Question

john measures the length of one side of his room with a tape measure. he repeats his measurements four times and records them in the table below:
table 1: recorded distances of one side of john’s room.
trial 1: 4.50 m
trial 2: 4.60 m
trial 3: 4.30 m
trial 4: 4.40 m
among the recorded measurements, which one should john choose that best represents the length of one side of his room?
multiple choice
4.50 m
4.30 m
4.60 m
4.40 m
neither of the above.
john should calculate the statistical average of his data since the mean (or the average) represents the best value among his recorded set of measurements.

Explanation:

Step1: Identify the measurements

The measurements are \( 4.50 \, \text{m} \), \( 4.60 \, \text{m} \), \( 4.30 \, \text{m} \), and \( 4.40 \, \text{m} \).

Step2: Calculate the mean

The formula for the mean \( \bar{x} \) is \( \bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n} \), where \( x_i \) are the individual measurements and \( n \) is the number of measurements.
First, sum the measurements: \( 4.50 + 4.60 + 4.30 + 4.40 = 17.80 \, \text{m} \).
Then, divide by the number of measurements (\( n = 4 \)): \( \bar{x} = \frac{17.80}{4} = 4.45 \, \text{m} \). Wait, but looking at the options, maybe I misread. Wait, the problem says "the mean (or the average) represents the best value". Wait, but the options are 4.50, 4.30, 4.60, 4.40, or neither. Wait, maybe I made a mistake. Wait, let's recalculate: \( 4.50 + 4.60 = 9.10 \), \( 4.30 + 4.40 = 8.70 \), total \( 9.10 + 8.70 = 17.80 \). Divide by 4: \( 17.80 \div 4 = 4.45 \). None of the options is 4.45, so the answer is "Neither of the above".

Answer:

Neither of the above