gcse edexcel statistics chapter 4 summary

statistics chapter 4 summary (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

statistics chapter 4 summary (frequency)

• 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

statistics chapter 4 summary (grouped)

• 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 mid-point 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 mid-point)
• ∑f

statistics chapter 4 summary

• Weighted mean
• 11.) The weighted mean of a set of data is given by;
• Meanw= ∑wx
• ∑w

statistics chapter 4 summary

• 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.) For discrete data, when n values are written in ascending order;
• The lower quartile, Q1, is the value of the ¼(n + 1)th observation
• The median, Q2, is the value of the ½(n + 1)th observation
• The upper quartile, Q3, is the value of the ¾(n + 1)th observation
• 16.) Inter-quartile range (IQR) = upper quartile – lower quartile
• 17.) For continuous data Q1 is the value of the 1/4nth observation, Q2 is the value of the 1/2nth observation and Q3 is the value of the 3/4nth observation.
• 18.) A set is divided into 100 parts to form percentiles.
• 19.) When the set is divided into 10 equal parts, these are called deciles.

statistics chapter 4 summary

• Box Plots
• 20.) A box plot represents important features of the data; The maximum and minimum values, the median, and the upper and lower quartiles.
• 21.) If the median is closer to the upper quartile than it is to the lower quartile the data is negatively skewed.
• 22.) If the median is closer to the lower quartile than it is to the upper quartile they are positively skewed.
• 23.) If the median is equidistant fro both the upper and lower quartiles they are symmetrical.
• 24.) An outlier is any value that is more than 1.5 times the inter-quartile range below the lower quartile or more then 1.5 times the inter-quartile range above the upper quartile.

statistics chapter 4 summary

• Index numbers
• 30.) Index number= (Current price/ base year price) x100
• 31.) Chain base index number= (Current price/ previous year’s price) x 100
• 32.) Weighted index number =
• (Current weighted mean price/base year weighted mean price) x 100

statistics chapter 4 summary

• Variance and standard deviation
• 25.) The variance is a measure of dispersion or spread.
• It is given by;
• Var(x)= (x1-mean)2 + (x2-mean)2 + (x3-mean)2 +…+ (xn-mean)2
• n
• 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

statistics chapter 4 summary

• 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