Stats

Question 1

Discrete data vs CONTINOUS

Answer 1

Discrete can only take certain values, and her euse things like bar chart

CONTINOUS are any values over a range , and csntbe listed as this is infinite without being missed out

Question 2

Remmeber to not overlap any data with discrete data
And how choose intervals?
But for CONTINOUS?

Answer 2

So honbeloew,

Yiu can use inequalities

Use the ones thst gived best feel for the data without too small

Question 3

Why stem and leaf diagram good!

Answer 3

Yiu lose raw data when grouping in frewuency, but stem and leaf preserves raw data whilst organising them to see thr distribution

Makes easy to see the mode and calculate median too
And can compare two things side by side

And ken5h if line gives shape of each distribution
, and asored too

Question 4

How to represent discrete/ categorical data

Answer 4

Use bar charts frewuency diagrams and pie chart

Reason pie chart could be better as ti shoes you the distribution as a proprtionsl easy tk see, as it scaled to 360 so easy to compare side by side

But loses raw data , ehwreas bar chsrt preserved

Question 5

Why use a vertical line chart

Dot plot

Answer 5

Again ti respresent discrete data, but thin line is good because bar charts the width of the line is sometimes cinfused with the range of values it represents when even tho it jus represent done value

Dot plot allows you to see data much. Ore Emily’s as you can give a key to the dots and then comparing data very easy

Question 6

Why do we use a histogram instead of a frequency against class

Answer 6

This gives distorted picture of the data, as if your class width is big, the area is huge, making it seem like there’s more when there isn’t

Thus we plot against area , and maybe a scale factor too

Here frewuency don’t have ti be equal but proteins, to area so valid comsoriodms csn be made

And to do this frequency density against class width should be llotted
And be more specific too

Question 7

Skews of data

Answer 7

If more data is positive then it’s negriabley skeewd
If more data negative then positbe oh sekewed
And same is symmetrical

Question 8

What is midrange

Answer 8

Midrange is addition of highest sndlowest and divide by 2, whereas range is higher - lowest

Question 9

Mean median möde

Answer 9

Mean can be easily influence by car ash outliers as it takes an all data values

Median typically not influenced by outliers, gives a good representation of the average, but should only be used if no outliers

Möde is most frequent , only good if there is high frequency data ,motherwise pojtnelss

Midrange is also susceptible to outliers in this case, assumes data is symmetrical etc typically don’t use this

Question 10

How to find mean median mode range in frewuency tables

Answer 10

Mean = frewuency times x and then Ober total frewuency
Median is given, as itd already ordered, if it’s even add one and divide by 2, so it’s gonna be between 10 and 11 basically find those and mean it rest od easy

Question 11

But for grouped data?

Answer 11

Mean is midpoint times frewuency average

Median is grouped so DONT ADD ONE ,
Jus divide by 2, and linearly extrapolate and calm

Question 12

Remember for ages what to do

Answer 12

If there are ages, you have to make it next year, because 29 years old are 29 until 30, so midpoint would be in 5s or whatever

Question 13

How to linear interpolate

Answer 13

Grouped data
= jus divide by 2
Find how much in cumulative
Divide by frewuency multiply by class width and add it on

Question 14

Bis plot

Answer 14

Plots the median the lowest the highest the lower quartile (25% and upper too)

Find these by finding the median = if it’s odd, discord this and find median of the other two

But if itdeven keep and find even medians of other two aswell

Question 15

How to compare box plots

Answer 15

Compare them by
- saying the range
- higher median = higher average
And interquartile shows spread of middle 50% data , so if bigger than greater spread

You can also use box plots to detect skew, if the median closer to upper quartile than that means most of data is on higher values = negatively skewed

Question 16

Outliers with quaritle d

Answer 16

Is anything thst is 1.5 the iqr above the upper and below the lower

Question 17

Cumulative frewuency curved

Answer 17

Plot them sgaidnt the upper boundaries , and then can use to find mkedisn , 50% of data and quartile etc

And if itsdiscrete data, it’s a less than or equal to mark , so make sure to consider thst

Question 18

Standard deviation

Answer 18

Is jsed alongside the mean jus as median with IQR

Deviation is the distance between the value and the mean, can give negative values
But these all add up to 0 so no point in using them
Instead if we swaure them they get rid of the negatives

However to compare to samples of data the number of data points mudt be tsken into coconut
So divide by the number, nut there are only n-1 independent measures as yiu cns deduec the last one if you know the first 4, as they add to 0

So divide this by j-1 and yiu have variance
Swaure root and yiu have standard deviation

Question 19

Formula for standard deviation

Answer 19

SQUARE ROOT of sum of x 2 - n x mean sqaured
Over n-1 and this is square root

Question 20

But if you using a frewuency tbsle how to find standard deviation

Answer 20

Sum of f x X2 and everything else the same !

Square

Question 21

Finally using standard deviation for outliers?

Answer 21

All data which are over 2 standard deviations above or below the mean are outliers

And IQR was 1.5
So Yh +- 2 standard deviation from mean value!

Question 22

Remember with correlations on scatter graphs, what to be wary about when making conclusion

Answer 22

Be wary thst if it’s a low correlation or even high , it suggests only never MEANS
Correlations nevernimlloes causation so yeah

Question 23

What is a discrete uniform distribution

Answer 23

Where all have the SAME CHANCES KF BEING SELECTED