S1 Exploring Data

Question 0

What is qualitative data?

Answer 0

Things that aren’t numbers. Eye colour, favourite flavour of something. Can be shown in pie charts and bar charts.

Question 1

What are the types of data?

Answer 1

Categorical or qualitative

Numerical or quantitive

Question 2

What is quantitive data?

Answer 2

It is in numbers. It is more useful as it allows you to work out averages and measures of spread.
There is continuous and discrete data.

Question 3

Explain the difference between continuous and discrete data.

Answer 3

Continuous. Any value in a range. Something that you measure.
Discrete. Only takes set values. Something you count.

Question 4

What is a distribution?

Answer 4

The shape of the data when draw on a frequency graph.

Question 5

What are the types of skew.

Answer 5

A positive skew is when the data is skewed towards the Y axis. Towards 0.
Negative skew is when the data to skewed to the right. Towards the larger numbers.

Question 6

What would a bimodal distribution look like?

Answer 6

There would be 2 lumps in it. Like a camel.

Question 7

What does unimodal mean?

Answer 7

There is one large lump.

Question 8

What is a uniform distribution?

Answer 8

Where everything is roughly the same value.

Question 9

What is the advantage and disadvantage of using the mean?

Answer 9

It takes into account all the data. However it can be skewed by extreme values.

Question 10

How do you find the mid range?

Answer 10

Add the largest and the smallest value together and divide by 2.

Question 11

What is the inter quartile range?

Answer 11

It is the range of the middle 50% of values.

Question 12

How is S”xx” found?

Answer 12

Square each value and multiply by its frequency. Add together.
Get the mean and square it. Multiply by the total frequency(not the sum of the squared frequency). Take this away from the sum of the first numbers.

Question 13

How is the SD found using S”xx”?

Answer 13

Find the square root of S”xx” divided by one less than the total frequency.

Question 14

If you were simply provided with a long list of numbers, how would you find the S”xx”?

Answer 14

Just square all the numbers and add them together and minus the mean² times the number of the numbers.

Question 15

What is an outlier?

Answer 15

A value more than 2 SD away from the mean?

Question 16

What is done with outliers ?

Answer 16

They are investigated. If there are true, they are included.

Question 17

What does the table of a probability distribution show?

Answer 17

The probability of different outcomes. There should add up to one.

Question 18

How is expectation calculated?

Answer 18

Multiply the P of a result by the result its self. Then add together.

Question 19

How is variance calculated?

Answer 19

Square the different results and multiply by the probabilities. Add together.Then minus the square of the expectation.

Question 20

How can variance be calculated with the standard deviation?

Answer 20

Square the standard deviation.

Question 21

What is the symbol for standard deviation?

Answer 21

Sigma.

Question 22

What is the symbol for expectance ?

Answer 22

u

Question 23

What does X~B(n,p)mean?

Answer 23

The event Xis binomial distributed.
p is the probability.
n is the number of events.

Question 24

How would p(x≥3) be found using the tables?

Answer 24

1-p(x≤2)

Question 28

How is expectation found when you have the binomial distribution?

Answer 28

Times the probability by the number of events.

Question 29

How is a conclusion produced when hypothesis testing?

Answer 29

Reject or accept H1. Put it in context.

Question 30

What is the binomial distribution with hypothesis testing?

Answer 30

The probability is the first one given in the question.

The no. you use is from the second sample.

Question 31

What is the probability you look for in hypothesis testing using the tables?

Answer 31

The probability of something more unlikely than what was in the second sample.

Question 32

What is the critical value?

Answer 32

The first out come from a test that is inside the significance level.

Question 33

What are the critical regions?

Answer 33

All outcomes and values that are within the significance level.

Question 34

What do you do if you have to find the critical region when you are given a significance level?

Answer 34

Start at 1 on the right table and work your way down until you get to the first value that is within that level.

Question 35

What is different with significance levels in two tail tests?

Answer 35

You halve it for each critical range.

Question 36

How would you find P(6≤X≤11)?

Answer 36

Do P(X≤11) - P(x≤5)

Question 37

How would you find P(3<10)

Answer 37

P(X≤9)-P(x≤3)

Question 38

What is the mean square deviation?

Answer 38

Sxx ÷n

Question 39

If you wanted to put negative values on a stem and leaf diagram, how do you do it?

Answer 39

You would have a -0 and other - numbers as well as 0 and the others.

Question 40

What is a percentile or a decile?

Answer 40

The 10th percentile would be a value where 10% of the data blew it would be less than it. If you got 20 people of different heights and you where the 4th tallest 16 people would be shorter than you and you would by the 80th percentile.
The first decile is the same as the 10th percentile, the second the same as the 20th percentile and so on.

Question 41

When doing a hypothesis test for the Probability of something, whay must you write?

Answer 41

Let p be the probability of thing happening in the population.
X∼B(18, p) 18 has been used as an example for the sample size.

Question 42

How is frequency density found?

Answer 42

Frequency ÷ group width.

Question 43

With a stem and leaf digram, what must you remember?

Answer 43

A key with units if applicable.

Question 44

When finding the SD from a histogram, how do you find nxbar²?

Answer 44

Don’t find the mean, square it and multiply it by the number of variables.
Find the total of xf. Square it. Divide by the number of numbers. Use this instead.

Question 45

When drawing a probability distribution table, what heading goes with what line of the table?

Answer 45

r on the top

P(X=r) on the bottom

Question 46

How do you find an estimate for the median from grouped data?

Answer 46

Find what position the median will be. If total frequency was 10 it would be the 5.5th value.
Find what group this is in.
Add the bottom value for the group to the position of the median minus the frequencies before it divided by the frequency of the group multiplied by the group width.