Question

Please type answers - An Introduction to Statistics An Active Learning Approach Activity 2-1

You should have found ∑X = 160, N = 16, so M = 10. Make sure you understand how each of these values was computed. 20. Although you have been able to compute the mean for a long time now, you probably don’t know “what the mean does” or how it “defines” center. The mean defines center by balancing deviation scores. In other words, the mean is the only value that perfectly balances all the positive and negative deviation scores in the distribution. What is a deviation score? Every value in a distribution is a certain distance from the mean; this distance from the mean is the value’s deviation score. In this case, we are working with a sample, and so the deviation score is computed as (X − M). For a population, the computations are the same, but the notation for the mean is µ rather than M; therefore, the deviation score notation when dealing with population is (X − µ). To understand how the mean balances deviation scores, compute each value’s deviation score by using the formula (X − M). For example, all scores of 8 have a deviation score of (X − M) = (8 − 10) = −2. The following graph has three boxes: one for the six scores less than the mean, a second for the three scores at the mean, and a third for the seven scores greater than the mean. Compute the deviation scores for each score and put them in the tables below. After you have computed the deviation scores, sum the deviations (Σ(X − M)) that are above, below, and at the mean.

56 AN INTRODUCTION TO STATISTICS deviation score. In tion score. In this case, we are working with a sample, and so the deviation puted as (X-M). For a population, the computations are the same, but then can isu rather than M; therefore, the deviation score notation when dealing wi -). To understand how the mean balances deviation scores, compute each deviation score by using the formula (X-M). For example, all scores of 8 have a Score of (X-M) = (8 - 10) = -2. The following graph has three boxes: one for the than the mean, a second for the three scores at the mean, and a third for the seve Sater than the mean. Compute the deviation scores for each score and put the below. After you have computed the deviation scores, sum the deviations (Z(X-M above, below, and at the mean. viation score is he notation for od with populat each value's have a deviation the six scores ne seven scores hem in the tales Sox-M)) that are Scores Below the Mean Deviation Score (X-M) Scores At the Mean Deviation Score (X-M) Scores Above the Mean Deviation (X-M) Score 10 10 11 10 (X-M) = (X-M) = 12 12 E(X - M) = M = Frequency 24 25. 0 TTT 5 6 7 8 9 10 11 12 13 14 Scores on Variable 15

Answer 1

Scores Below the Mean
Score	Deviation(X-M)
8	-2
8	-2
9	-1
9	-1
9	-1
9	-1
Σ(X-M) =	-8

Scores At the Mean
Score	Deviation(X-M)
10	0
10	0
10	0
Σ(X-M) =	0

Scores Above the Mean
Score	Deviation(X-M)
11	1
11	1
11	1
11	1
11	1
11	1
12	2
Σ(X-M) =	8

Sum of deviation = -8 + 0 + 8 = 0

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P.s. in the Above mean column. there should be only one 12.