Question

5 people were asked how many songs are on their MP3 player, and the results
are shown below. Tabby has 131 songs and wants to know whether she has
more songs on her MP3 player than most other people.
a) Which average should she use to compare?
b) What is the value of this average for the five numbers shown below?
212
88
62
125
183

Answer 1

Answer:

125

Step-by-step explanation:

a) Tabby should use the median to compare her number of songs to the others. The median is the middle number when the numbers are arranged in order from least to greatest. In this case, the median is 125, so Tabby has more songs than 2 people and fewer songs than 3 people.

Answer 2

Answer:

a) she should use mean to compare.

b) The value of this average for the five numbers is 125.

Step-by-step explanation:

To compare the number of songs Tabby has on her MP3 player with the averages of the given data, she can consider using either the mean (arithmetic average) and median. Let's calculate each of these:

The data set is: 212, 88, 62, 125, 183.

a) Mean (Arithmetic Average):

$\sf \text{Mean} = \dfrac{\text{Sum of all values}}{\text{Number of values}}$

$\sf \text{Mean} = \dfrac{212 + 88 + 62 + 125 + 183}{5}$

$\sf \text{Mean} = \dfrac{670}{5} = 134$

b) Median:

To find the median, arrange the data in ascending order and find the middle value.

Ordered data set: 62, 88, 125, 183, 212.

Since there are an odd number of values (5), the median is the middle value, which is 125..

Now, Tabby can compare her 131 songs with the calculated averages:

• Mean: 134
• Median: 125

Since Tabby's 131 songs are closer to the mean (134) than the median (125), she may consider comparing with the mean.

In this case, Tabby has fewer songs than the mean but more than the median, so she has a moderate amount of songs compared to the average.