Skip to main content

Normal Distribution or Bell Curve

 


The bell curve is also known as the normal curve or normal distribution. The bell curve has mathematical properties that allow researchers to draw conclusions about where scores (or data) are located relative to other scores (or data).

Click hyperlinks for more details.

The three measures of central tendency (mode, median, mean) are at the same middle point in a normal curve. The numbers representing the middle of the bell curve divide the distribution in half.

On the x-axis in the normal distribution, the mean is at zero and there are standard deviation units above and below the mean. 

The height of the curve indicates the percentage of scores in that area. You can see that a large percentage of the scores are between 1 and -1 standard deviations. About 68% of scores fall between +1 and -1 standard deviations from the mean. 

Look at the illustration below to see that there are about 34% of the scores in falling one standard deviation above the mean and another 34% in one standard deviation below the mean. Thus, 34% + 34% = 68%.

**********

Example: Intelligence test scores (IQ) appear to be distributed like the normal distribution within each age group. The mean IQ is 100 and one standard deviation is 15 points on most IQ tests. Thus, 68% of people of a similar age have IQ scores between 85 and 115.

Knowing that 100 is the average or mean IQ then we know that half of people taking the test are below average intelligence (as measured by the test) and half are above average intelligence.

Learn more about test scores in Applied Statistics: Concepts for Counselors available at  AMAZON   or   GOOGLE

**********

 The ends of the normal distribution are called tails. Extreme scores are in the tails. Consider the low level of the the distribution at - 2.5 or +2.5 standard deviations. At these points, the curve almost touches the x-axis; however, it never the lines of the curve never quite touch the x-axis.

Only a small percentage of scores is beyond 2.5 standard deviations in either direction. Theoretically, the tails of the curve never touch the baseline. Only a small fraction of a percent of scores is beyond 3 standard deviations.

The picture below illustrates the percentage of scores (or data) within different areas of the curve. For example, on a normally distributed test, 34.1% of scores will fall between the mean and 1 standard deviation above the mean. Because the curve is symmetrical, the same percentage will be between the mean and 1 standard deviation below the mean.


Read more about distributions in Chapter 10 of

Applied Statistics Concepts for Counselors at AMAZON    or    GOOGLE








Related posts/ pages

A-Z list of statistics

Skewed distributions


Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 

 

 

Comments

Popular posts from this blog

Personal Self-Concept Questionnaire (PSQ)

  The Personal Self-Concept Questionnaire  ( PSQ )   Overview The Personal Self-Concept Questionnaire (PSQ) measures self-concept based on ratings of 18 items, which are grouped into four categories: Self-fulfilment, autonomy, honesty, and emotional self-concept. It is a likert-type rating scale with high internal consistency values and has been used with youth and adults. Subscales : The PSQ has four subscales 1. Self-fulfilment (6 items) 2. Autonomy (4 items) 3. Honesty (3 items) 4. Emotional self-concept (5 items)  ðŸ‘‰ [ Read more about Self-Concept and Self-Identity] The PSQ is a Likert-type scale with five response options ranging from totally disagree to totally agree. Reliability and Validity In the first study, coefficient alpha = .85 and in study two, alpha = .83. Data analysis supported a four-dimensional model (see the four categories above). Positive correlations with other self-concept measures were statistically significant. Other notes The authors e...

Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ)

  Scale name: Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) Scale overview: The Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) is a 29-item self-report measure of both mathematics self-efficacy and mathematics anxiety. Author: Diana Kathleen May Response Type: Items are rated on a 5-point Likert-type scale following a “no response” option: 1 = Never 2 = Seldom 3 = Sometimes 4 = Often 5 = usually Sample items 1. I feel confident enough to ask questions  in my mathematics class. 6. I worry that I will not be able to get a  good grade in my mathematics course.   Subscales and basic statistics for the MSEAQ       Self-Efficacy M = 44.11, SD = 10.78, alpha = .93       Anxiety M = 46.47, SD = 12.61, alpha = .93       Total Scale M = 90.58, SD = 22.78, alpha = .96 Reliability: See the Cronbach’s alpha levels reported above. Validity: There were significant ...

Spiritual Bypass Scale (SBS-13)

  Assessment name:   Spiritual Bypass Scale-13 (SBS-13) Scale overview: To assess the observed spiritual bypassing phenomenon, Fox et al. (2017) developed the 13 item Spiritual Bypass Scale . Authors: Fox, Cashwell, and Picciotto    [ Read more about Spiritual Bypassing in Psychotherapy] Response Type: The 13 items are rated on a four-point scale of agreement. Scale items Data analyses from two ethnically diverse US adult samples supported two factors (Psychological Avoidance, PA; Spiritualizing, SP). PA example: When I am in pain, I believe God will deliver me from it SP example: When someone I know is in trouble, I believe it is because they have done something wrong spiritually.   Psychometric properties Cronbach’salphas: Total scale = .85, PA = .82; Sp = .75. The total SBS score was associated with the ASPIRES subscales except for connectedness. PA was associated with depression and SP with stress and anxiety (DASS-21). The over...