Get the solution to "Find the mode, mean, and standard deviation of..."

Ben Shaver

Answered question

2021-12-07

Find the mode, mean, and standard deviation of the following data: 3, 2, 3, 4, 6

Answer & Explanation

levurdondishav4

Beginner2021-12-08Added 38 answers

Step 1
Given Data:
Data Set: 3, 2, 3, 4, 6
There are five numbers in the given data set. So,

n = 5

.
There is number 3, which is repeated a larger number of times compared to any other number. So, 3 is the mode of the given set.
Thus, the mode of the given set is 3.
Step 2
The mean of the given set is,

m = \frac{\sum_{i = 1}^{5} x_{i}}{n}

= \frac{3 + 2 + 3 + 4 + 6}{5}

= 3.6

Thus, the mean of the given set is 3.6.
Step 3
The standard derivative of the given set is,

σ = \sqrt{\frac{{(x_{1} - m)}^{2} + {(x_{2} - m)}^{2} + {(x_{3} - m)}^{2} + {(x_{4} - m)}^{2} + {(x_{5} - m)}^{2}}{n - 1}}

= \sqrt{\frac{{(3 - 3.6)}^{2} + {(2 - 3.6)}^{2} + {(3 - 3.6)}^{2} + {(4 - 3.6)}^{2} + {(6 - 3.6)}^{2}}{5 - 1}}

= \sqrt{\frac{{(- 0.6)}^{2} + {(- 1.6)}^{2} + {(- 0.6)}^{2} + {(0.4)}^{2} + {(2.4)}^{2}}{4}}

= \sqrt{\frac{0.36 + 2.56 + 0.36 + 0.16 + 5.76}{4}}

= 1.52

Thus, the standard deviation of the given set is 1.52.

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