Chapter 2

Question 1

Percentile

Answer 1

The pth percentile is the value of a quantitative variable which is greater than p% of the data. In other words, p% of the data are below that value. Example: Kassidy is 61.5 inches tall, and in the 26th percentile….this means that 26% of 14 year old girls are 61.5 inches or shorter.
Very good example!

Question 2

What is a Matched Pair Experiment? Name an example.

Answer 2

A matched pair experiment is one where each case is assigned both treatments, in random order, rather than one where some cases receive one treatment, and some receive the other. We are then able to see the response in both cases.

Example: Testing the effectiveness of a migraine medication with a matched pair design would mean each person is given a placebo, AND the medication in random order, and followed each time.

Question 3

Range

Answer 3

The difference between the largest and smallest value in a set of data, wether it be values given, a box-blot, histogram, bar graph, etc. The range is of a data set is found by subtracting the sample minimum from the maximum.
Example: If you were given data of the ages of 5 random US citizens; 18, 20, 24, 32, 48,…. the range would be 30 ( 48-18) Largest value minus the smallest value.

Example2: If we were to be asked to find the range between 8,25,34,40,52 the range would be 44.

Question 4

Explanatory Variable

Answer 4

An explanatory variable is an independent variable that is manipulated and acts directly upon the subject (dependent variable). This variable induces a change in the response variable which changes in accordance with what has been imposed upon it.

Example: The amount of sugar in a multitude of ice cream brands and children’s subsequent hyperactivity levels in correlation and repsonse to these sugar amounts and how much the cases (children) are exposed to them, with the explanatory variable being the amount of sugar in the ice cream and how this impacts the children’s hyperactivity levels. The sugar amount (explanatory variable) is directly acting on the children’s hyperactivity levels and thus bringing about a change on the dependent variable (hyperactivity levels).

Question 5

Z-Score

Answer 5

Z-Score tells us how many standard deviations our point in from the mean. Values of a Z-Score that is less than -2 or grater than 2 is and indication of a extreme value.

Example: Let’s say that the mean weight of all people is 150 lbs, with a standard deviation of 25. This means that if you were comparing a person that weight 190lbs to the population they would have a Z-Score of 1.6(190-150 = 40 / 25 = 1.6). Which means they are 1.6 above the mean.

Question 6

Dataset

Answer 6

A Dataset is a collection of information organized on a table. The table can vary in appearance, but typically use rows and columns to distingush the data into organized and readable charts. Each of the elements can be manipulated to update the information as it changes or more becomes available.

Question 7

Categorical Variable

Answer 7

Represents data that may be divided into groups. Nominal variable has two or more categories. An example of a categorical variable would be hair due to hair having many different colors.

Question 8

Quantitative Variable

Answer 8

A quantitative variable measures or records a numerical quantity for each case. numerical operations like adding and averaging make sense for quantitative variables.
EX: average of test scores like the ACT and SAT, amazon rating

Question 9

Pie Chart

Answer 9

Pie Chart is defined as a type of graph that displays data in circular graph and it has what we call slices and each slice of the pie is relative to the size of category in the whole group. Example: Pie chart representing students 3 courses then each slice will hold one course with its corresponding value.

Question 10

5 Number Summary

Answer 10

The 5 number summary is used to summarize data. The five numbers are:

Minimum

the first quartile Q1 (The lower half of the data)

the median

the third quartile Q3 (the upper half of the data)

Maximum

3, 4, 4, 7, 10, 12, 13, 13, 13, 15, 27

1. ) You wanna start by ascending your numbers from smallest to greatest.
2. ) Then find the smallest number, which is going to be your minimum
3. ) then your Maximum, the largest number
4. )Next finding the median, which is 12

(I find it easier to add parenthesis, to find Q1 and Q2)

(3, 4, 4,7, 10) 12 (13, 13, 13, 15, 27)

5. ) to find Q1, you would start from the smallest number to the number before 12, and find the median of that lower half. which is 4
6. ) to find Q3, you would start with the number 13 to 27, and find the median of that upper half, which is 13

Min: 3

Q1: 4

Median: 12

Q3: 13

Max: 27