Chapter 2: Modeling Distributions of Quantitative Data

Question 1

Define Percentiles

Answer 1

The percent of data “less than or equal to” a certain data value

Question 2

Interpretation of Percentiles

Answer 2

__Percentile__ % of __context__ are less than or equal to __value__.

ex. 1 = __75__% of __high school student SAT scores__ are less than or equal to __1200__.

ex. 2 = The SAT score of __1200__ is at __75__th percentile of __high school student SAT scores__.

Question 3

Define Standardized Scores (Z-scores)

Answer 3

measures how many “standard deviations” a data point is “above/below” the mean.

(data point - mean)/(standard deviation)

Question 4

Define Standardization

Answer 4

a point’s location in the distribution depends of “both” distance from the “center” and the distribution’s “spread” or “variation”

Question 5

Interpretation of Z-Score

Answer 5

__specific value with context__ is __z-score__ standard deviations __above/below__ the mean.
- above when z-score is positive
- below when z-score is negative

ex. __A quiz score of 71__ is __1.43__ standard deviations __below__ the mean. (z = -1.43)

Question 6

Description of Cumulative Relative Frequency Graph

Answer 6

y- axis = cumulative proportion (0-1)
x- axis = variable

can find IQR or percentiles by drawing dotted lines and following the graph.

Question 7

Transforming Data (addition/subtraction)

Answer 7

Mean = add/subtract
S.D. = X change
Shape = X change

Question 8

Transforming Data (multiply/divide)

Answer 8

Mean = multiply/divide
S.D. = multiply/divide
Shape = X change

Question 9

Define Density Curve

Answer 9

a curve that
1. is always on or above the horizontal axis
2. has area exactly 1 underneath it

describes the overall pattern of a distribution. The area under the curve and above any interval of values on the horizontal axis is the proportion of all observations that fall in that interval.

Question 10

Identifying mean and median of a density curve

Answer 10

mean = balancing point
median = equal area point

Question 11

Define Normal Curve

Answer 11

1. symmetric and bell shaped
2. the mean=median, both located at the exact center

Question 12

Define Empirical Rule

Answer 12

a.k.a the 68-95-99.7 Rule

The normal curves below shows markings 1, 2, and 3 standard deviations away from the mean. For each, shade the middle area and write the percent of data covered in that middle area.
1 SD away on both sides = 68 %
2 SD away on both sides = 95 %
3 SD away on both sides = 99.7 %

Question 13

Strategy of Normal Curve Problems

Answer 13

1. Draw and Label curve (include mean, SD, tick marks, shade area/point in question)
2. perform calculations (show work)
3. answer the question with context

Question 14

Using standard normal table

Answer 14

ex. z<2.45
–> draw a normal curve with N(0,1)
–> since it is “<”, draw a line of 2.45 above the mean of 0 and shade left side of the line –> find the area

Question 15

Normal Distribution and the Calculator

Answer 15

1. when finding percentages from values, use [Normal cdf]
2. when finding values from percentages, use [inv norm]

Question 16

Assessing Normality

Answer 16

checking normality using norm cdf or inv norm

1. find X bar and S of given data set
2. find IQR and calculate IQR dance values for 1 sd, 2 sd, and 3 sd.
3. find proportion of data in the interval of 1 sd, 2 sd, and 3 sd. Compare with 68, 95, 99.7 %
4. When Normal Probability Plot is checked on calculator, the graph should be linear.

Question 17

Normal Probability Plot

Answer 17

scatter plot of the ordered pair (data value, expected z-score) for each of the individuals in a quantitative data set.

1. enter values in sheets
2. plot them
3. menu - 1 - 4 and check the linearity