Question

1. the new york premier theater is hosting a concert at which all proceeds will go to the charity. the seating chart is shown here! the seating options for the color - coded seats are priced as follows: rear mezzanine 54 seats, each at $150; middle mezzanine 87 seats, each at $200; front mezzanine and orchestra 512 seats, each at $300; front and center orchestra 167 seats, each at $500. a. construct a frequency distribution with column headings “seat type”, “price”, and “number of seats”. b. if all of the seats were sold for this concert, what would be the total amount to be donated to charity? c. determine the mean, median, and mode seat prices. round to the nearest cent. financial algebra workbook 1.1

Explanation:

Step1: Construct frequency - distribution table

Seat Type	Price	Number of Seats
Middle Mezzanine	200	87
Front Mezzanine and Orchestra	300	512
Front and Center Orchestra	500	167

Step2: Calculate total donation amount

The total donation amount is the sum of the product of the price and the number of seats for each seat - type.

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Step3: Calculate the mean seat price

First, find the total number of seats $n=54 + 87+512+167=820$.
The total money from all seats is $262600$.
The mean $\bar{x}=\frac{262600}{820}\approx320.24$

Step4: Calculate the median seat price

Arrange the number of seats in ascending order of price: 54 (at $150$), 87 (at $200$), 512 (at $300$), 167 (at $500$).
The cumulative frequencies are: 54, $54 + 87=141$, $141+512 = 653$, $653+167 = 820$.
Since $n = 820$ (even), the median is the average of the $\frac{n}{2}=410$ - th and $(\frac{n}{2}+1)=411$ - th ordered values. Both of these values fall in the "Front Mezzanine and Orchestra" category with a price of $300$. So the median is $300$.

Step5: Calculate the mode seat price

The seat - type with the highest number of seats is "Front Mezzanine and Orchestra" with 512 seats. So the mode is $300$.

Answer:

a.

Seat Type	Price	Number of Seats
Middle Mezzanine	200	87
Front Mezzanine and Orchestra	300	512
Front and Center Orchestra	500	167

b. $262600$
c. Mean: $\$320.24$, Median: $\$300$, Mode: $\$300$