Visual Representations of Data

Question 1

Define tabulation of scores

Answer 1

has a set of categories and frequency within each category (how many people got that score)
- representation of how scores are distributed over the scale
- all value are organised from highest to lowest
N = total number of observations
X = scale categories
f = scores
Xf = sum of all the scores

Question 2

define histogram

Answer 2

• visual representation of the distribution of scores
• rectangles represent frequencies of observation at each score/interval
• only 1 show 1 set of data
• quantitative data
  -has real limits
  -NOT a bar graph
  p (proportion) = frequency/ total # of observations = 1.0
  N = total # of observation
  % = p x 100%
• frequency or proportion as a y value has no effect on the shape of the histogram

Question 3

how to find a grouped frequency distribution table for a histogram?

Answer 3

1. find range (high - low)
2. determine the number of internal needed
3. find interval width (want round, easy number): range/ # intervals
4. identify the upper and lower bounds of the interval (lower must be a multiple of the interval width
5. tabulate the data
6. interval limits: apparent (same numbers) and real (one decimal place more precise)

Question 4

define polygons

Answer 4

• combining multiple sets of data together
• can be used for just 1 set of data too
• better to use % when sample size are not the same
• can use frequency or percentage

Question 5

define bar graphs

Answer 5

• nominal data: no limits (ex. gender)
• ordinal data: when intervals are not the same

Question 6

how can a graph be misleading?

Answer 6

• the y-axis should always begin at the minimum
  score and extend a little past the highest observed score
• height of the blocks should be 3/4 of the width

Question 7

define population distributions

Answer 7

smooth curve: used to depict continuous data in population to indicate frequencies are relative as opposed to exact

• central tendency, variability, and shape

Question 8

how is central tendency, variability, and shape related to distribution?

Answer 8

central tendency: the values that capture teh center of the distribution
variability: the scores tendency to be close to the center or to spread out
shape: score are either symmetrically distributed (population normally, normal or bi-model) or skewed (to the negative or positive direction, usually samples)

Question 9

define percentiles

Answer 9

• points in a distribution below which a given percent of the scores lie
• P88 = 88% of the scores lie below
• higher percent is better

Question 10

define quartiles

Answer 10

divide the distribution into 4 equal parts
- Q1 = P25
- Q3 = P75
- quartiles are between the 4 25% sections

Question 11

define box-and-whiskers plot

Answer 11

• visual representation of the 3 quartiles
• box represents interquartile range (Q3 - Q1)
• Whiskers descend from the box down the Xmin and go up to Xmax
• length of whiskers can extend to 1.5 times the box length
• outliers are scores that lay beyond the whiskers
• can see variance, centrality, symmetrically
• independent and dependent variables

Question 12

define cumulative frequency/percentage

Answer 12

(cf) is the total number of observations equal to or below a score or interval in the frequency distribution
(c%) is the percentile rank of a score or interval in the frequency distribution
% = p(100) = f/N(100)
c% = (cf/N)(100)

Question 13

define interpolation

Answer 13

used to estimate value within intervals using 4 steps

Question 14

what are the 4 steps for interpolation?

Answer 14

1. what is interval value (X and c%)
2. calculate fraction on known scale: distance (top of interval/interval width)
3. distance from unknown scale: fraction x interval width
4. calculate position on unknown scale: X = upper limit - distance or percentile = upper limit - distance