Question

The mean number of tickets sold daily by a comedy show over a seven –day period was 52.The show sold 46 tickets on the last day of that period .Find the mean number of tickets that were sold daily over the first six days.

Answer 1

Hint: The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list
Where,
N = Number of observations
\[{f_1},{f_2},{f_3},...,{f_n}\] = Different values of frequency f.
\[{x_1},{x_2},{x_3},...,{x_n}\] = Different values of variable x.

Complete step-by-step solution:
Firstly in order to find the mean number for the six day period, begin by figuring out the total number of tickets that were sold.
Total mean of tickets sold on a daily basis = 52
Tickets sold in 7 days = \[52 \times 7 = 364\]
Since 46 tickets were sold on the last day then the tickets sold before the last day would be calculated by subtracting 46 tickets from the total number of tickets.
Tickets sold before last day = \[364 - 46 = 318\]
Now in order to find the mean number for the six day period, out the total number of tickets that were sold divide the tickets sold before by 6 number of days.
Mean = total no. of tickets /no. of days
$\Rightarrow$Mean = \[\dfrac{{318}}{6}\]
$\Rightarrow$Mean = $53$

Therefore the mean is equal to 53.

Note: We know that finding the mean number of tickets that were sold daily over the first six days could have been done manually as it has been performed for seven number of days. Although we have standard formula for calculating mean,
\[\overline x = \dfrac{{\sum {fx} }}{{\sum f }}\]
But here we haven’t been provided with any class intervals. Thus our data was discrete. Therefore we have to apply a discrete formula of mean.