Unit 3 Stat - Normal distributions

Ogive

• Shows cumulative relative frequency

• Can’t be negative slope

  • Horizontal slope = gap in the data bc no values

z-score formula

• Z-score = how many standard deviations above the mean the value is

Transforming data

• Adding & multiplying changes measures of position (min, Q1, med, mean, max, basically single points etc)

• Only multiplying changes measures of spread (SD, IQR, range)

Density curves

• Area under curve always = 1

• The area under the curve btwn 2 points gives the proportion of all observations that fall within that range

• < is the same as <= sign

• P(x < 1) means what is the % probability that x is less than 1 (use normalcdf)

mean, SD symbols

x̄ = sample mean

μ = population mean

S_x = sample SD

σ = population SD

note: use population mean & SD for normal curves & stuff

Normal distribution curve empirical rule

• 68, 95, 99.7, 100

If the question asks “what is the % at exactly -3 standard deviations?” what is the answer

0. This is a line segment, not an area. so no percentage

Normal distribution question; find the % above/below a value

Normal distribution question; find the % btwn values

Normal distribution question; finding value from %

How to assess normality

• Enter data into calc

• 2nd → y= → plot 1 → select scatterplot, the one all the way on the right

• Draw a sketch, write a sentence

• If line is linear + not much space inbetween dots, say “since the normal probability plot” is roughly linear, the data are approximately normally distributed

• If there is a cluster of data values on the right, then its skewed left, and vice versa

• you CANT assess normality using a boxplot - only shows a summary, not the actual values