CHAPTER 4 Displaying and summarizing quantitative data

Question 1

How are quantitative data represented

Answer 1

1.HISTOGRAM
. The Horizontal axis the bins are joined together with equal widths
. It is a summary of the distribution of quantitative variable but they don;t show the data values themselves
2. STEM AND LEAF
3. DOTPLOTS

Question 2

RELATIVE FREQUENCY HISTOGRAMS

Answer 2

replaces the counts on the vertical axis with the percentage of the total number of cases falling in each bin.
. The Horizontal axis the bins are joined together with equal widths

Question 3

STEM AND LEAF

Answer 3

Is like a histogram, but shows the individual values

Question 4

DOT PLOTS

Answer 4

A simple display that places a dot along an axis for each case in the data ( similar to stem and leaf)

Question 5

QUANTITATIVE DATA CONDITION

Answer 5

Values of quantative variables whose units are known

Question 6

MODE

Answer 6

SINGLE VALUE THAT APPEARS MOST OFTEN ( for categorical values)
. for quantitative it is the HUMPS ( UNIMODAL, BIMODAL, MULIMODAL, UNIFORM)

Question 7

Uniform

Answer 7

Is a histogram in which all the bars are approximately the same height

Question 8

TAILS

Answer 8

the thinner ends of a histogram

Question 9

SKEWED

Answer 9

if one TAIL stretches out further than another. the graph is skewed toward the longer tail

Question 10

OUTLIERS

Answer 10

Extreme values that don’t appear to belong to the rest of the data… unsually high oe low values

Question 11

GAP

Answer 11

A region that has no values

Question 12

CENTER OF MEASURE

Answer 12

A single, typical value of a data set

Question 13

2 types of Center of Measure

Answer 13

1. Mean

2. Median

Question 14

MEDIAN

Answer 14

The middle value

Question 15

IQR

Answer 15

Upper percentile- lower percentile

It is a reasonable summary of the spread of a distribution except when the dat is strongly bimodal

Question 16

Q1( lower) and Q3( upper)

Answer 16

are also known as the 25th and 75th percentiles of data ( since the lower quartile falls above 25% of the data and the upper quartile falls above 75% of the data

Question 17

Q2

Answer 17

median ( 50th percentile)

Question 18

5 N SUMMARY of a distribution

Answer 18

reports its median, quartiles, and extremes ( maximum and minimum)
1. minimum
2. maximum
3. Q3
4. median
5 Q1

Question 19

N

Answer 19

The number of data values

Question 20

bar over a symbol

Answer 20

find the mean

Question 21

Why is the median considered to be RESISTANT to values

Answer 21

because it resist values that are extraordinarily large or small and ignores their distance from the center

Question 22

STANDARD DEVIATION (S)

Answer 22

takes into account how far each value is from the mean.

Like the mean the standard deviation is only for symmetric data

Question 23

VARIANCE (s^2)

Answer 23

The squared average deviation of individual data value from the mean

Question 24

If data values are far from center ( what happens to the spread)

Answer 24

The spread ( IQR and SD) will be large

Question 25

If data values are close center ( what happens to the spread)

Answer 25

The spread ( IQR and SD) will be small)

Question 26

What does measures of value tell

Answer 26

How well other summaries describe the data

Question 27

When data is skewed what measure of center should be used

Answer 27

The median ( spread: IQR)

Question 28

When data is symmetric what measure of center should be used

Answer 28

The mean (spread : STD)

Question 29

STEPS TO REPRESENTING Quantitaive DATA

Answer 29

1 Make a histogram or stem leaf display

2. Discuss the center and spread
   a. If the shape is skewed report the median and IQR
   b. If the shape is symmetric report the mean and standard deviation ( for unimodal symmetric data the IQR is usually larger than the standard deviation.
3. Discuss any unusual features ( modes, outliers)

Question 30

median is paired with

Answer 30

IQR

Question 31

mean is paired with

Answer 31

standard deviation

Question 32

a Histograms x and axis

Answer 32

x axis - the WHAT that was measured

y axis - the COUNT

Question 33

BAR GRAPHS -bars

Answer 33

indicate how many cases /counts of categorical data are piled into each category

Question 34

histogram bars

Answer 34

represent counts of data piled into intervals of quantitative variable

Question 35

what statistical summaries require the data must be in order

Answer 35

1. median

2 quartiles/percentiles, IQR

Question 36

summary statistics that are resistant to ouliers

Answer 36

1. Median

2. IQR

Question 37

summary statistics that are not resistant to ouliers

used only on symmetric data

Answer 37

mean and standard deviation ( they are sensitive to outliers

Question 38

3 things to look at for a histogram

Answer 38

1 shape: symmetry, mode, skewed

2. center
3. spread

Question 39

MIDRANGE

Answer 39

average of the minimum and maximum values

Question 40

RANGE

Answer 40

. single value

. maximum-minimum

Question 41

MEASURES OF SPREAD

Answer 41

range, IQR,variance , standard deviation

They tell how well other summaries describe the data