Answer:
a) Mean = 4.6, median = 3, mode =2
b) Mean = 13.8, median = 9, mode = 6
c) Option C) Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c
Step-by-step explanation:
We are given the following data:
2, 2, 3, 6, 10
a) Mean, median and mode
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{23}{5} = 4.6[/tex]
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data: 2, 2, 3, 6, 10
[tex]\text{Median} = 3^{rd}\text{ term} = 3[/tex]
Mode is the most frequent observation in data.
Mode = 2
b) Multiplying data set by 3
6, 6, 9, 18, 30
[tex]Mean =\displaystyle\frac{69}{5} = 13.8[/tex]
[tex]\text{Median} = 3^{rd}\text{ term} = 9[/tex]
Mode = 6
C) Comparison
The mean, median and mode of the new data increased by a factor of 3.
Option C) Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c
