chapter 4 : forecasting @ summarising and analysing data (frequency…
chapter 4 :
summarising and analysing data
two variables are said to be correlated if a change in the volume of one variable is accompanied by a change in the value of another variable. this is what is meant by
two variables might be
perfectly correlated,partly correlated
. correlation can be
the degree of linear correlation between two variables is measured by the
, r. the nearer r is to +1 or -1, the stronger the relationship.
coefficient of determination
, r² (alternatively R²) measures the proportion of the total variation in the value of one variable that can be explained by variations in the value of the other variable, it denotes the strength of the
association between two variables.
linear regression analysis
least squares method
) is one technique for estimating a line of best fit. once an equation for a line of best fit has been determined, forecasts can be made.
as with all forecasting technique, the results from regression analysis will not be wholly reliable. there are a number of factors which affect the reliability of forecasts made using regression analysis.
the high-low method is a simple forecasting technique.
is a series of figures or values recorded over time.
there are four components of a time series:
trend, seasonal variations, cyclical variations
one method of finding the trend is by the use of
. remember that when finding the moving averages of an even number of results, a second moving average has to be calculated so that trend values can relate to specific actual figures.
seasonal variations are the difference between actual and trend figures (additive model). an average of the seasonal variations for each time period within the cycle must be determined and then adjusted so that the total of the seasonal variations sums to zero.
are often used by economic commentators.
forecasting using time series analysis involves calculating a trend line, extrapolating the trend line and adjusting the forecasts by appropriate seasonal variations. the trend line can be extrapolated by eye or by using a common sense 'rule of thumb' approach.
all forecasts are subject to error, but the likely errors vary from case to case .
further into the future
the forecasts is for, the
it is likely to be.
available on which to base the forecast, the
of trend and seasonal variations
cannot be guaranteed to continue
in the future.
(d) there is always the danger of
upsetting the pattern of trend and seasonal variation.
an index is a measure, over time, of the average changes in the value (price or quantity) of a group of items relative to the situation at some period in the past.
cover more than one item.
is used to reflect the importance of each item in the index.
weighted aggregate indices
are found by applying weights and then calculating the index.
there are two types of weighted aggregate index, the
(which uses quantities/prices from the base period as the weights) and the
(which uses quantities/prices from the current period as weights).
fisher's ideal index
is the geometric mean of the laspeyre and paasche indices,
index numbers are a very useful way of summarising a large amount of data in a single series of numbers. you should number, however, that any summary hides some detail and that index numbers should therefore be interpreted with caution.
the product life cycle model shows how sales of a product can be expected to vary with the passage of time.
is data where the frequency is shown in terms of a range.
is data where the frequency is shown in terms of a specific measure or value.
can only take on a countable number of values.
can take on any value.
are used if values of particular variables occur more than once.
a cumulative frequency distribution can be graphed as an
can be represented pictorially by means of a
. the number of observations in a class is represented by the
covered by the bar, rather than by its height.
is the best known type of average and is widely understood.
arithmetic mean of ungrouped data
= sum of values of items (x) / number of items(n)
arithmetic mean of grouped data
= sum of demand x frequency(fx) / number of items (n)
is an average which means 'the most frequently occurring value'.
mode of a grouped frequency distribution
can be calculated from a histogram.
is the value of the middle member of an array. the middle item of an odd number of items is calculated as the (n + 1) ^th / 2 item.
of a grouped frequency distribution can be established from an ogive.
, which is the square root of the
, is the most important measure of spread used in statistics. make sure you understand how to calculate this standard deviation of a set of data.
the spreads of two distributions can be compared using the
coefficient of variation.
an expected value is a weighted average value of the different possible outcomes from a decision, where weightings are based on the probability of each possible outcome.
indicate what an outcome is likely to be in the long term, if the decision can be repeated many times over. fortunately, many business transactions do occur over and over again.
is an analysis of the proportion of times each particular value occurs in a set of items. there are a number of different probability distributions but the only one that you need to know about for management accounting is the
properties of the normal distribution are as follows:
it is symmetrical and bell-shaped
-it has a mean, µ (pronounce mew)
the area under the curve totals exactly 1
the area to the left of µ = area to the right of µ = 0.5
the normal distribution can be used to calculate probabilities. sketching a graph of a normal distribution curve often helps in normal distribution problems.
z = (x - µ) / standard deviation
z : the number of standard deviations above or below the mean (z score)
x : the value of the variable under consideration
µ : the mean
if you are given the
of a distribution, remember to first calculate the standard deviation by taking its square root.