Answer:
a) Mean = 2.8
b) Median = 3
c) Mode = 4
d) Mid range = 2.5
e) Option C) Only the mode makes sense since the data is nominal.
Step-by-step explanation:
We are given the following data set in the question:
1, 4, 4, 4, 2, 1, 4, 3, 1, 4, 4, 3, 3, 1
a) Mean
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{39}{14} = 2.78 \approx 2.8[/tex]
b) Median
[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:
1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4
[tex]\text{Median} = \dfrac{7^{th}+8^{th}}{2} = \dfrac{3+3}{2} = 3[/tex]
c) Mode
Mode is the observation with highest frequency. Since 4 appeared maximum time
Mode = 4
d) Mid range
It is the average of the smallest and largest observation of data.
[tex]\text{Mid Range} = \dfrac{1+4}{2} = 2.5[/tex]
e) Measure of center
Option C) Only the mode makes sense since the data is nominal.
