16 - Averages and the normal distribution

Question 1

grouped data definition

Answer 1

where the frequency is shown in terms of a range

Question 2

ungrouped data definition

Answer 2

individual data points

Question 3

how to find mode from grouped data (most commonly in a histogram)

Answer 3

identify highest frequency class, draw diagonal line from top of block to either side of the highest class
intercept = estimated modal value readable from x axis

Question 4

how to find median from an ogive

Answer 4

median rank = cumulative total of the variable / 2

then look across y axis at this rank

Question 5

advantages and disadvantages of mean

Answer 5

+
- used frequently
- understood
- uses all data

• may not be value in distribution
• distorted by extreme high low values
• ignores dispersion

Question 6

advantages and disadvantages of mode

Answer 6

+
- not distorted by high/low values
- corresponds to actual value in data

• ignores dispersion
• doesnt take all data into account

Question 7

advantages and disadvantages of median

Answer 7

+
- not distorted by high/low values
- corresponds to actual value in distribution

• ignores dispersion
• limited use

Question 8

what is dispersion

Answer 8

method of determining location or central point of distribution

shows the spread of a variable about its average

standard deviation is a measure of dispersion, larger the SD, more dispersed the data is

Question 9

what is x in grouped data

Answer 9

the mid point

Question 10

how to work out fx2 (squared)

Answer 10

frequency multiplied by x2

Question 11

what is the coefficient of the variance

Answer 11

standard deviation as a % of the mean - higher %, higher dispersion

Question 12

properties of standard deviation

Answer 12

• based on all values in distribution
• suitable for further statistical analysis
• more difficult to understand

Question 13

what is variance

Answer 13

square of standard deviation

Question 14

what is range and quartiles

Answer 14

RANGE = measure of spread between highest and lowest values

QUARTILES = divide distribution into quarters

Question 15

interquartile range

Answer 15

Q3 - Q1

Question 16

quartile deviation

Answer 16

1/2 (upper quartile - lower quartile)

Question 17

decile

Answer 17

distribution in 1/10ths

Question 18

normal distribution

Answer 18

distribution symmetrical around the mean - important as it arises in real life

Question 19

reason for bell shape

Answer 19

higher concentration closer to mean and lower away from mean

is always symmetrical and either side represents 50%

Question 20

what is the total area under the curve

Answer 20

100% of population

Question 21

properties of normal distribution

Answer 21

• width is measured as standard deviation, 3 standard deviations on each side of mean
• range is 6 standard deviations

Question 22

what is a Z score

Answer 22

distance from the mean in the normal distribution measured by number of standard deviations they represent

eg,
translates 1.9 standard deviations away from the mean into a % away from mean

Question 23

adjustment factor formula

Answer 23

standard class width / current class width

Question 24

how to find the likelihood of something from raw numbers

Answer 24

1. identify z score using formula given of x - mean / SD
2. read off the table to find the % within that z score
3. manipulate figure to find out what q is asking eg, more, less or between

Question 25

how to find the value of x when given a % above or below

Answer 25

1. identify what z score to find, eg if we are finding 80% above, we need to find a z score from 30% (50% already accounted for by the mean)
2. find z score with this % then substitute into the formula
3. solve formula to find x