Question

Find the​

Answer 1

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

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{39}{14} = 2.78 \approx 2.8$

b) Median

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data:

1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4

$\text{Median} = \dfrac{7^{th}+8^{th}}{2} = \dfrac{3+3}{2} = 3$

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.

$\text{Mid Range} = \dfrac{1+4}{2} = 2.5$

e) Measure of center

Option C) Only the mode makes sense since the data is nominal.