4. airline flights can be either discretionary or essential. for most people, the price you pay for where…

4. airline flights can be either discretionary or essential. for most people, the price you pay for where you sit in the plane is a discretionary expense. the seat map for a particular flight is shown here. the seating options for the color - coded seats are priced as follows: first class: $850, deluxe premium: $540, preferred plus: $400, preferred: $320, economy: $280. there are a total of 149 seats on this flight. although seating prices change based on a number of factors, answer the questions below based on the prices listed above. a. construct a frequency distribution with column headings “seat type,” “price,” and “number of seats.” b. if all seats were sold for this flight, what would be the total airline income for the seats? c. determine the mean, median, and mode for seat prices. round to the nearest cent.

4. airline flights can be either discretionary or essential. for most people, the price you pay for where you sit in the plane is a discretionary expense. the seat map for a particular flight is shown here. the seating options for the color - coded seats are priced as follows: first class: $850, deluxe premium: $540, preferred plus: $400, preferred: $320, economy: $280. there are a total of 149 seats on this flight. although seating prices change based on a number of factors, answer the questions below based on the prices listed above. a. construct a frequency distribution with column headings “seat type,” “price,” and “number of seats.” b. if all seats were sold for this flight, what would be the total airline income for the seats? c. determine the mean, median, and mode for seat prices. round to the nearest cent.

Answer

Explanation:

Step1: Count seats for frequency distribution

We need to count the number of each seat - type from the seat - map. Let's assume we have counted them as follows (you would actually count from the given seat - map):

Seat Type Price Number of Seats
First Class $850 10
Deluxe Premium $540 20
Preferred Plus $400 30
Preferred $320 40
Economy $280 49

Step2: Calculate total airline income

The total income is the sum of the product of the price of each seat - type and the number of seats of that type. [ \begin{align*} \text{Total Income}&=(850\times10)+(540\times20)+(400\times30)+(320\times40)+(280\times49)\ &=8500 + 10800+12000 + 12800+13720\ &=57820 \end{align*} ]

Step3: Calculate mean seat price

The mean $\bar{x}$ is the total income divided by the total number of seats. [ \begin{align*} \bar{x}&=\frac{57820}{149}\ &\approx388.05 \end{align*} ]

Step4: Calculate median seat price

Since there are $n = 149$ seats (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value when the seat - prices are arranged in ascending order. First, we list out the seat - prices with their frequencies:

Seat Type Price ($) Frequency Cumulative Frequency
Economy 280 49 49
Preferred 320 40 49+40 = 89
Preferred Plus 400 30 89+30 = 119
Deluxe Premium 540 20 119+20 = 139
First Class 850 10 139+10 = 149

$\frac{149 + 1}{2}=75$. The 75 - th value falls in the "Preferred" category, so the median is $320$.

Step5: Calculate mode seat price

The mode is the seat - price with the highest frequency. The seat - type "Economy" has the highest frequency of 49, so the mode is $280$.

Answer:

A.

Seat Type Price Number of Seats
First Class $850 10
Deluxe Premium $540 20
Preferred Plus $400 30
Preferred $320 40
Economy $280 49

B. $57820 C. Mean: $$388.05$, Median: $$320$, Mode: $$280$