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psy230
chapter 2
| Question | Answer |
|---|---|
| Most commonly used score,representative value of a group of scores (distribution) best measure of;the ordinary average; the sum of all scores divided by the # of scores = the average; arithmatic av group of scores: sum of scores /# of scores | Mean (M) |
| Sum of; add up all the scores following; add up all the numbers following; most common arithmatic symbolused in statistics | E (Sum Of) |
| stands for the scores in the distribution of the variable X; if there is only one variable it is called X; if a second variable it is Y and sometime X with sub scripts ie X1, X2 | X (Scores in the distribution of the variable X) |
| italic capital N stands for number the number of scores in a distribution | N (The number of scores) |
| another measure of the representative (or typical) value in a groupof scores. most common SINGLE value in a distribution. the value with the largest frequency in a frequency table, the high point or peak of a distribution's frquency polygon or histogram | Mode |
| Middle score when all scores in a distribution are arranged from highest to lowest | Median |
| Score with an extreme value ( very high or very low) in relation to the other scores in the distribution | Outlier |
| you can describe a group of scores (distribution) by: it refers to the middle of the group of scores; it gives the central tendency of a group of scores. its an efficient way to describe a group of scores. | Representative (typical) value |
| a measure of variability (variance) | variance |
| a measure of variability (variance) | standard deviation |
| it describes a particular score in terms of how much the scores will vary from the average; by combining the mean with standard deviation creates ______ | Z score |
| Three representative scores: | Mean, mode, and median |
| In a perfectly symmetrical unimodal distribution the ______ is the same as the ___________ | Mode, Mean |
| Name and define 3 measures of the representative value of a group of scores | the mean is the ordibary average the sum of the scores divided by the number of scores The mode is the most frequent score in a distribution. the median is the middle score that is, if you line the scores up for high to low, the score half way along |
| write the formula for the mean and define each symbol | M=(EX)/N; M=mean, E= sum of (add all the following scores up), X is forthe variable whoses scores you are adding up; N= the number of scores |
| Figure the mean of the following scores 2,8,3,6,& 6 | M=(EX)/N= (2+8+3+6+6)/5=5. |
| For the following scores, Find A) the mode and B) the Median, 5,4,2,8,2 | A) 2 B) 4 |
| researchers want to know how spread out the scores are in a distribution. This shows the amount of __________ in the distribution | variability |
| Measure of how spread out a set of scores are; average of the squared deviations from the mean; the variance is the average of ea. scores squared difference from the mean | Variance |
| Score minus the mean | deviation score |
| Square of the difference between a score and the mean | squared deviation score |
| total over all the scores of each scores squared difference from the mean | sum of squared deviations |
| subtract the mean from each score; square each of these deviations scores; add up the squared deviation scores divide the sum of squared deviation by the number of scores is the procedures for? | four steps to figure variance |
| The most widely used way of describing the spread of a group of scores is the ____ ______; it is directly related to the variance and is figured by taking the square root of the variance. | standard deviation |
| square root of the average squared deviations from the mean; the most common descriptive statistic for variation; approximately the average amount that scores in a distribution vary from the mean. it is only the positive square root of the variance; | standard deviation |
| if the variance of a distribution is 400 the standard deviation is __ if the variance if 9 the standard deviation is __. square root of a number is pos. or neg to equal the number ie 9= 3x3 or -3x-3 only the pos.# is considered the standard deviation | 20,3 |
| equation to get variance, symbol for variance | SD2 (standard deviation squared) |
| equation to get standard deviation; symbol for standard deviation | SD (standard deviation) |
| formulas for the variance | SD2 = Ʃ(X-M)2 N |
| formula for standard deviation | SD= √SD2 |
| equation mathematically equaivalent to the definitional formula. It is easier to use for figuring by hand, but does not directly show the meaning of the procedure; it is a short cut formula to simplify the figuring of variance and standard deviation | computational formula (definitional as well) |
| Equation for a statistical procedure directly showing the meaning of the procedure | Definitional formula |
| computational formula that squares each score, then take sum of these squared scores. | ƩX^2 |
| Computational formula that means add up all scores first then take square of the sum | (ƩX)^2 |
| this formula tends to make it harder to understand the menaing of what you are figuring? | computational formula |
| A formula that is used to strengthen your understanding of what the figure means? | Definititional formulas |
| The variances and standard deviations given in research articles usually figured using? | N-1 |
| Define the variance? | the variance is the average of the squared deviations of each score from the mean |
| describe what the variance tells you about a distribution and how this is different from what the mean tells you? | the variance tells you how spread out the scores are (that is, their variability) while the mean tells you the representative value of the distribution. |
| Define the standard deviation? | it is the square root of the average of the squared deviations from the mean. |
| describe the standard deviation relation to the variance and explain what it tells you aproximtely about a group of scores | the standard deviation is the square root of the variance; the standard deviation tells you approximately the average amount that scores from the mean. |
| Give the full formula for the variance and indicate what each of the symbols mean | SD^2 = [Ʃ(X-M)^2]/N, SD^2 is the variance;Ʃ means the sum of what follows; X is for the scores for the variables being studied; M is the mean of the scores; N is the number of scores. |
| Figure the A) variance and B) standard deviation for the following scores: s, 4, 3, and 7 (M=4). | A) SD^2 = [Ʃ(X-M)^2]/N = [(2-4)^2 + (4-4)^2 + (3-4)^2 + (7-4)^2 /4 = 14/4= 3.5 B) SD=√SD^2 = √3.5 = 1.87 |
| explain the difference between definitional and computational formulas? | definitional, standard formula its straight forward form, shows the formula meaning of whats figured. Computational is mathematically equivalent variation of definitional & easier to use if figuring by hand w/lots of scores, tends not to show the meaning |
| What is the difference between the formula for the variance you learned in this chapter and the formula that isusually used to figure the variance in research articles? | the formula for the variance in this chapter divides the sum of the squared deviation by N (# of scores). the variance in research articles is usually figured by dividing the sum of squared deviations by N-1 (1 less than the # of scores) |
| number of standard deviations a score is above (or below if it is negative) the mean of its distribution; it is thus an ordinary score transformed so that it better describes that scores location in a distribution | Z score |
| Ordinary score (or any number in a distribution before it has been made into a Z score or otherwise transformed). | Raw score |
| makes use of the mean and standard deviation to describe a particular score; it is the number of standard deviations the actual score is above or below the mean. | Z score (if actual score is below mean it is negative and above positive) |
| formula to change a raw score to a Z score | Z=(X-M)/SD; A Z score is the raw score minus the mean, divided by the standard deviation. |
| Formula to change a Z score to a raw score | X=(Z)(SD) + M; The raw score is the Z score multiplied by the standard deviation, plus the mean. |
| What is a Z score (that is, how is it related to a raw score)? | A Z score is the number of standard deviations a raw score is above or below the mean |
| Write the formula for changing qa raw score to a Z score and define each of the symbols | Z=(X-M)/SD;Z is the Z score, X is the raw score, M is the mean, SD is the standard deviation |
| For a particular group of scores, M=20 and SD=5: Give the Z score for A) 30, B) 15, C) 20, and D) 22.5 | A) Z=(X-M)/SD;=(30-20)/5=10/5=2; B)-1; C)0; D)+.5 |
| Write a formula changing Z score to Raw score and define each symbol | X=(Z)(SD) + M; X is the raw score; Z is the Z score; SD is the standard deviation; M is the mean |
| For a particular group of scores, M=10 and SD=2. Give the raw score for a Z score of A) +2, B) +.5, C) 0, and D) -3 | A)X=(Z)(SD) + M; =(2)(2)+10 = 4+10=14; B) 11; C) 10; D) 4. |
| Suppose a person has a Z score for overall health of +2 and a Z score of overall sense of humor of +1. What does it mean to say that this person is healthier than she is funny? | she is above the average in health (in terms of how much people typically vary from average health) than this person is above the average in humor (in terms of how much people typically vary from the average in humor) |
| The mean and standard deviation and sometimes variance are commonly reported in _____ ____ | research articles |
| The ___ and the _____ are less often reported in a research article and ____ ____ are rarely reported | Median, mode, Z score |
| ___ and ______ ________ are often listed in tables | Means, standard deviations |
| The __ is the most commonly used way of describing the represenative value of a group of scores. the ____ is the ordinary average (the sum of the scores dicided by the number of scores) In symbols ___ = (ƩX)/N | Mean, Mean, M= |
| Other, less frequently used ways of describing the representative value of a group of scores are the ____ (the most common single value) and the ____ (the value of the middle score if all scores were lined up from highest to lowest) | Mode, Median |
| The ____ among a group of scores can be described by the variance (the average of the squared deviations of each score from the mean) In symbols SD^2 = [Ʃ(X-M)^2]/N | Variation |
| A __ ____ is the number of standard deviations A ___ ____ is above or below the mean. With a __ ___ you can compare scores on variables that have different scales. | Z score, Raw score, Z score |
| ______ and ____ ______ are oten given in research articles in the text or in tables. __ ___ rarely are reported in research articles. | Means, Standard deviations, Z scores. |
| The ____ _____ can describe variation among a group of scores; it is the square root of the variance; it can be best understood as aproximately the average amount that scores differ from the mean: answer and its symbol | Standard deviation SD= √SD^2 |
Created by:
larue10510