Numerical Methods Part 1 M1A:3

Question 1

A measurement that represent the middle or center of the data

Answer 1

Central tendency

Question 2

The average of the population data is what?

Answer 2

Population mean (u)

Question 3

A number that is calculated from all of the population measurements that describes some aspect of the population

Answer 3

Population parameter

Question 4

A number calculated using the sample measurements that describes some aspect of the sample

Answer 4

Sample statistic

Question 5

What are the 3 measures of central tendancy and how do you get them?

Answer 5

Mean: the average or expected value. Add all and divide by number.

Median: the middle number. If there are two get the middle two numbers mean

Mode: the most frequent number is the set

Question 6

The sample mean (x line over it) is what?

Answer 6

For a sample of size n the sample mean is a point estimate of the population mean.

It is the value to expect, on average, in the long run.

Question 7

What must you do so the median is accurate

Answer 7

Arrange in order highest to lowest

Question 8

A population or sample measurement that occurs most frequently

Answer 8

Mode

Question 9

When data is arranged in classes, the class with the highest frequency is what?

Answer 9

The modal class, the highest class in the fequency

Question 10

Of the mean median and mode are equal then the distribution is called what?

Answer 10

A normal distribution otherwise it is left or right skewed.

Question 11

When do you want to use the mode as central tendency?

Answer 11

When there are outliers that will throw off the average.

Question 12

Name the three measures of variation

Answer 12

1. Range
2. Variance
3. Standard deviation

Question 13

The largest minus the smallest measurements of a distribution is called what?

Answer 13

The range

Question 14

The average of the squared deviations of all the population measurements from the population mean

Answer 14

Variance

Question 15

The square root of the variance

Answer 15

The standard deviation

Question 16

What is this calculation?

= (x1-u)^2 + (x2-u)^2 + (Xn-u)^2
-——————————————
N
This one?

= (x1-u)^2 + (x2-u)^2+ (xn-u)^2
-——————————————
N-1

Answer 16

1. The population variance
2. The sample variance don’t have the population total so had to calculate a sample variance so you use -1 and make a degrees of freedom

Question 17

What are the three things you must have in order to use the empirical rule?

Answer 17

1. A normal curve
2. A mean
3. A standard deviations

Question 18

If the population measurements fall within one standard deviation of the mean it falls in what percentage?

Answer 18

68.4% of all measurements will fall within one standard deviation from the mean.

Question 19

If the population measurements fall within two standard deviation s of the mean it falls in what percentage?

Answer 19

95.5% of all measurements will fall within one standard deviation from the mean.

Question 20

If the population measurements fall within three standard deviations of the mean it falls in what percentage?

Answer 20

99.7% of all measurements will fall within one standard deviation from the mean.

Question 21

For any x in a population sample, the associated z score is what (use the formula) and what is it?

Answer 21

Z= x-mean
—————
Stan dev

The z score is the number of standard deviations that x is from the mean

Question 22

Positive and negative z scores are associated with the mean how?

Answer 22

• A positive z score is for x above the mean

- A positive z score is for x below the mean

Question 23

When there are two or more populations that have different means and different standard deviations you use this formula to measure the size of the standard deviation relative to the mean.

Tell which population is less variation

Answer 23

The coefficient of variation

= standard deviation/mean x 100%

Question 24

If you don’t have a normal distribution and have a skewed curve.

For set measurements arranged in increasing order, measurements fall at or below the value and (100-p) percent of fall at or above the value.
This is what?

Answer 24

Percents and quartiles

Question 25

Explain the breakdown of the quartiles. Give an example of when we use them.

Answer 25

• the first quartile Q1 is the 25th percentile
• the second quartile Q2 is in the 50th percentile (median)
• the third quartile Q3 is in the 75th percentile

The interquartile range IQR is Q3-Q1

This is used in grades with classes

Question 26

If you arrange the data in increasing order and calculate using this formula

į= (p/100)n

What are you trying to obtain and what is it called?

Answer 26

You are calculating percentiles; p is the percentile to find.

Question 27

If your answer to į is 1.2 then what would you do?

Answer 27

Round to the higher integer so the answer is 1.2=2

Question 28

To summarize data from a distribution that is skewed you’ll want to obtain what?

Answer 28

1. The smallest measurement
2. The first quartile
3. The median
4. The third quartile
5. The largest measurement

Question 29

Measurements that are different from the other measurements: much higher or lower

Answer 29

An outlier