Answer:
The researcher used a ratio scale of measurement for the number of people using their cell phone.
Mean: (3+4+4+5+6+8)/6 = 30/6 = 5
Median: arrange the data in ascending order: 3, 4, 4, 5, 6, 8. The median is the middle value which is 5.
Mode: there is no mode as no value occurs more than once.
Range: 8-3 = 5
Variance:
s^2 = Σ(x-ȳ)^2 / (n-1)
s^2 = [(3-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (6-5)^2 + (8-5)^2] / (6-1)
s^2 = 5.6
Standard deviation: s = sqrt(s^2) = sqrt(5.6) ≈ 2.37
To find the number of people using their cell phone associated with +1 SD, we add one standard deviation to the mean:
Mean + 1 SD = 5 + 2.37 ≈ 7.37
Therefore, approximately 7 people using their cell phone are associated with +1 SD.
To find the number of people using their cell phone that reflects 96% of the sample, we need to find the z-score that corresponds to the 96th percentile. From a standard normal distribution table, we find that the z-score is approximately 1.75. We can use this z-score to find the corresponding value in our data set using the formula:
z = (x - ȳ) / s
Rearranging, we get:
x = z * s + ȳ
x = 1.75 * 2.37 + 5
x ≈ 9.3
Therefore, approximately 9 people using their cell phone reflect 96% of the sample.
Explanation: