Chapter #8 - 10/21/24

Question 1

Explain what is meant by a frequency curve for the possible values of measurement variable :

Answer 1

A frequency curve is a smooth line that shows the overall pattern of data for a measurement variable, like height, weight, or test scores. It tells us how often each possible value occurs across the range of data.

Question 2

Describe the characteristics of a bell-shaped frequency curve :

Answer 2

A bell-shaped frequency curve, also called a normal distribution, has these key characteristics:
- Symmetry: It’s perfectly symmetrical around the center.
- Mean = Median = Mode: All three are located at the center peak.
- Tails: The curve gradually tapers off on both sides, extending towards infinity without touching the axis.
- 68-95-99.7 Rule: About 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.

Question 3

Explain how the Empirical Rule is used to provide information about a normal distribution with specific mean and standard deviation :

Answer 3

The Empirical Rule helps us understand how data is distributed in a normal distribution:
- 68% of data falls within 1 standard deviation of the mean.
(This means that about 68% of values are between the mean minus one standard deviation and the mean plus one standard deviation.)

• 95% of data falls within 2 standard deviations of the mean. (So, about 95% of values lie between the mean minus two standard deviations and the mean plus two standard deviations.)
• 99.7% of data falls within 3 standard deviations of the mean. (Nearly all values (99.7%) are between the mean minus three standard deviations and the mean plus three standard deviations.)

Question 4

Suppose you are taking a class with 200 students and you learn that your score on the last exam was at 70th percentile. What does that mean?

Answer 4

how many students in class were below you

Question 5

what is a “standardized score”?

Answer 5

the number of standard deviations an individual falls above or below thte mean for the whole group

Question 6

what is a “bell shaped curve” ? what does it look like ?

Question 7

what are frequency curves ?

Answer 7

Smoothed-out histogram by connecting tops of rectangles with smooth curve

Question 8

TRUE OR FALSE

all frequency curves are bell-shaped?

Answer 8

FALSE

not all frequency curves are bell-shaped

Question 9

describe a frequency curve that follow a right skewed distribution :

Answer 9

values to the left more clumped together; values to the right more spread out

Question 10

describe a frequency curve that follow a left skewed distribution :

Answer 10

values to the right more clumped together; values to the left more spread out

Question 11

describe mean and median in regards to a right skewed frequency curve :

Answer 11

mean > median

Question 12

describe mean and median in regards to a right skewed frequency curve :

Answer 12

mean < median

Question 13

FILL IN THE BLANK

the long right tail pulls the mean to the _______

Answer 13

right

Question 14

what does the total area frequency curve =

Answer 14

1 for 100%

Question 15

proportion of population of measurements falling in a certain range =

Answer 15

area under curve over the range

Question 16

when does the mean = the median ?

Answer 16

in symmetric distributions

Question 17

economy/money usually equals what ?

Answer 17

skewed to the right usually

Question 18

height usually equals what ?

Answer 18

symmetric

Question 19

many populations of measurements follow approximately a normal curve :

Answer 19

• physical measurements within a homogeneous population - heights of male adults
• many psychological attributes (IQ)
• standard academic tests given to a large group (SAT scores)

Question 20

all normal curves have the same shape :

Answer 20

symmetric, unimodal and bell-shaped

Question 21

FILL IN THE BLANK

normal curves are completely describe by giving its ______ and _____________

Answer 21

mean μ and standard deviation σ

Question 22

where is the mean located in normal curves ?

Answer 22

at the center of the curve and is the same as the median

Question 23

in a normal curve, what does changing the mean do to the cuvre ?

Answer 23

moves the curve along the horizontal line (increasing the standard deviation makes the area under the curve to be less concentrated around the mean)

Question 24

what does your percentile = ?

Answer 24

the percentage of the population that falls below you

Question 25

what does finding percentiles for nomal curves require :

Answer 25

• your own value
  the mean for the population of value (μ)
• the standard deviation for the population (σ)

Question 26

TRUE OR FALSE

the standard normal (bell-shape) curve can be used to find percentiles

Answer 26

TRUE

Question 27

what is another name for standardized score ?

Answer 27

z-score

Question 28

what are IQ scores with a noraml distributions mean and standard deviation ?

Answer 28

IQ scores have a normal distribution with a mean of 100 and a stadard deviation of 15

Question 29

what is the formula for standardized score ?

Answer 29

χ - μ / σ

Question 30

what does “χ” represent ?

Answer 30

observed value

Question 31

what does “μ” stand for ?

Answer 31

mean

Question 32

what does “σ” stand for ?

Answer 32

standard deviation

Question 33

suppose you IQ score was 115, what is you standardized score ? (mean of 100 and standard deviation of 15)

Answer 33

(115 - 100) / 15 = +1

Question 34

if your IQ score is +1, what does this mean ?

Answer 34

your IQ is 1 standard deviation above the mean

Question 35

what is a normal curve with a mean = 0 and a standard deviation = 1 called ?

Answer 35

standard normal curve

Question 36

what is a z table ?

Answer 36

a chart that shows the probability, or area, under a standard normal curve (bell curve) for different z-scores. A z-score represents how many standard deviations a data point is from the mean. By looking up a z-score in the z-table, you can find the percentage of data that falls below that score in a normal distribution.

Question 37

how do you read a z table ?

Answer 37

So, for a z-score of 1.28, you’d look up 1.2 on the left and 0.08 on the top, which will give you a value close to 0.8997. This means 89.97% of the data lies to the left of a z-score of 1.28.

Question 38

how to find a percentile from an observed value ?

Answer 38

1) find the standardized score = (bserved value - mean) / s.d., where s.d. = standard deviation (dont forget to keep the plus or minus sign)
2) look up the percentile in table

Question 39

1) Suppose your IQ score was 115
2) Standardized score = (115 – 100)/15 = +1
3) Your IQ is 1 standard deviation above the mean.
4) From Table 8.1 you would be at the 84th percentile.

what would you IQ be higher than ?

Answer 39

that of 84% of the population

Question 40

what is the empirical rule ? (for any normal curve)

Answer 40

• 68% of the values fall within 1 standard deviation of the mean in either direction
• 95% of the values fall within 2 standard deviations of the mean in either direction
• 99.7% of the values fall within 3 standard deviations of the mean in either direction

Question 41

when would a measurement be considered an extreme outlier ?

Answer 41

if it fell more than 3 standard deviations above or below the mean

Question 42

what is the empirical rule ?

Answer 42

The empirical rule is a guideline for data that follows a normal distribution (bell-shaped curve). It says:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.