The table below shows the ages of a class of 60 students enrolled in the HSC course at TAFE Digital.

Question

Age Frequency

18 14

19 25

20 16

21 5

Using the statistical mode on your calculator, find the population standard

deviation of these ages.

Answer 1

Hi...

Sorry to hear about your calculator issues. I'd like to show you how it can be done free style. Hopefully this helps you.

Standard Deviation is the SQUARE ROOT of the Variance, SD = √(variance)

The Variance = ∑[(x - µ)²/ N]

where

x is each data value, µ is the mean of the data set and N is the total number of data points in the set.

You are given the frequency of each value, so the mean or µ is ∑(x • frequency) / N

N = 14 + 25 + 16 + 5 = 60

µ = [18(14) + 19(25) + 20(16) + 21(5)] = 252 + 475 + 320 + 105 = 1152/60 = 19.2

To determine the variance you need to calculate the difference of EACH data value from the mean and square it. Be sure to take into account the frequency of each data value. Best to put together a table to show your work;

Age Frequency (x - µ) (x - µ)² ∑(x - µ)²

18 14 18 - 19.2 = -1.2 1.44 1.44(14) = 20.16

19 25 19 - 19.2 = -0.2 0.04 0.04(25) = 1.00

20 16 20 - 19.2 = 0.8 0.64 0.64(16) = 10.24

21 5 21 - 19.2 = 1.8 3,24 3.24(5) = 16.2

Total of ∑(x - µ)² = 47.6 and so the Variance is 47.6/60 = 0.793

So the Standard Deviation for this data set is the √(0.793) = 0.89

Hope this helps...