Statistics Midterm

Question 1

Descriptive statistics

Answer 1

Consists of collection, organisation, summarisation and presentation of data.

Question 2

Inferential statistics

Answer 2

Consists of generalising from samples to population, performing estimations, hypothesis testing, determining relationships among variables, and making predictions.

Question 3

Population

Answer 3

Consists of all subjects that are being studied.

Question 4

Sample

Answer 4

Is a group of subjects selected from the population.

Question 5

Parameter

Answer 5

A measure that describes a characteristic of a population.

Question 6

Statistic

Answer 6

A measure that describes a characteristic of a sample.

Question 7

Selection bias

Answer 7

A distortion of evidence or data that arises from the way that the data are collected.

Question 8

Variable

Answer 8

A characteristic or attribute that can assume different values.

Question 9

Data

Answer 9

The values that variables can assume.

Question 10

Qualitative variable

Answer 10

The characteristic being studied is non numeric.

Question 11

Quantitative variable

Answer 11

Information is reported numerically.

Question 12

Discrete variable

Answer 12

Can only take on a finite number of values. (ex people)

Question 13

Continuous variables

Answer 13

Can only take on an infinite number of values. (ex hight/ time)

Question 14

Nominal level of measurement

Answer 14

Classifies data into mutually exclusive (no overlapping), exhaustive categories in which no order or ranking can be imposed.

Question 15

Ordinal level of measurement

Answer 15

Classifies data into categories that can be ranked. (precise differences between the ranks do not exist).

Question 16

Interval level of measurement

Answer 16

Ranks data, and precise differences between units of measurement do exist. However, there is no meaningful zero. (ex temperature)

Question 17

Ratio level of measurement

Answer 17

Ranks data, and precise differences between units of measurement do exist. A true zero exists.

Question 18

Frequency table (categorical frequency distribution)

Answer 18

The organisation of qualitative data into table form, using mutually exclusive classes and showing the number of observations in each class.

Question 19

Relative frequency

Answer 19

Class frequency / total frequency

Question 20

Pie chart

Answer 20

degrees = class relative frequency * 360

Question 21

Building frequency tables

Answer 21

You should have: class limit, class boundaries, class midpoint, frequency, cumulative frequency, relative frequency + sometimes cumulative relative frequency.

Rules: between 5 to 20 classes, the classes must be mutually exclusive, the classes must be continuous, the classes must be exhaustive (cover full data range), the classes must be equal width.

Procedure: determine class range, decide number of classes, decide the width, set class limits and boundaries, count the number of occurrences in each class.

Question 22

Cumulative frequency

Answer 22

The total number of values that are less than a given upper class boundary.

Question 23

Class midpoint

Answer 23

Lower + upper class limit / 2

Question 24

Histogram

Answer 24

Display the data by using vertical bars of various heights to represent the frequencies.
Vertical line: frequencies
Horizontal line: class boundaries

Question 25

Frequency polygon

Answer 25

Display the data by using lines that connect points plotted for the frequencies at the midpoint of the classes.
Vertical line: frequencies
Horizontal line: class midpoint

Question 26

Ogive / cumulative frequency

Answer 26

Represents the cumulative frequencies for the classes in a frequency distribution. The line will alway go up.
Vertical line: cumulative frequency
Horizontal line: upper class boundaries

Question 27

Mean

Answer 27

The sum of the values, divided by the total number of values.

Question 28

Rounding rule of the mean

Answer 28

The mean should be rounded to one more decimal place than occurs in the raw data.

Question 29

X-bar x̄

Answer 29

Sample mean

Question 30

μ

Answer 30

Population mean

Question 31

Weighted mean

Answer 31

When some values are of more importance. Ex calculating the grade.

Question 32

Median

Answer 32

The midpoint of an ordered data set. (when the data is arranged in order.

Question 33

Mode

Answer 33

The value that occurs most often in the dataset.

If you don’t have a mode, it’s called bimodal.

Question 34

Midrange

Answer 34

lowest + highest values / 2

Question 35

Normally distributed data

Answer 35

When it looks like a pyramid. Zero skewness. It has approximately the same amount of values on both sides. The top is in the middle.

The mean is the most used to find the average.

Question 36

Positive skewness

Answer 36

When the top is on the right. (ex with salaries)

The median is the most used to find the average.

Question 37

Negative skewness

Answer 37

The top is to the left. (ex exam grades.)

The median is the most used to find the average.

Question 38

Range

Answer 38

Highest value - lowest value

Question 39

Variance

Answer 39

The average of the squares of the distance each value is from the mean.

1. Find the mean
2. Value - mean
3. Square the result
4. Add the result together
5. (sample) Divide the result by the total number of numbers in the data set minus one.
   (population) Divide the result by the total number of numbers in the data set.

Question 40

Standard deviation

Answer 40

The square root of the variance.

Question 41

Chebyshev’s theorem

Answer 41

1-(1/k^2)

Step 1: difference between value and mean / standard deviation

Step 2: 1-(1/k^2)