Chapter 2 Measures Of Location And Spread - Year 1 Flashcards
What may make the data’s 90 percentile un calculable?
Where P90 would be there is an open bounded group
How do you work out the range in a frequency table with groups?
You take the extreme ends
What does this mean?
X bar
This stands for the mean
What does this mean?
The “sum of” all values of x
What are the measures of spread?
Range
Standard deviation
Interquartile range
Variance
What are the measures of location?
Maximum
Minimum
Quartiles
Percentiles
Deciles
-Median (the last 3 are measures of central tendency)
-Mode
-Mean
What are then measures of central tendency?
Median
Mode
Mean
Define measures of location
Single values which describe a position in a data set
Define measures of central tendency?
Measures of location which are to do with the centre of the data
Define measures of spread?
To do with how data is spread out
How so you calculate the mean?
Write out the formular
Substitute the numbers in
State the answer
How do you use your calculator to work out the mean of ungrouped data?
Press menu
Press 6 (statistics)
Press 1 (1 - variable)
Enter the data
Press AC
Press options
Press 2 (1 variable calc)
Write down the formular
Enter the numbers in
Then state the answer
On your calculator, how do you turn on the frequency bit of the table?
Press:
Shift - menu setup
Down arrow
3 statistics
1 on
How do you use your calculator to calculate the mean easily of grouped data (data with inequalities)?
You take the midpoint of each group and then use that as your frequency
Menu - 6
Enter the data
Press AC
Press options
Press 2
Write down the formular
Enter the numbers in
Then state the answer
What is the mode?
The most frequent piece of data
What is the median?
The middle piece of data once the data has been ordered chronological
How do you calculate the median of ungrouped data?
(n+1) ÷ 2
How do you find the median of listed data if the answer is in the middle?
You take the midpoint of the 2 values
How do you find the position of median in grouped data?
Just n/2
Not (n+1) ÷2
How do you use interpolation to work out the value of the median?
Find the sum of the frequency and ÷ 2. Then find which class your value lies in
Then draw the grid below and substitute your values into the equation a/b=c/d. Solve for c and then add it to the starting width of the class.
Why may linear interpolation be inaccurate?
We assume that all data is evenly distributed within each group
What do we need to do to make this work?
Why won’t it work in its current form?
There are gaps in the data. Therefore we need to convert them into an inequality.
It won’t work as data such as 9.9 isn’t included in these groups.
How do you find the quartiles in a list or ungrouped data?
Find the median. Then split the data in 2 parts where you find the median in each but separately
(n+1) ÷ 2
What do you need to use to work out the Quartiles in grouped data?
Interpolation
How do you work out the IQR?
Q3-Q1
Why might we use the IQR instead of the range?
Disadvantages?
How could you fix this?
We get to miss any extreme data at each end if the data
However, we are discounting a lot of data that may be representable
To fix this problem you could calculate an interpercentile range
Give an example of a percentile?
Give an example of a decile?
Give an example of an interpercentile range?
How do you convert percentiles to deciles?
÷10
How do you convert deciles into percentiles
X10
What may you need to use to work out a percentile?
Interpolation
What does this mean:
The 90th percentile (or the 9th decile)
It wants the 90th % of data.
How do you calculate which value of the data a percentile wants?
You ÷ the number on the percentile by 100 (to get the number which you would multiply by if it was a %)
Then do the sum of frequency X that number
How do you work out the value of the data the decile wants?
You ÷ the number on the decile by 10 (to get the number which you would multiply by if it was a %)
Then do the sum of frequency X that number
What is variance?
A measure of spread that takes all values into account. By definition it is the average squared distance from the mean.
What is the symbol for variance?
What is the formular for variance?
What is the symbol for standard deviation?
What is the formular for standard deviation?
How do you work out variance and standard deviation on a calculator?
Press
Menu
6
1
Fill in the data
AC
Options
2
Why may we code?
To make our data easier to use
Explain how the code x=(y+10)will effect:
The mean, SD and the variance?
Mean - increase by 10
SD won’t change
Variance
Explain how the code x=(3y) will effect:
The mean, SD and the variance?
Mean - 3 times bigger
SD - 3 times bigger
Variance
Explain how the code x=(2y-10) will effect:
The mean, SD and the variance?
Mean - 2 times bigger then 10 smaller
Standard deviation - 2 times bigger only
Variance
You may be asked to decode a question once given the code. How do you do this?
Work out the answer in a coded answer
Then but that answer into the formular (usually as equals to)
Then solve it. Keep in mind what effects the mean, variance, Standard deviation
When is the only time what letter is used matter in this topic?
Coding
What may a question be asking you if it gives you these 2 values?
What is the common mistake?
The standard deviation
You may square the Σx^2 term although it is already squared
