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You visit six randomly selected locations on campus and observe the number of people in the area using their cell phone. The data is as follows: 3, 4, 4, 5, 6, 8 1.

1. What scale of measurement was used by the researcher?
2. Calculate the mean, median, mode for the data set.
3. Calculate the range, variance and standard deviation for the data set (use the formula for sample).
4. Based on the sample, what is the number of people using their cell phone associated with +1 SD?
5. What number of people using their cell phone reflects 96% of the sample?​

User Ying Xiong
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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:

User Ramp
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