Statistics - Single Variable, Ch 18

Question 1

descriptive statistics

Answer 1

Allows us to measure the center and spread of the data

Question 2

a population

Answer 2

a collection of individuals or objects about which we want to draw conclusions

Question 3

a census

Answer 3

the process of collecting data from the whole population

Question 4

sample

Answer 4

a group of individuals from the population.
Conclusions based on a sample are not as accurate as conclusions based on the whole population, but if the sample is chosed carefully (if it is representative of the whole), then reliable conclusions can be drawn.

Question 5

a survey

Answer 5

the process of collecting data from a sample

Question 6

a biased sample

Answer 6

a sample in which the data has been unfairly influenced by the collection process and is therefore not truly representative of the whole population

Question 7

a categorical variable

Answer 7

describes a particular quality or characteristic
Examples: Continent of Birth (Europe, Asia, North America, Africa); occupation of workers at hospital (nurse, doctor, cleaner, secretary, etc.)

Question 8

a quantitative variable

Answer 8

A variable in which data is given in number form. Often called a numerical variable.

Question 9

a discrete quantitative variable

Answer 9

Takes an exact number value; it is usually the result of counting.
Examples: the number of goals scored, the number of boxes in a truck

Question 10

a continuous quantitative variable

Answer 10

Takes any numerical value within a RANGE. It is usually the result of measuring.
Examples: the weight of pumpkins (likely between a 1 kg and 15 k range), the width of a child’s hand (likely between 2 cm and 10 cm).

Question 11

stem-and-leaf diagram

Answer 11

A way of presenting data. The stem shows the first number(s) of a number while the leaf column shows the “ones” digit. For example, if you have the numbers 8, 12, 15, 24, then your stem column will have a 0 (for the 8), 1, and 2, while the leaf column will show the 8 (aligned with 0), the 2 and 5 aligned with the ‘1’ (for 12 and 15), and 4 (to go with the 2 for “24”).

A back-to-back stem-and-leaf diagram (p. 279) lets you compare two sets of data (for two different things).

Question 12

symmetrical distribution

Answer 12

Like a perfect (bell) curve charting data: if the curve that you can draw over the data is symmetrical, it’s said to have a symmetrical distribution

Question 13

positive skew

Answer 13

If, when you draw a curve over your data, it has a long “tail” to your right (if the right side is “stretched”), then it’s said to have a positive skew

Question 14

class intervals

Answer 14

If you don’t want to chart every number, every data point, then you’ll bunch them into groups or ranges (10-19, 20-29, 30-39) , so you have a class interval of 10 and you just chart how many things fall into each class interval (range).

Question 15

modal class

Answer 15

Refers to the class interval that occurs the most frequently in the data.
If most of the people living in a city are between the ages of 30 and 39, then that’s the modal class.

Question 16

frequency histogram

Answer 16

A bar chart where there’s no white space between the bars. You use it to show that the data is continuous instead of discrete (separate). (p. 281)

Question 17

a bimodal data set

Answer 17

A bimodal data set has two values that are “tied” for occuring the most frequently.

Question 18

the mean

Answer 18

The “mean” is the statistical name for the arithmetic average – written as an x with a bar over it, which you read as “x bar.”
You get it by adding all the data values together and dividing by the number of data values.
Example: In data set {2,5,5, 8, 10} you’ve got five pieces of data (five numbers) adding up to 30, and 30 divided by 5 = 6, so the mean is 6.

Question 19

the median

Answer 19

The median is the MIDDLE VALUE of an ordered data set.
For a data set with an odd number of data values {2, ,6, 7, 13, 19}, then the median is 7–the middle number.
For a data set with an even number of data values {2, 6, 7, 13, 19, 22}, you take the middle two numbers and find the average (7+13=20 and 20/2=10) – so 10 is the median.
When you find the median, you can say half of the data are above that number and half are below.

Question 20

the range

Answer 20

The range is the difference between the maximum (largest) and the minimum (smallest) data value.
Say your data set is { 2 3 1 3 2 2 4 5 1 5 2 1}
The largest value above is 5 and the smallest is 1: 5-1=4, so the range is 4.
The range is considered to be a relatively uninformative measure of the “spread” of data because it only uses two data values and can be influenced by outliers that aren’t representative of the data set.

Question 21

quartile

Answer 21

The median divides the ordered data set into two halves. Divide those halves in half again and you get:
QUARTILES
The middle value of the lower half is called the “lower quartile” or “25th percentile.”
The middle value of the upper half is called the “upper quartile” or the “75th percentile.”

Question 22

interquartile range (IQR)

Answer 22

The IQR is the range of the middle half – or 50% – or the data.
IQR = upper quartile - lower quartile

			(p. 290)

Question 23

How to estimate the center (midpoint) of data in class intervals

Answer 23

Make a chart showing the frequency of each class interval. Note the midpoint of each interval. Multiply frequency x interval midpoint, add them all up and divide by the total frequency. (See Example 11 on p. 292)

Question 24

cumulative frequency graph

Answer 24

The cumulative frequency gives a running total of the scores up to a particular value. It is the total frequency up to that value.

In a cumulative frequency graph, we plot the cumulative frequencies on the vertical axis. We can use the graph to find percentiles, including the quartiles and the median.

We can use cumulative frequency to calculate the a data value’s percentile:
percentile = cumulative frequency divided by the number of data values, and then multiply that by 100%.
(See p. 295-6)