Averages including estimating the mean from grouped data, scatter graphs and correlation, cumulative frequency and box plots, histograms, and sampling.
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1.How do you find the mean?
Add all the values and divide by how many there are.
2.How do you find the median?
Put the values in order and find the middle one. With an even number of values, take the mean of the middle two.
3.How do you find the mode?
The value that occurs most often.
4.How do you find the range?
Subtract the smallest value from the largest.
5.Is the range an average?
No. It measures spread, not a typical value.
6.Which average is affected most by extreme values?
The mean, because every value contributes to the total.
7.When is the median a better choice than the mean?
When the data contains extreme values that would distort the mean.
8.How do you find the mean from a frequency table?
Multiply each value by its frequency, add those products, then divide by the total frequency.
9.How do you estimate the mean from grouped data?
Use the midpoint of each class, multiply by the frequency, add the products, and divide by the total frequency.
10.Why is the mean from grouped data only an estimate?
The exact values are unknown, so the midpoint is used as an approximation for every value in the class.
11.What is the modal class?
The class interval with the highest frequency.
12.What is the class containing the median?
The class that contains the middle value, found by counting through the cumulative frequencies.
13.What does a scatter graph show?
The relationship between two variables.
14.What is positive correlation?
As one variable increases, so does the other.
15.What is negative correlation?
As one variable increases, the other decreases.
16.What does a line of best fit do?
It shows the trend, passing as close as possible to the points with roughly equal numbers either side.
17.What is interpolation?
Using the line of best fit to estimate a value within the range of the data, which is reasonably reliable.
18.What is extrapolation, and why is it risky?
Estimating beyond the range of the data. The trend may not continue, so the estimate may be wrong.
19.Does correlation prove causation?
No. Two variables can be linked without one causing the other.
20.What does cumulative frequency mean?
A running total of the frequencies as you move through the classes.
21.How do you find the median from a cumulative frequency graph?
Go halfway up the cumulative frequency axis, across to the curve, and down to read the value.
22.What is the interquartile range?
The upper quartile minus the lower quartile, which measures the spread of the middle half of the data.
23.Why is the interquartile range often better than the range?
It ignores the extreme values at both ends, so it is not distorted by outliers.
24.What five values does a box plot show?
The minimum, lower quartile, median, upper quartile and maximum.
25.What is plotted on the vertical axis of a histogram?
Frequency density, not frequency.
26.How do you calculate frequency density?
Frequency divided by class width.
27.What represents the frequency on a histogram?
The area of each bar.
28.What is a biased sample?
One that does not fairly represent the population, so conclusions drawn from it may be wrong.
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