Mean, Median, Mode and Range
The mean is the average you mean when you say average.
The range is the difference between the smallest and the biggest numbers.
I always like to put the numbers in order of size when finding the median.
If two numbers occur with the same frequency and it’s a higher frequency than any other numbers, it’s called bimodal, which I like to remember by thinking of my bicycle which has two wheels.
The mode is the most popular.
Don’t forget the golden rule of averages; if all your numbers are between 40 and 50, the average won’t be 382.
Some people talk about the MMR debate (although technically it has been scientifically shown that there is no link) but there’s never any debate about MMMR (the mean, median, mode and range).
Only three of MMMR are averages (clue: they begin with M).
mkyou2tube's frankly disturbing ''The Averages Song' (loosely based on the exploits of two characters from the ever-popular soap opera Eastenders) is a unique introduction to the definitions of the M, M, M and R,
The range is the difference between the smallest and the biggest numbers.
I always like to put the numbers in order of size when finding the median.
If two numbers occur with the same frequency and it’s a higher frequency than any other numbers, it’s called bimodal, which I like to remember by thinking of my bicycle which has two wheels.
The mode is the most popular.
Don’t forget the golden rule of averages; if all your numbers are between 40 and 50, the average won’t be 382.
Some people talk about the MMR debate (although technically it has been scientifically shown that there is no link) but there’s never any debate about MMMR (the mean, median, mode and range).
Only three of MMMR are averages (clue: they begin with M).
mkyou2tube's frankly disturbing ''The Averages Song' (loosely based on the exploits of two characters from the ever-popular soap opera Eastenders) is a unique introduction to the definitions of the M, M, M and R,
Questionnaires
When designing option boxes, I try to avoid overlap or gaps at the beginning and/or end.
I always make sure that my questions aren’t biased.
I find it very convenient when administering a questionnaire to random passers-by in the town centre to include timescales.
When asked for your gender, only select either M or F.
I always make sure that my questions aren’t biased.
I find it very convenient when administering a questionnaire to random passers-by in the town centre to include timescales.
When asked for your gender, only select either M or F.
Stem and Leaf Diagrams
When I were a lad, a plant had a vertical stem and leaves stored horizontally with numbers printed upon them. Plants these days don't know they're born.
When I were a lad, cats had rectangular noses and one horizontal whisker poking out each side with extra strips of vibrissae running perpendicular at either end. Hence what today’s youth label box plots used to be known as box and whisker plots. Cats these days don’t know they’re born.
When I draw a stem and leaf diagram I always include a key as well as brackets at the end of each row.
Stem and leaf diagrams look nothing like stems and/or leaves.
When I were a lad, cats had rectangular noses and one horizontal whisker poking out each side with extra strips of vibrissae running perpendicular at either end. Hence what today’s youth label box plots used to be known as box and whisker plots. Cats these days don’t know they’re born.
When I draw a stem and leaf diagram I always include a key as well as brackets at the end of each row.
Stem and leaf diagrams look nothing like stems and/or leaves.
Box Plots
Box plots have five vertical lines, representing from left to right the minimum, the lower quartile, the median, the upper quartile and the maximum.
Quartiles divide the data into quartiles and are denoted Q1, Q2 and Q3 (where Q2 is also called the median).
To find quartiles from a list, split your data into two halves, erasing the median should you be starting with an odd number of data items. Then the lower and upper quartiles are the medians of the lower and upper halves.
mkyou2tube's 'A Plot Called Box' features the concept of plotting a box-and-whisker plot.
Quartiles divide the data into quartiles and are denoted Q1, Q2 and Q3 (where Q2 is also called the median).
To find quartiles from a list, split your data into two halves, erasing the median should you be starting with an odd number of data items. Then the lower and upper quartiles are the medians of the lower and upper halves.
mkyou2tube's 'A Plot Called Box' features the concept of plotting a box-and-whisker plot.
Pie Charts
My mother's shepherd’s pie was rectangular, unlike her shepherd’s pie chart which she used to show the proportions of different sheep types such as Blue faced Leicester, Cotswold and Lonk on her farm.
I find it helpful to think of a pie chart as the chart that’s in the shape of a pie, but being vegetarian it’s more likely to feature spinach and feta than chicken and mushroom.
Every pie chart I have ever drawn has been flat so I prefer to call it a pizza chart.
I find it helpful to think of a pie chart as the chart that’s in the shape of a pie, but being vegetarian it’s more likely to feature spinach and feta than chicken and mushroom.
Every pie chart I have ever drawn has been flat so I prefer to call it a pizza chart.
Scatter Diagrams
On a scatter diagram, if the data goes up the correlation is positive and if the data goes down, it’s negative. Similarly when I’m feeling up my mood is positive and likewise if I’m feeling down then my mood is negative.
Estimating the Mean
When estimating the mean I start by determining the midpoint of each class interval.
The mean calculated by this method is only an estimate because the data has been grouped.
Should a table be presented that is limited to two columns, the classes and the frequencies, I add two more columns entitled x and fx which denote the midpoint and the product of the midpoint and the frequency.
mkyou2tube's Lily Allen/Professor Green/SOS Band/Beats International tribute 'Estimate the Mean' shows one how to estimate the mean.
The mean calculated by this method is only an estimate because the data has been grouped.
Should a table be presented that is limited to two columns, the classes and the frequencies, I add two more columns entitled x and fx which denote the midpoint and the product of the midpoint and the frequency.
mkyou2tube's Lily Allen/Professor Green/SOS Band/Beats International tribute 'Estimate the Mean' shows one how to estimate the mean.
Cumulative Frequency
In the same way that the median is the value above which lies half the data and below which lies the other half, the 95th percentile is the value above which 5% of the data lies and below which the other 95% lies.
Accumulate means to gather together. When calculating cumulative frequencies, we gather together the individual frequencies one at a time to form the subtotals.
The median on a cumulative frequency graph can be found halfway up and the quartiles a quarter and three-quarters of the way up.
Plot subtotals at upper limits.
mkyou2tube's 'A Plot Called Box' also features the concept of plotting a cumulative frequency ogive.
And if you dislike music and just want to be told what to do, why not watch the dull but informative 'Cumulative Frequency' video.
Accumulate means to gather together. When calculating cumulative frequencies, we gather together the individual frequencies one at a time to form the subtotals.
The median on a cumulative frequency graph can be found halfway up and the quartiles a quarter and three-quarters of the way up.
Plot subtotals at upper limits.
mkyou2tube's 'A Plot Called Box' also features the concept of plotting a cumulative frequency ogive.
And if you dislike music and just want to be told what to do, why not watch the dull but informative 'Cumulative Frequency' video.
Time Series and Moving Averages
I always shed a tear when considering a time series. I guess that’s why they call them moving averages.
For a four-point moving average, add up four numbers and divide by four. For the next four-point moving average, discard the oldest value and introduce the next value.
Moving averages are good for investigating unemployment or sales of sunglasses.
For a four-point moving average, add up four numbers and divide by four. For the next four-point moving average, discard the oldest value and introduce the next value.
Moving averages are good for investigating unemployment or sales of sunglasses.
Probability
Whenever I draw a tree diagram, I always make sure that the numbers on each pair of branches add up to 1.
I learnt at school that a coin has two faces called Heads and Tails.
I find that when I’m drawing a tree diagram, I need to spread it out a bit or it gets really messy.
If I have a bag containing three different colours of beads, I like to take one out, record its colour and then put it back and start again. I always find it useful to use three branches, one for each colour, when illustrating my hobby in a tree diagram.
Probability may be the study of chance, but I never miss a chance to draw a tree diagram (or Venn diagram or two-way table as appropriate).
I have discovered that if there are ten buttons in a bag and I remove one button, then there are nine buttons in the bag.
If the chance of it raining is 35%, then the chance of it not raining is 100% - 35%, whatever that is.
There are 120 ways of arranging the letters in the word LOUIS.
There are fewer ways of arranging the letters in the word HARRY than the word LOUIS.
I learnt at school that a coin has two faces called Heads and Tails.
I find that when I’m drawing a tree diagram, I need to spread it out a bit or it gets really messy.
If I have a bag containing three different colours of beads, I like to take one out, record its colour and then put it back and start again. I always find it useful to use three branches, one for each colour, when illustrating my hobby in a tree diagram.
Probability may be the study of chance, but I never miss a chance to draw a tree diagram (or Venn diagram or two-way table as appropriate).
I have discovered that if there are ten buttons in a bag and I remove one button, then there are nine buttons in the bag.
If the chance of it raining is 35%, then the chance of it not raining is 100% - 35%, whatever that is.
There are 120 ways of arranging the letters in the word LOUIS.
There are fewer ways of arranging the letters in the word HARRY than the word LOUIS.
Histograms
mkyou2tube's video on 'Histograms' is a hoot. The pseudo-American rap may irk.