Called as measures of location
These are also called as measures of location or measures of central tendency. They indicate the canter or most typical value of a data set lies. This includes three important measures they are mean, median and mode. Mean and median can only apply for quantitative data, but mode can be used with either quantitative or qualitative data.
This is the most commonly used measure which is the average of a data set. This is the sum of the observations divided by the number of observations.
Advantages of mean-objective
- Easy to calculate
- Easy to understand.
- Calculated from all the data.
Disadvantages-affected by-outlying values
- May be some distance from most values.
Median of a data set is the number that divides the bottom 50% of the data from the top 50%.
Advantages-Easy to understand
- Give a value that actually occurred
- Not being affected by outlying values.
Disadvantages-Does not consider all the data
- Can be used only with cardinal data.
- Not easy to use in other analyses.
Mode of a data set is the number that occur frequently (more than one)
Advantages-being an actual value
- Not affected by outlying value
Disadvantages-there can be more than one mode or none
- Does not consider all the data
- Cannot be used in further analyses.
Comparison of mean, median and mode
For this garage ,its representative values are as follows
As we can see mean and median are not varying by huge amount but mode on the other hand varies.
Here the owner has to select which price he has to charge among all these.
Mode is very high and it doesn't consider all the values, so if the owner charge £430 it will be costly and the customers switch to competitors owner should not choose mode.
Now the selection is between mean and median. Both of them look reasonable and close to most of the cost of the October. Median is usually preferred when the data set have more extreme observations. Unless it is likely to select mean because it consider all the data.
From the overview of the cost of October it doesn't have more extreme values at all. So the mean value wouldn't have affected heavily.
Therefore it is advisable that the owner choose mean value that is £335
Measures of Dispersion
Representative measures only indicate the location of a set of data and two data sets can have same mean, median and mode. In that case we cannot make any decision using representative values. To describe the difference we use a descriptive measure that indicates the amount of variation which is known as measures of dispersion or measures of spread.
This includes the following measurements:
- Range-Range is simply the difference between the highest value and the lowest value. It is easy to calculate and understand but it only consider the largest and smallest value and ignore all the other values and it is highly affected by extreme values.
- Quartile range- Quartile range is the difference between 3rd quartile and 1st quartile. It also easy to calculate but it does not consider all the values in a data set so it is not a good indicator.
- Variance and Standard Deviation- Variance measures how far the observations are from the mean.
This is the most important statistics because it consider all the observations and is used for further analyses. Standard deviation is the square root of variance. Both variance and standard deviation provide useful information for decision making and making comparisons.
From the calculation range is £284 and quartile range is £170 but because of the defects of them we cannot use them to derive further decisions. Variance is 8426.9 and standard deviation is 91.79. From the figures we can see observations are highly deviated from the mean. Variance and standard deviations are used to compare two data set. So the owner of this garage can compare these two figures with a similar garage or the cost of November and make decisions such as select the price which has smaller variance and standard deviation.
Quartiles and percentiles also like representative measure. They indicate the percentage of value below a certain value i.e.3rd quartile indicate 75% of the observations are below a certain amount and 25% of observations are above.
From the above figures we can see only 25% of the values are above £418 so we shouldn't charge a price above than that if we do so we will lose many of their customers.25% of the observations are above £248.5 so we have to select a price between £248 and £ 418. Earlier we have found out the mean is £335. This is between 2nd quartile and 60% of percentile. So from the use of quartile and percentile we can select £335 as service price. Thus quartile and percentile help us in decision making.
Correlation coefficient measures the strength of the linear relationship between two variables. It is denoted by "r". Value of "r" always lie between -1 and +1. If "r" is closer to +1, two variables have strong positive relationship. Correlation coefficient also help to make business decisions.
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