Question

pre-algebra ic sem 2 fall 2025
summarizing data sets with statistics
comparing data from two different sets
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 data for CDs

CDs data (in order): \(150,350,550,750,750,1000\)
Median: \(\frac{550 + 750}{2}=650\)
Range: \(1000 - 150 = 850\)
Mean: \(\frac{150+350+550+750+750+1000}{6}=\frac{3550}{6}\approx591.67\)

Step2: Find the data for Digital

Digital data (in order): \(75,275,275,475,675,875\)
Median: \(\frac{275 + 475}{2}=375\)
Range: \(875 - 75=800\)
Mean: \(\frac{75 + 275+275+475+675+875}{6}=\frac{2650}{6}\approx441.67\)

Step3: Check each option

• Option 1 (The median of CDs is 400): False (CDs median is 650)
• Option 2 (Both have the same median): False (CDs median 650, Digital median 375)
• Option 3 (Both have the same inter - quartile range):

First, find quartiles.
For CDs: \(Q_1=\frac{350 + 550}{2} = 450\), \(Q_3=\frac{750+750}{2}=750\), \(IQR = 750 - 450=300\)
For Digital: \(Q_1=\frac{275+275}{2}=275\), \(Q_3=\frac{675 + 875}{2}=775\), \(IQR=775 - 275 = 500\). False

• Option 4 (The range of digital is 800): True (\(875-75 = 800\))
• Option 5 (CDs have a higher mean than digital): True (\(591.67>441.67\))
• Option 6 (Digital’s mean is around 467): False (Digital’s mean \(\approx441.67\))

Answer:

The range of digital is 800, CDs have a higher mean than digital.