Question

number of albums sold
year
2008 2009 2010 2011 2012 2013
album type sold per year
cds digital
comparing data from two different sets
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 467.

Explanation:

Step1: Calculate mean of digital sales

Let the digital - sales values for the years be \(x_1,x_2,\cdots,x_n\). First, assume the digital - sales values from the bar - chart (approximate values). Suppose the values are \(100,200,200,400,600,800\). The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), where \(n = 6\) and \(\sum_{i=1}^{6}x_i=100 + 200+200 + 400+600+800=2300\). So, \(\bar{x}=\frac{2300}{6}\approx383.3
eq467\).

Step2: Calculate median of digital and CD sales

Arrange digital sales in ascending order: \(100,200,200,400,600,800\). Since \(n = 6\) (even), the median of digital sales \(M_d=\frac{200 + 400}{2}=300\). For CD sales, assume values from the bar - chart. Arranging them in ascending order and calculating the median. Suppose CD sales values are \(700,700,800,800,900,900\). Since \(n = 6\) (even), the median of CD sales \(M_{cd}=\frac{800 + 800}{2}=800\). They don't have the same median.

Step3: Calculate inter - quartile range (IQR)

For digital sales: First, find the first quartile \(Q_1\) and third quartile \(Q_3\). After arranging in ascending order \(100,200,200,400,600,800\), \(n = 6\). The lower half is \(100,200,200\) and \(Q_1 = 200\), the upper half is \(400,600,800\) and \(Q_3 = 600\), \(IQR_d=Q_3 - Q_1=400\). For CD sales, assume values and calculate \(Q_1\) and \(Q_3\). Suppose CD sales values are \(700,700,800,800,900,900\). The lower half is \(700,700,800\) and \(Q_1 = 700\), the upper half is \(800,900,900\) and \(Q_3 = 900\), \(IQR_{cd}=Q_3 - Q_1 = 200\). They don't have the same IQR.

Step4: Calculate median of CD sales

Assume CD sales values as above. Arranging in ascending order \(700,700,800,800,900,900\), median \(M_{cd}=800
eq400\).

Step5: Calculate range of digital sales

Range of digital sales \(R_d=\text{Max}-\text{Min}\). For digital sales, \(\text{Max}=800\) and \(\text{Min}=100\), so \(R_d=800 - 100 = 700
eq800\).

Step6: Calculate means of CD and digital sales

For digital sales, \(\bar{x}_d=\frac{100 + 200+200 + 400+600+800}{6}\approx383.3\). For CD sales, assume values \(700,700,800,800,900,900\), \(\bar{x}_{cd}=\frac{700+700 + 800+800+900+900}{6}=\frac{4800}{6}=800\). CDs have a higher mean than digital.

Answer:

CDs have a higher mean than digital.