SOLUTION: The eye colour of 360 individuals is partially recorded in the table below. Due to administrative error some of the information is missing. Eye Colour Frequency

Click here to see ALL problems on Probability-and-statistics

Question 1083701: The eye colour of 360 individuals is partially recorded in the table below. Due to administrative error some of the information is missing.
Eye Colour Frequency Relative Frequency
blue 126
brown 90
green 36
grey 72
hazel

(i) Determine the frequency of eye colour �hazel�.
(ii) Determine the relative frequencies of each eye colour and fill in the table.
(iii) What type of variable is �Eye Colour�?
(iv) Represent the data on a bar chart.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Given Table

Eye Colour Frequency Relative Frequency
blue 126
brown 90
green 36
grey 72
hazel x
Total 360

Right now x is unknown, but can be found later. It's simply a placeholder for a number.

------------------------------------------------------------------

Part (i)

The values in the frequency column add up to the total of 360.
Use this fact to solve for x.

126+90+36+72+x = 360
324+x = 360
324+x-324 = 360-324
x = 36

There are 36 individuals who have hazel eyes.

The table updates to

Eye Colour Frequency Relative Frequency
blue 126
brown 90
green 36
grey 72
hazel 36
Total 360

------------------------------------------------------------------

Part (ii)

Divide each frequency by the total (360)

The relative frequency for blue eyes is 126/360 = 0.35 which is equivalent to 35%
The relative frequency for brown eyes is 90/360 = 0.25 which is equivalent to 25%
The relative frequency for green eyes is 36/360 = 0.1 which is equivalent to 10%
The relative frequency for grey eyes is 72/360 = 0.2 which is equivalent to 20%
The relative frequency for hazel eyes is 36/360 = 0.1 which is equivalent to 10%

The table further updates to

Eye Colour Frequency Relative Frequency
blue 126 0.35 = 35%
brown 90 0.25 = 25%
green 36 0.1 = 10%
grey 72 0.2 = 20%
hazel 36 0.1 = 10%
Total 360 1 = 100%

------------------------------------------------------------------

Part (iii)

"Eye color" is a categorical variable because there are a finite number of choices to pick from when it comes to eye color.
With categorical variables, there is no overlap with any of the choices.

"Eye color" is a nominal variable as well because we can assign a name to it, but we cannot sort it or do math on the values.
It makes no sense to add up or divide eye colors.

------------------------------------------------------------------

Part (iv)

To make the bar chart, plot the different colors along the x axis.
The height of each bar is equal to its corresponding frequency

The chart was generated with Excel (other free programs like Open Office can do the same thing)