Question

album type sold per year
which of these statements is true? choose four correct answers.
the median of cds is 400.
both have the same median.
both have the same interquartile range.
the range of digital is 800.
cds have a higher mean than digital.
digitals mean is around 467.

Explanation:

Step1: Find the number of CDs sold each year

From the bar - graph, the number of CDs sold (in order from 2008 - 2013) is \(1000,800,800,600,400,200\)

Step2: Calculate the median of CDs

Arrange the data in ascending order: \(200,400,600,800,800,1000\)
Since \(n = 6\) (even), median\(=\frac{600 + 800}{2}=700\)

Step3: Find the number of digital albums sold each year

From the bar - graph, the number of digital albums sold (in order from 2008 - 2013) is \(100,300,300,500,700,900\)

Step4: Calculate the median of digital albums

Arrange the data in ascending order: \(100,300,300,500,700,900\)
Since \(n = 6\) (even), median\(=\frac{300+500}{2}=400\)

Step5: Calculate the range of digital albums

Range\(=\text{Max}-\text{Min}\)
For digital albums, \(\text{Max}=900\), \(\text{Min}=100\)
Range\(=900 - 100=800\)

Step6: Calculate the inter - quartile range (IQR)

For CDs:
First, find \(Q_1\) and \(Q_3\)
\(Q_1\) is the median of the first half of the data \(\{200,400,600\}\), \(Q_1 = 400\)
\(Q_3\) is the median of the second half of the data\(\{800,800,1000\}\), \(Q_3=800\)
\(IQR_{CDs}=Q_3 - Q_1=800 - 400 = 400\)
For digital albums:
\(Q_1\) is the median of the first half of the data\(\{100,300,300\}\), \(Q_1 = 300\)
\(Q_3\) is the median of the second half of the data\(\{500,700,900\}\), \(Q_3 = 700\)
\(IQR_{digital}=Q_3 - Q_1=700 - 300=400\)

Step7: Calculate the mean of CDs

\(\text{Mean}_{CDs}=\frac{1000 + 800+800+600+400+200}{6}=\frac{3800}{6}\approx633.33\)

Step8: Calculate the mean of digital albums

\(\text{Mean}_{digital}=\frac{100 + 300+300+500+700+900}{6}=\frac{2800}{6}\approx467\)

Answer:

• Both have the same interquartile range.
• The range of digital is 800.
• CDs have a higher mean than digital.
• Digital's mean is around 467.