Question

If a person with a height of 58 inches takes 2,601 steps per mile, a person with a height of 64 inches takes 2,357 steps per mile, and a person with a height of 76 inches takes 1,985 steps per mile, what is the average number of steps of three 58-inch people, five 64-inch people, and two 76-inch people. Afterwards, find the weighted average number of steps. How does the average compare with the weighted average? Which value is a more accurate representation of the data?

Answer 1

1. Average Number of Steps of

= Total of the different steps / divided by 3

= 6,943/3

= 2,314.3 steps

2. Weighted Average Number of Steps of 3, 58-inch, 5, 64-inc, and 2, 76-inch people

= Total steps by the 10 people divided by 10

= 23,558/10

= 2,355.8 steps

3. The difference is not much.

4. The weighted average (2,355.8 steps) is a more accurate representation of the data. The calculation of the ordinary average steps is more confusing than the weighted average steps.

Explanation:

1. Calculation of the Weighted Average Number of Steps of:

3, 58-inch people = 3 x 2,601 = 7,803

5, 64-inch people = 5 x 2,357 = 11,785

2, 76-inch people = 2 x 1,985 = 3,970

10 persons' total steps = 23,558

2. Calculation of the ordinary average:

58-inch people = 2,601

64-inch people = 2,357

76-inch people = 1,985

Total steps 6,943