GCSE Statistics Chapter 4 Summary- Summarising Data

After completing this chapter, you will be able to;

  • Work out measures of central tendency;
    • Find the mean, mode and median of raw data given as a list or as a frequency distribution
    • Estimate the mean and median of a grouped frequency distribution and identify the modal class
    • Understand the effects of transformations of data on the averages
    • Understand when each of these averages is appropriate
    • Calculate the weighted mean
  • Work out measures of dispersion;
    • Work out the range of data given as a list or frequency distribution
    • Work out quartiles and percentiles
    • Draw box plots
    • Identify outliers
    • Calculate and use variance and standard deviation
    • Compare distributions of data
  • Use simple index numbers, chain base index numbers and weighted index numbers;
    • Know about the retail prices index.
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Averages
1.) An average is a single value used to describe a set of data.
2.) The mode is the value that occurs most often.
3.) The median is the middle number in a list after the numbers have been put in
order.
4.) When the number of data values, n, is odd the median is the value of the ½(n
+ 1)th observation.
When n is even the median is the mean of the ½(n)th observation and the ½(n +
2)th observation)
5.) The mean is worked out by adding up the numbers then dividing by how
many numbers there are.
6.) Mean= x
n
Mode, median and mean of discrete data in a frequency table
7.) When discrete data is given in a frequency table:
Mode is the one with the highest frequency
Median = ½(n + 1)th value
Mean = fx
f
Mode, median and mean of grouped data
8.) When information is presented in a table of grouped data, the modal class is
the class with the largest frequency.
9.) For grouped data the median is the value of the 1/2nth observation.
There are two ways of estimating the median
Using the midpoint of a cumulative frequency diagram
Using interpolation
10.) An estimated mean can be found from a grouped set of data using the
formula
Mean = (f x midpoint)
f
Weighted mean
11.) The weighted mean of a set of data is given by
Meanw= wx
w

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Measures of spread
12.) Range = largest value ­ smallest value
13.) The lower quartile is the value such that one quarter (25%) of the values
are less than or equal to it.
14.) The upper quartile is the value such that three quarters (75%) of the values
are less than or equal to it.
15.…read more

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A friendlier formula for variance is
Var(x)= x12 + x22 + x32 +...+ xn2
n
26.) The standard deviation is the square root of the variance.
Standard deviation (SD) = R(x mean)2/n
Comparing data sets
27.) A full comparison need, at least, both a measure of central tendency and
a measure of dispersion or spread.
28.) Another comparison that could be made is the skewness of the
distributions.
29.) Standardised score (z)=
score mean
Standard deviation
Index numbers
30.…read more

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