Q3: The following data give the amounts (in dollars) spent on refreshments by 30 spectators randomly selected from those who patronized the concession stands at a recent Major League Baseball game. 4.95 27.99 8.00 5.80 4.50 2.99 4.85 6.00 9.00 15.75 9.50 3.05 5.65 21.00 16.60 18.00 21.77 12.35 7.75 10.45 3.85 28.45 8.35 17.70 19.50 11.65 11.45 3.00 6.55 16.50 a. Construct a frequency distribution table using the less-than method to write classes. Take $0 as the lower boundary of the first class and $6 as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. Draw a histogram for the frequency distribution.
Answers
➳Let the all three parts be a, b and c.
Rate on a = 4%
Rate on b = 6%
Rate on c = 8%
Now here is a thing to understand, when Time isn't mentioned for interest. We can take any time for all of them and that will be cancelled inevitably, so let's take time as 1 year.
• According to the Question :
⇒ a × 4% × 1 = b × 6% × 1 = c × 8% × 1
Cancelling Like terms i.e. % and 1 from all
⇒ a × 4 = b × 6 = c × 8
⇒ 4a = 6b = 8c
Dividing each term by 2
⇒ 2a = 3b = 4c
To bring on equal scale, we will multiply each of them by LCM(2, 3, 4) = 12
⇒ a/2 × 12 = b/3 × 12 = c/4 × 12
⇒ 6a = 4b = 3b
⇒ a : b : c = 6 : 4 : 3
Now we have ratio of each part, so we can find the exact figure. Let a, b and c be 6x, 4x and 3x
⠀⠀⠀⠀⠀───────────────
• Different parts will be as follow :
⇢ a + b + c = 2600
⇢ 6x + 4x + 3x = 2600
⇢ 13x = 2600
⇢ x = 2600/13
⇢ x = 200
a = 6x = 6(200) = Rs. 1200
b = 4x = 4(200) = Rs. 800
c = 3x = 3(200) = Rs. 600
∴ Hence, all three parts are of Rs. 1200, Rs. 800 and Rs. 600 respectively.
Answer:
4.95 27.99 8.00 5.80 4.50 2.99 4.85 6.00 9.00 15.75 9.50 3.05 5.65 21.00 16.60 18.00 21.77 12.35 7.75 10.45 3.85 28.45 8.35 17.70 19.50 ...
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