{2} = 3\]
Next, to find, the mode is the value which appears the most often in the data. It is possible to have more than one mode. And if all numbers occur the same number of times there is no mode.
The most recurring number from the given data set is 2 because it came out 5 times.
Hence for the given set of data 4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6, 2. The value of
Mean is 3.5
Median is 3
Mode is 2.
So, the correct answer is “Mean is 3.5, Median is 3, Mode is 2.”.

Note: In this kind of problems, we have sequence of numbers, the main thing we have to arrange the sequence in order, we have to arrange in ascend \[ \Rightarrow \,\,\,\,\,4 + 5 + 3 + 3 + 1 + 2 + 3 + 2 + 4 + 8 + 2 + 4 + 4 + 5 + 2 + 3 + 6 + 2 = 63\] ing order. If the numbers are repeated then don’t neglect the number instead of that we have to write the number. Then find mode mean and median by using formulas.