P+S 2 Flashcards
(18 cards)
What is a time series graph
A line graph which shows data such as measurements sales or frequencies over time. They can be use to show the pattern or trend in data over a set period of time and are useful for making predictions about the future.
The x axis is always the time frame
the coords are plotted and joined with a straight line and dont always start at 0,0 and end at the other corner of the graph
How do you find the median of a frequency Table
you add up all the numbers in the frequency column, divide it by 2 to find the position of the middle value, then look through the list to find out where the middle value is by adding up all of the frequencies in a cumulative frequency table and working out where the position of the median is from there
How do you find the mean in a frequency graph
Add up all the numbers in frequency column, make a fx column (frequency * x), add up all the numbers there, then do that number/total frequency
If the x column in a frequency table is a range what do you use when working out the fx column or a graph
the middle value of the range
In a histogram, what are the x and y axis and how do we know the frequency
X axis is what ur measuring (ie: height)
Y axis is frequency DENSITY (frequency/length of the range)
frequency is the area of the bar that is shown
Formula with frequency density, frequency and the range of x (ie: 130 < x < 140) (what ur measuring)
f = f.d * width of the bar (ie: the width would be 10 if the range is between 130 to 140)
How do we find the median using a histogram
As the median is the middle, we find the total number of things, then we divide by 2 and work out in which range is it in
Why are histograms estimates
They are in grouped data so any grouped data would be an estimate since we don’t know the exact values for certain items
Cumulative frequency graphs are drawn with a ____ _____ and use ____ ____ ______ in the range of values with the cumulative frequency as the _ axis and what ur measuring as the _ axis
smooth curve
the largest item (ie: if a range is 10 < x < 20 you would plot it with 20 as the x axis instead of 15)
y
x
How do we find the median on a cumulative frequency graph and why will this be an estimate
It is the middle so we need to do the middle of the cumulative frequency, draw a line from there to the graph, then draw a line down to the “what youre measuring” or x axis and record it. This will still be an estimate, even though it isn’t a range of values as the graph may not be perfect
How do we find the LQ UQ and IQR on a cumulative frequency graph
LQ: Half the median and record it (ie: if the median was 20 on the cumulative frequency then go to 10, draw a straight line from there to the graph, and record the x axis corresponding to it)
UQ: same as LQ but do (half of median) * 3 and then continue
IQR: UQ - LQ
How do we draw a box plot
the first vertical line starts at LQ
Next at median
Last at UQ
draw a box surrounding that all
draw lines extending out the box for however much the cumulative frequency graph goes for
Draw 2 vertical lines at the very end of the box plot, showing the start and end
How do we compare 2 box plots
talk about things like the range, median, IQR and talk about their effects if you can like
“Class B had a lower IQR meaning most of their marks weren’t as spread out but they had a higher range so there were some extremities in the class”
“Class A had a higher median though meaning that the average mark was higher”
How do you construct a stem and leaf diagram
An example would look like this
1| 1, 1, 1, 2, 3, 3, 4, 4
2| 0, 0, 1, 2, 2, 2, 3
3| 4, 4, 5
4| 0, 1, 2
1|0 = 10cm
YOU NEED THAT KEY ABOVE with UNITS
The left side is the 10s column, the right side is an ORDERED 1s unit.
for numbers that need to be ordered such as 158, you would need a 15 on the left. You NEVER put a double digit number on the right
How do we find out the median of a stem and leaf diagram
We cross out each number, staring with the first then the last, then the 2nd and then 2nd to last, in a chromatic order until we get to the middle
If you get a question like
50 people were asked which fruits they liked from apples, bananas and
oranges.
11 people like all three fruits.
33 people like apples.
6 like apples and bananas but not oranges.
15 like bananas and oranges.
5 of the people do not like any of the fruits.
All 25 people who like oranges like at least one other fruit.
Two of the 50 people are chosen at random.
Work out the probability that they both like bananas.
where there are multiple interconnections between things wyd
Draw a Venn diagram to visually show all the things there and because it is represented in such ways then it becomes much easier to count how many people are part of a certain group
ie: you will draw a Venn diagram of 3 circles: apples bananas and oranges and so visually represent the data
Here are seven number cards.
1 1 2 2 3 3 3
Helen takes a card at random.
She does not replace the card.
Helen then takes another card at random.
(a) Calculate the probability that both cards have the same number on them.
(b) calculate the probability that the 2nd card is greater than the 1st
wyd
a) P(1,1) + P(2,2) + P(3,3)
once you take out one card and dont replace it, the numerator and denominator decrease by 1 as there is 1 less card there and 1 less card you need
To find the probability of 1 AND 1 you ened to multiply them together
You add it all up to get the final probability as it can be EITHER/OR one of these 3 situations
b) P(1,2) + P(1,3) + P(2,3)
Once you take out the card, only the denominator decreases but the numerator just changes to whatever card you need as the number of that card hasn’t changed but the total number of cards has
whats the purpose of a histogram
to visualize the distribution of continuous numerical data, providing a quick way to understand the shape, center, and spread of the data
