Chapter 2: Descriptive Statistics

Sampling variability

Sampling variability

the observed value of a statistic depending on the particular sample selected from the population and it will vary from sample to sample

Standard error of the mean

indicates how different the population means is likely to be from a sample mean.

The central limit theorem

states that the distribution of sample means approximates a normal distribution as the sample size gets larger.

Standard deviation

a number that is equal to the square root of the variance and measures how far data values are from their mean

Variance

average of the squares of the deviation

Symmetrical

a figure or shape that can be divided into two equal parts by a line

Skewed to the left

the graph is pulled out to the left.

Skewed to the right

the graph is pulled out to the right.

Mean

a number that measures the central tendency of the data; a common name it is 'average.'

Median

a number that separates ordered data into halves

The sample mean

The average number of the sample

Population mean

The average number of the population.

Mode

The value that appears most often in a set of data.

The Law of Large Numbers

if you take samples of larger and larger size from any population, then the mean x of the sample is very likely to get closer and closer to µ.

Sampling distribution

a probability distribution of a statistic that comes from choosing random samples of a given population

Relative frequency distribution

the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes

Relative frequency table

a data representation in which grouped data is displayed along with the corresponding frequencies

Box plots

a graph that gives a quick picture of the middle 50% of the data

x

the number of data values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile.

y

the number of data values equal to the data value for which you want to find the percentile.

n

the total number of data.

Formula for percentile

x + (0.5y/n) (100)

k

the kth percentile. It may or may not be part of the data.

i

the index (ranking or position of a data value)

n

the total number of data

kth percentile

i = (k/100)(n + 1)

Quartiles

the numbers that separate the data into quarters; may or may not be part of the data

Percentiles

a number that divides ordered data into hundredths

First quartile

the value that is the median of the lower half of the ordered data set

Interquartile range

is the range of the middle 50 percent of the data values; found by subtracting the first quartile from the third quartile.

IQR

Q3 - Q1

Smaller outlier

Q1 - IQR(1.5)

Larger outlier

Q2 - IQR(1.5)

Histogram

a graphical representation in the x-y form of the distribution of data in a data set; x represents the data and y represents the frequency or relative frequency. The graph consists of contiguous rectangles.

Frequency Polygons

looks like a line graph but uses intervals to display ranges of large amounts of data

Convenient starting point

a lower value carried out to one more decimal place than the value with the most decimal places

Discrete data

type of data that includes whole, concrete numbers with specific and fixed data values determined by counting

Paired data set

two data sets that have a one-to-one relationship so that

Stem-and-leaf graph or stemplot

easy to compute the median and other quantiles. Each data point is converted into stem and leaf, e.g., 438 (stem

Outlier

an observation that does not fit the rest of the data

Line graph

A graph used to show changes over time

X-axis

this is the explanatory variable

Data values

the content that fills a space in a record

Y-axis

the response variable

Frequency

the number of times a value of the data occurs

Bar graphs

used to display grouped data or categorical data; the identity of the sample points within the respective groups is lost