The data represents the annual salaries of 1, 000 professional musicians in a ci

Question

The data represents the annual salaries of 1, 000 professional musicians in a city. How many musicians make $60k or more? (Your work counts for 1 point, and your answer counts for 1 point) Find the median salary of this group of musicians. (Your work counts for 1 point, and your answer counts for 1 point). Find the range of the salaries of this group of musicians. (Your work counts for 1 point, and your answer counts for 1 point) Find the inter-quartile range of the salaries of this group of musicians. (Your work counts for 1 point, and your answer counts for 1 point)

Explanation / Answer

Here as per graph, total % musicians with 60k or more are 15% +8% + 7% +10% = 40%

So total required musicians = 40% of 1000 = 400

This is the answer of part (a)

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Now for getting its median, we find the cummulative frequency of all the bars as :

Salaries Total musicians Cummulative frequency

20-30 120 120

30 -40 130 250

40 -50 250 500

50 -60 100 600

60- 70 150 750

70- 80 100 850

80-90 80 930

90-100 70 1000

Now here as N/2 = 500, so its median class will be one with cummulative frequency less than 500 so clearly its median class is 40-50 and thus we use the formula that

median = L +(N/2-cf)/f where L=40, cf = just preciding class cummulative frequency = 250 and f= frequency of this class= 250

Thus

median = 40 + (500- 250)/250 = 40+1= 41

So required median salary is 41 K.

This is the answer of part (b)

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Clearly as minimum salary is 20k and maximum salary is shown 100k, so range = max.salary - min salary

= 100 k - 20 k = 80k

That is the answer of part (c)

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