Question

A sample of 12 people was asked how much change they had in their pockets and wallets. The responses (in cents) are 52 25 15 0 104 44 60 30 33 81 40 5 Determine the mean, median, and mode for these data.

Answer 1

Answer:

Mean = 40.75

Median = 36.5

No mode.                            

Step-by-step explanation:

We are given the following data:

52, 25, 15, 0, 104, 44, 60, 30, 33, 81, 40, 5

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{489}{12} = 40.75$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 0, 5, 15, 25, 30, 33, 40, 44, 52, 60, 81, 104

$\text{Median} = \dfrac{6^{th}+7^{th}}{2}=\dfrac{33+40}{2} =36.5$

Mode is the most frequent observation in the data.

Since all the observations repeated exactly once, there is no mode.