Question

1-92 calculate the mean of each data set below. can you find any shortcuts that allow you to find the mean without having to do much calculation? a) 6, 10, 6, 10 b) 11, 12, 12, 13, 12 c) 0, 5, 4, 8, 0, 7

Explanation:

Part (a)

Step1: Identify data and count

Data: 6, 10, 6, 10. Number of values \( n = 4 \).

Step2: Sum the data (shortcut: pair 6s and 10s)

Sum \( = (6 + 6) + (10 + 10) = 12 + 20 = 32 \).

Step3: Calculate mean

Mean \( = \frac{\text{Sum}}{n} = \frac{32}{4} = 8 \).

Step1: Identify data and count

Data: 11, 12, 12, 13, 12. Number of values \( n = 5 \).

Step2: Sum using shortcut (count 12s)

12 appears 3 times, 11 and 13 once. Sum \( = 11 + 12\times3 + 13 = 11 + 36 + 13 = 60 \).

Step3: Calculate mean

Mean \( = \frac{60}{5} = 12 \).

Step1: Identify data and count

Data: 0, 5, 4, 8, 0, 7. Number of values \( n = 6 \).

Step2: Sum the data

Sum \( = 0 + 5 + 4 + 8 + 0 + 7 = 24 \).

Step3: Calculate mean

Mean \( = \frac{24}{6} = 4 \).

Answer:

8

Part (b)