Question

comparing data from two different sets
album type sold per year
cds digital
which of these statements is true? check all that apply.
cds have a higher mean than digital.
the range of digital is 800.
the median of cds is 400.
both have the same interquartile range.
both have the same median.
digitals mean is around 457.

Explanation:

Step1: Calculate CDs mean

Assume the number of CDs sold in 2008 - 2013 are \(x_1,x_2,x_3,x_4,x_5,x_6\) (from the bar - chart values). Mean of CDs \(\bar{x}_{CD}=\frac{x_1 + x_2+x_3+x_4+x_5+x_6}{6}\). From the chart, \(x_1 = 1000,x_2 = 800,x_3 = 800,x_4 = 600,x_5 = 400,x_6 = 200\). \(\bar{x}_{CD}=\frac{1000 + 800+800+600+400+200}{6}=\frac{3800}{6}\approx633\).

Step2: Calculate digital mean

Assume the number of digital albums sold in 2008 - 2013 are \(y_1,y_2,y_3,y_4,y_5,y_6\). From the chart, \(y_1 = 100,y_2 = 300,y_3 = 300,y_4 = 500,y_5 = 700,y_6 = 900\). Mean of digital \(\bar{y}_{digital}=\frac{100 + 300+300+500+700+900}{6}=\frac{2800}{6}\approx467\). So CDs have a higher mean than digital.

Step3: Calculate range of digital

Range of a data - set is \(max - min\). For digital, \(max = 900\) and \(min = 100\), range \(=900 - 100=800\).

Step4: Calculate median of CDs

Arrange CD values in ascending order: \(200,400,600,800,800,1000\). Since \(n = 6\) (even), median \(=\frac{600 + 800}{2}=700
eq400\).

Step5: Inter - quartile range (IQR)

To calculate IQR, we first need to find the first quartile \(Q_1\) and the third quartile \(Q_3\). But without exact data points for quartile calculation from the bar - chart (assuming evenly distributed within each bar), we can't accurately say they have the same IQR.

Step6: Median comparison

We already found CD median is 700 and for digital, arrange values in ascending order: \(100,300,300,500,700,900\), median \(=\frac{300 + 500}{2}=400\). They don't have the same median.

Answer:

CDs have a higher mean than digital.
The range of digital is 800.
Digital's mean is around 467.