S1 Exploring Data Flashcards
What is qualitative data?
Things that aren’t numbers. Eye colour, favourite flavour of something. Can be shown in pie charts and bar charts.
What are the types of data?
Categorical or qualitative
Numerical or quantitive
What is quantitive data?
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.
Explain the difference between continuous and discrete data.
Continuous. Any value in a range. Something that you measure.
Discrete. Only takes set values. Something you count.
What is a distribution?
The shape of the data when draw on a frequency graph.
What are the types of skew.
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.
What would a bimodal distribution look like?
There would be 2 lumps in it. Like a camel.
What does unimodal mean?
There is one large lump.
What is a uniform distribution?
Where everything is roughly the same value.
What is the advantage and disadvantage of using the mean?
It takes into account all the data. However it can be skewed by extreme values.
How do you find the mid range?
Add the largest and the smallest value together and divide by 2.
What is the inter quartile range?
It is the range of the middle 50% of values.
How is S”xx” found?
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.
How is the SD found using S”xx”?
Find the square root of S”xx” divided by one less than the total frequency.
If you were simply provided with a long list of numbers, how would you find the S”xx”?
Just square all the numbers and add them together and minus the mean² times the number of the numbers.
What is an outlier?
A value more than 2 SD away from the mean?
What is done with outliers ?
They are investigated. If there are true, they are included.
What does the table of a probability distribution show?
The probability of different outcomes. There should add up to one.
How is expectation calculated?
Multiply the P of a result by the result its self. Then add together.
How is variance calculated?
Square the different results and multiply by the probabilities. Add together.Then minus the square of the expectation.
How can variance be calculated with the standard deviation?
Square the standard deviation.
What is the symbol for standard deviation?
Sigma.
What is the symbol for expectance ?
u
What does X~B(n,p)mean?
The event Xis binomial distributed.
p is the probability.
n is the number of events.
How would p(x≥3) be found using the tables?
1-p(x≤2)
How is expectation found when you have the binomial distribution?
Times the probability by the number of events.
How is a conclusion produced when hypothesis testing?
Reject or accept H1. Put it in context.
What is the binomial distribution with hypothesis testing?
The probability is the first one given in the question.
The no. you use is from the second sample.
What is the probability you look for in hypothesis testing using the tables?
The probability of something more unlikely than what was in the second sample.
What is the critical value?
The first out come from a test that is inside the significance level.
What are the critical regions?
All outcomes and values that are within the significance level.
What do you do if you have to find the critical region when you are given a significance level?
Start at 1 on the right table and work your way down until you get to the first value that is within that level.
What is different with significance levels in two tail tests?
You halve it for each critical range.
How would you find P(6≤X≤11)?
Do P(X≤11) - P(x≤5)
How would you find P(3<10)
P(X≤9)-P(x≤3)
What is the mean square deviation?
Sxx ÷n
If you wanted to put negative values on a stem and leaf diagram, how do you do it?
You would have a -0 and other - numbers as well as 0 and the others.
What is a percentile or a decile?
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.
When doing a hypothesis test for the Probability of something, whay must you write?
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.
How is frequency density found?
Frequency ÷ group width.
With a stem and leaf digram, what must you remember?
A key with units if applicable.
When finding the SD from a histogram, how do you find nxbar²?
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.
When drawing a probability distribution table, what heading goes with what line of the table?
r on the top
P(X=r) on the bottom
How do you find an estimate for the median from grouped data?
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.
