Problem Set 3.1: Characteristics of the Mean Criterion: Explain a distribution. Instructions: Read the following and answer the questions. Data: To study perception, a researcher selects a sample of participants (n = 12) and asks them to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher asks participants to report when they notice a difference in the weight of the two objects. Below is a list of the difference in weight (in pounds) when participants first noticed a difference. Answer the following questions based on the data given in the table. Difference in Weight 4 8 9 5 12 7 6 15 10 4 8 8 1. State the following values for this set of data: a) Mean _8 b) Median _8__ c) Mode(s) _8 2. What is the shape of this distribution? Hint: Use the values of the mean, median, and mode to infer the shape of this distribution. _________

To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.

Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12

Mean = (96)/12

Mean = 8

How to Find the Median?

The median is the center of the data when it is ordered.

Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15

The center (median) is the average of the two center values = (8 + 8)/2 = 16/2

Median = 8

How to Find the Mode?

The mode of the data is 8, because 8 appeared most in the data set.

The mean is 8.

The median is 8.

The mode is 8.

Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.

Therefore the shape of the data is: perfectly symmetrical distribution.

Learn more about the mean, mode, and median on:

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