Question

day of the week | number of hours of sleep per night
sunday | 8
monday | 6 1/2
tuesday | 6 1/2
wednesday | 7
thursday | 6
friday | 7
saturday | 8

the number of hours of sleep a person gets per night for one week is shown in the table above. what is the median number of hours of sleep per night for this week?

options: 6, 6 1/2, 7, 8

Explanation:

Step1: List the number of hours

The hours per night are: 8, \(6\frac{1}{2}\), \(6\frac{1}{2}\), 7, 6, 7, 8.

Step2: Convert mixed numbers to improper fractions

\(6\frac{1}{2}=\frac{13}{2}\), so we have 8, \(\frac{13}{2}\), \(\frac{13}{2}\), 7, 6, 7, 8.

Step3: Convert all to fractions with denominator 2

8 = \(\frac{16}{2}\), 7 = \(\frac{14}{2}\), 6 = \(\frac{12}{2}\). So the list becomes \(\frac{16}{2}\), \(\frac{13}{2}\), \(\frac{13}{2}\), \(\frac{14}{2}\), \(\frac{12}{2}\), \(\frac{14}{2}\), \(\frac{16}{2}\).

Step4: Sum the numerators

16 + 13 + 13 + 14 + 12 + 14 + 16 = 16×2 + 13×2 + 14×2 + 12 = 32 + 26 + 28 + 12 = 98.

Step5: Divide by the number of days (7) and the denominator (2)

The sum of hours is \(\frac{98}{2}=49\). The average is \(\frac{49}{7}=7\).

Answer:

7