Ch 4. Summarizing Univariate Data Using Statistics

What are the measures of center?

mean, median, mode

mean

the sum of observations divided by the total number of observations (aka: finding the average)

median

the midpoint

what symbol denotes the sample mean?

An X with a bar ___ over the top

how to find the midpoint?

1. arrange all observations in ascending order (small to large)

2. If the number of observations is odd, then the median is the middle value

3. If the number of observations is even, then the median is the average of the two middle values

how to interpret the median

50% of the observations are smaller than the median (or 50% of the observations are larger than the median)

ex: 10 out of 20 randomly selected tomatoes weigh less than 2 ozs (or 50% of 20 randomly selected....)

Mode

The value that occurs most frequently in a given data set.

if no value occurs more than once, there is _____

no mode

if one value occurs with the greatest frequency, it is _____

unimodal

if two valvues occur with the same greatest frequency, it is _____

bimodal

if more than 2 values occur with the same greatest frequency, it is ____

multimodial

_____ is less effected by extreme values

the median

If right skewed or left skewed, the best measure of center is the _____

sample median, as it is less effected by extreme values that create a skewed shape

measures of variation include

range, standard deviation, variance

Range

the difference between the largest and smallest value in a data set

Symmetric data distribution shape

the mean, median and mode are all equal

right-skewed distribution shape

the mean > median > mode

left-skewed distribution shape

mean < median < mode

variance

the square of standard deviation

measures of position include

percentile, quartile, z score

percentile

divide a data set into 100 equal parts, a data set has 99 percentiles (ex: p1, p2, ....p99)

quartile

divide a data set into 4 equal parts. A data set has 3 quartiles (ex: q1, q2, q3)

What does the 99th percentile mean?

p99 divides the bottom 99% of data from the top 1%. This means 99% of values will be smaller, and 1% will be bigger

What does the second quartile (Q2) mean?

Divides the bottom 50% from the top 50%. This means 50% of the values will be smaller, and 50% will be bigger.

How to find the data value for a specific quartile?

1. arrange in ascending order (small to large)

2. substitute P into the formula

i=P/100 times n (the total # of values)

if i is a whole number, round up to the next whole number, and use that number to find the position on the data set

if i is not a whole number, take the average of that number position and the one next to it

interquartile range

the difference between Q3 and Q1. 1QR = Q3-Q1

How to find the lower limit for interquartile range?

Q1-1.5 × 1QR

How to find the upper limit for interquartile range?

Q3 + 1.5 × 1QR

Outlier

An extremely large/small data value when compared with the rest of the data values in a set

What constitutes a potential outlier?

Any value smaller than the lower/larger limits

Five number summary

Includes 5 values of a data set. The median, minimum, maximum, Q1 and Q3

Box plot

a visual representation of the 5 number summary