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Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

Solutions

Chapter
Section
BuyFindarrow_forward

Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

A sample consists of the following n = 7 scores: 5, 0, 4, 5, 1, 2, and 4.

a. Compute the mean and standard deviation for the sample.

b. Find the z-score for each score in the sample.

c. Transform the original sample into a new sample with a mean of M = 50 and s = 10 .

To determine
  1. Mean and standard deviation for the sample.
  2. Z-score for each score in the sample.
  3. Transform the original sample into a new sample with a mean of M = 50 and s = 10.
Explanation

Given:
n = 7
Scores: 5,0,4,5,1,2,4
M = 50
s = 10

Formula used:

a)samplemean(M)=1ni=1nXisamplestandarddeviation(s)=1/n-1* i=1 n (X i -X¯) 2 b) z = x-μσc) x = M+z*s

Calculation:

  1. Sample mean = (5+0+4+5+1+2+4)/7 = 3
  2. X (x-xbar)2
    5 4
    0 9
    4 1
    5 4
    1 4
    2 1
    4 1
    21 24

    Sample standard deviation = 24/7-1 = 2

  3. z-scores are:
  4. 5,0,4,5,1,2,4

    For x = 5,
    Z = (5 − 3) / 2 = 1

    For x = 0,
    Z = (0-3) / 2 = -1.5

    In this way we will find all the z-scores.

    X z-scores
    5 1
    0 -1

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