Flashcards
BE428 Lecture 3: Examining Distributions (1 Variable)
Cards in this deck (26)
- 1how can categorical data be visualised?bar chart
pie chart - 2what is the difference between pie charts and bar charts?pie charts emphasise how the different categories relate to the whole
bar charts emphasise how the different categories compare with each other - 3how can data from one quantitative variable be displayed graphically?stem plot/dot plot
histogram
box plot - 4what is the principle of a stem and leaf diagram?separating each data point into a stem and leaf where:
leaf is right most digit
stem is anything but the right most digit - 5what are the steps in making a stem and leaf plot?1. separate each observation into a stem and leaf
2. write the stems in a vertical column with the smallest at the top
3. go through the data points and write each leaf in the row to the right of its stem
4. rearrange the leaves in an increasing order
5. if the data set is large, split each stem into 2 groups - 6what is the principle behind a histogram?break the range of values into intervals and count how many observations fall into each interval
- 7what are the two important points to remember about histograms?when data is displayed by a histogram some information is lost
data can be broken down into different intervals which affects the shape of the histogram - 8what three properties define the overall pattern of a histogram?shape
centre
spread - 9what is an outlier?deviations from the pattern
- 10what is a normal/gaussian/z distribution?50% of the distribution lies to the left of the mean and 50% lies to the right of the mean
it is a symmetrical, continuous distribution
"bell shaped curve" - 11what is skewness?means that one tail of a bell-shaped curve is drawn out more than the other
can be either left or right depending on which tail is drawn out - 12what are the types of modality?unimodal: symmetric, single-peaked
bimodal: symmetric, double-peaked
uniform: symmetric, no peaks
multimodal: non-symmetric, many peaks - 13what are the numerical measures of centre?mean (average value)
median (middle value)
mode (most frequent value) - 14what are the measures of spread?range
interquartile range (IQR)
standard deviation (SD)
standard error (SE)
confidence interval (CI) - 15what is the range?exactly the distance between the smallest data point and the largest one
- 16what is the inter-quartile range?measures the variability of a distribution by giving the range covered by the middle 50% of the data
- 17how is the inter-quartile range calculated?1. arrange the data in increasing order and find the median
2. find the median of the lower 50% of the data (Q1)
3. find the median of the upper 50% of the data (Q3)
4. IQR = Q3 - Q1 - 18how can IQR be used to detect outliers?below Q1 - (1.5*IQR)
above Q3 - (1.5*IQR) - 19what is a box plot?graphical representation of the distribution of a quantitative variable by visually displaying the "five number summary":
largest observation that is not an outlier
Q3
median
Q1
smallest observation that is not an outlier - 20what is standard deviation?quantifies the spread of a distribution by measuring how far the observations are from their mean
gives average between a data point and the mean
should be paired as a measure of spread with the mean as a measure of centre
strongly influenced by outliers - 21what are the standard deviation rules in the case of a normally distributed curve?68% of observations fall within 1 SD of the mean
95% of observations fall within 2 SD of the mean
99.7% of observations fall within 3 SD of the mean - 22what is the 95% confidence interval?the values calculated from the observations that fall within 2 SD of the mean
- 23what is the t distribution?wider distribution of the sample mean due to standard error being estimated
the exact shape of the t distribution depends on the number of degrees of freedom
more similar to normal distribution as the number of DOF increases - 24how is the number of degrees of freedom calculated?the total number of observations minus the number of parameters estimated form the sample
- 25how can confidence intervals be calculated using standard error and t distribution?if n < 30 the standard error and t distribution can be used to calculate CI
gives a range of values within which there is a percentage probability of the true mean occuring - 26what are the important notes about confidence intervals?the larger the sample size the narrower the confidence interval (as n increases, SE and critical t value decreases)
95% CI most common
if calculating the CI of a large sample (>30) use SD method
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- 4 BE428 Flashcards on BE428 Lecture 3: Examining Distributions (1 Variable), created by Caitlin M on 21/09/2018.
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- Caitlin M · Sep 2018
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- Sep 25, 2018
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