# Working out a marketing budget

How can Bo and Hayden best spend the rest of the festival marketing budget? Examine the early ticket sales to hypothesise which age groups are likely to attend the festival…

Ticket sales for the Salty Creek Community Festival have begun, and budget and marketing advisor Bo is working with one of the festival’s organisers, Hayden, to figure out the best way to spend the rest of the marketing budget. They decide to have a look at attendee numbers so far to draw some conclusions about which age groups are likely to attend the festival, and then create a marketing plan for those potential attendees.

Everyone who has purchased tickets so far has entered their age range, so Bo and Hayden can use the mode, median, and mean of the attendees’ ages to help develop the marketing plan.

 Age Range Tickets Sold 11-15 346 16-20 390 21-25 219 26-30 240 31-35 119 36-40 129 41-45 22 46-50 42 51-55 24 Over 55 31 TOTAL 1562

Using the table above, help Bo and Hayden calculate the mode and median of ticket sales so far.

Median and mode quiz transcript

Since the mode and median are different, finding the mean (or average) age of ticket buyers might be useful as well.

With age ranges instead of exact ages, it’s not possible to solve for the exact mean, but it can be estimated. Bo explains that they can use the middle value of each age range to represent the group, and adds a column to the table:

 Age Range Middle Value Tickets Sold 11-15 13 346 16-20 18 390 21-25 23 219 26-30 28 240 31-35 33 119 36-40 38 129 41-45 43 22 46-50 48 42 51-55 53 31 Over 55 58 31 TOTAL 1562

To find out the mean age of ticket buyers, they’ll need to find the weighted average, which accounts for the varying number of tickets sold in each age range. Bo adds another column to the table, and starts filling it in by multiplying the Middle Value column by the number of tickets sold to that age:

 Age Range Middle Value Tickets Sold Weighted Value 11-15 13 346 4498 16-20 18 390 7020 21-25 23 219 26-30 28 240 31-35 33 119 36-40 38 129 41-45 43 22 46-50 48 42 51-55 53 31 Over 55 58 31 TOTAL 1562

Help Bo and Hayden complete the table and calculate the mean.

Mean quiz transcript

With these statistics in mind, Bo and Hayden decide to dedicate the remaining marketing budget to people ages 16 to 25, with a bit more going to the 21 to 25 crowd. The mean, median and mode helped them see what ages of people are interested in attending and who might still want to buy tickets.

Students might be familiar with calculating the weighted mean to determine their grade point average (GPA) or weighted average mark (WAM). These calculations, along with median and mode, are also used to help analyse data in many areas of everyday life, from car prices to athletic performance.