Answer: Mean = 3.5 , median = 2.5, mode = 2, geometric mean = 2.74
Median is the most appropriate measure of central tendency.
The least appropriate = mean
Yes there is an outlier.
Step-by-step explanation:
Given responses : 5, 4, 2, 1, 1, 2, 10, 2, 3, 5.
First arrange them in increasing order, ![\sqrt[10]{1\times1\times2\times2\times2\times3\times4\times5\times5\times10 }\\\\=\sqrt[10]{24000} \approx2.74](https://tex.z-dn.net/?f=%5Csqrt%5B10%5D%7B1%5Ctimes1%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes3%5Ctimes4%5Ctimes5%5Ctimes5%5Ctimes10%20%7D%5C%5C%5C%5C%3D%5Csqrt%5B10%5D%7B24000%7D%20%5Capprox2.74)
Its sum = 35
Mean of n observations = (Sum of observations) ÷ n
Mean = (35) ÷ 10
=3.5
Here n =10 (even)
Median = average of middle most numbers = ![\dfrac{2+3}{2}=\dfrac52=2.5](https://tex.z-dn.net/?f=%5Cdfrac%7B2%2B3%7D%7B2%7D%3D%5Cdfrac52%3D2.5)
Mode = most repeated number = 2 (thrice)
geometric mean = ![\sqrt[n]{x_1\times x_2\times.... x_n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx_1%5Ctimes%20x_2%5Ctimes....%20x_n%7D)
10 is an outlier as it is very large as compare to other numbers.
When outlier is present in data , the median is the most appropriate measure of central tendency.
Mean affected badly by the outlier so it the least appropriate.