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## Business and Academic Skills

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**Business and Academic Skills**Describing data**Describing data**• Often within a business data is collected from many and various sources . • Need to describe the data and give it meaning. • If we can give it real meaning then managers may be able to use it in making decisions.**Describing data**• 216, 224, 2393, 2, 6, 77, 84, 7, 5, 3, 213, 242, 259, 214, 237, 217, 258, 218, 234, 211, 8, 64, 9, 276,223, 245, 212, 234, 264, 257, 278, 210, 9, 4, 114, 326, 441, 11, 242, 259, 514, 35, 119, 268, 208, 534, 11, 17, 186, 21, 3245, 49, 4, 2, 110, 236, 364, 160, 375, 210, 476, 98, 12, 134, 908, 765, 456, Without undertaking any calculations or drawing any pictures: In less than ten words accurately explain this group of data.**Compare the following 2 groups of data**Group 1 Group 2 216, 224, 239, 213, 242, 259, 214, 237, 217, 258, 218, 234, 211, 276, 223, 245, 212, 234, 264, 257, 278, 210, • 8, 6, 4, 9, 3, 2, 9, 4, 6,7, 7, 8, 4, 1, 7, 9, 4, 2,4, 7, 5, 3, Without undertaking any calculations or drawing any pictures: In less than ten words accurately explain the differences between the 2 groups.**Compare the following 2 groups of data**Group 3 Group 2 216, 224, 239, 213, 242,259, 214, 237, 217, 258,218, 234, 211, 276, 223,245, 212, 234, 264, 257, 278, 210, • 186, 213, 245, 110, 236,364, 160, 375, 210, 114, 326, 441, 11, 242, 259, 514, 35, 119, 268, 208, 534, 11 Without undertaking any calculations: In less than ten words accurately explain the differences between the 2 groups?**Compare the following 2 groups of data**Group 1 Group 4 6, 6, 4, 9, 3, 2, 9, 4, 8,7, 4, 8, 4, 7, 7, 9, 4, 9,4, 7, 5, 3, 6, 8, 4, 3, 2,2, 9, 6, 4, 8, 7, 7, 4, 1,9, 7, 2, 4, 4, 3, 7, 5, • 8, 6, 4, 9, 3, 2, 9, 4, 6,7, 7, 8, 4, 1, 7, 9, 4, 2,4, 7, 5, 3, Without undertaking any calculations or drawing any pictures: In less than ten words accurately explain the differences between the 2 groups.**Describing Groups of Data**• Possible issues • Often too much data to easily understand. • Using just words can loose accuracy, and create generalities. • Open to different interpretations • Possible actions • Put into tabular form. • Draw appropriate pictures. (Graphs) • Have some conventions for describing the data**Crisp Problem**• You love potato crisps. You eat 1 packet per day with your lunch time sandwich. You equally like two different brands which cost the same amount of money per packet. • Each brand is running a loyalty promotion so that if you collect 30 vouchers over the next 30 working days they will give you a £5 note. The voucher is in the form of a stamp given to you by the canteen each time you buy the crisps. • You can only get one voucher stamp per day. • How will you decide which brand to buy? • List the factors which might affect you decision.**Crisp Problem**• To help the following information is made available. • Brand A Number crisps per packet 60 Variation on number of crisps + 2 per packet. • Brand B Number crisps per packet 58 Variation on number of crisps + 8 per packet. • Does this information help, if so how?**Describing data**• Groups of data can be described by 4 main factors. • Shape of the data (shown by the picture of the data) • How big are the numbers • Measurement of a typical value. • Measurement of central tendency • Measurement of the spread of the data • How many pieces of data are there in the group**Frequency distribution**• If there is sufficient data, and the number of divisions can be increased so that there are more of them, the graph can be changed to frequency diagram. • The first example is of the “normal distribution” It is often assumed that the group of data being gathered is part of a much larger population which would have this distribution. • The second example is of data which comes a larger population which is skewed to one end or the other.**Frequency distribution (Example 1)**Frequency**Frequency distribution (example 2)**Skewed to lower values Skewed to Higher values**Our interest in graphs**• What are we really interest in when we produce a graph? • The shape of the graph: • Tall thin • Short fat • Regular shape • Skewness • Interpretation of the shape if we had a large quantity of data**The number scale**• The number scale can be represented by a straight line going from –ve to +ve with 0 in the middle. • The number scale helps determine size and whether one value or values is greater or less than another. • By placing groups of data on the scale we can see if one group has larger values than another. Group 1 Group 2 Group 3 0**The number scale**• If the group is diverse then may cover large amount of the scale need a single point to establish the position of the group on the scale. Some form of typical value. • Referred to as the Measurement of Central Tendency for that group of which there are 2 main measurements. • Arithmetic mean (Average) • Median**The number scale**• If the group is diverse then may cover large amount of the scale need a single point to establish the position of the group on the scale. Some form of typical value. • Referred to as the Measurement of Central Tendency for that group of which there are 3 main measurements. • Arithmetic mean (Average) • Median • Mode**Measurement of central tendency**• Arithmetic Mean (average) {excel function =average(values)} • Defined as: The sum of all the values divided by the number of values.(Note This will be a derived value determined by the formula for the arithmetic mean) • Median {excel function =median(values)} • Defined as:The physical middle value when the values are placed in order. (Note Excel automatically deals with the sort within the function)**Measurement of central tendency**• Arithmetic Mean (average) {excel function =average(values)} • Defined as: The sum of all the values divided by the number of values.(Note This will be a derived value determined by the formula for the arithmetic mean)**Measurement of central tendency**• Median {excel function =median(values)} • Defined as:The physical middle value when the values are placed in order. (Note For an even number of values the median lines in the middle of the 2 numbers physically at the centre)**Compare the following 2 groups of data**Group 3 Group 2 216, 224, 239, 213, 242,259, 214, 237, 217, 258,218, 234, 211, 276, 223,245, 212, 234, 264, 257, 278, 210, • 186, 213, 245, 110, 236,364, 160, 375, 210, 114, 326, 441, 11, 242, 259, 514, 35, 119, 268, 208, 534, 11 Exercise Calculate the arithmetic mean and median for groups 3 and 2**Spread of data**• The measure of central tendency positions the group of data on the number scale. • However differing groups of data can have the same or similar measures. • A measurement of the spread of the data helps us to understand some more about the data. • Three main measures of spread • Range of the data • Inter-quartile range (used with the median) • The standard deviation (used with the mean)**Range**• The range of a group of data is the difference between the value of the highest and the lowest value within the group. • There is no direct excel function to measure the range thus we need to establish the maximum and minimum values and subtract one from the other. • We can use the following formula for the range:=(max(group reference)-(min(group reference)))**Range Example group 1**This in effect tells us the total width of the data group. Tells us whether the total group is close together or far apart.**Inter-quartile range**• The median is the physical middle value when the values are placed in order. • If the data is placed in order it is possible to obtain the value at any point in the group range. • A Percentile is the mechanism for obtaining this value. • The group data is broken normally into 100 equal intervals, and a percentile returns the value at the require point. • For example : given the numbers 0,1,2,3,4,5,6,7,8,9,10 in a group • The value of 10% percentile = 1 • The value of 25% percentile =2.5 etc**Inter-quartile range**The excel function is =percentile(range of data, Percentile point) Thus for group 1 the 25% percentile would be :**Inter-quartile range**• The lower quartile is the value of the 25% (0.25)percentile • The upper quartile is the value of the 75% (0.75)percentile • The inter-quartile range is defined as the difference between the values of the upper and lower quartile. • Thus this tells us the range of the middle 50% of the data**Inter-quartile range**• Again there is no direct excel function but the value can be calculated using the following formula:=(percentile(range data,0.75)-percentile(range data,0.25))**Inter-quartile range**This result indicates that middle 50% of the data lies close together . Should be considered with the median.**Compare the following 2 groups of data**Group 3 Group 2 216, 224, 239, 213, 242,259, 214, 237, 217, 258,218, 234, 211, 276, 223,245, 212, 234, 264, 257, 278, 210, • 186, 213, 245, 110, 236,364, 160, 375, 210, 114, 326, 441, 11, 242, 259, 514, 35, 119, 268, 208, 534, 11 Exercise Calculate the range and inter quartile range for groups 3 and 2**Standard deviation**• The arithmetic mean is the most commonly used measurement of central tendency. • To measure the spread of the data we use the standard deviation. • Unlike the other two values this is not a measurement of range • It is a measurement of how well the data is clustered around the arithmetic mean value. • The lower the value the closer the clustering**Standard deviation**• The standard deviation is a derived statistical formula. • This formula can vary depending on the way that he data has been collected, however if you a reasonable amount of data all the different formula’s give roughly the same answer. • Any error due to using the wrong formula is most likely very small compared with other errors involved in the total process. • The excel formula we shall use is =stdevp(range)**Compare the following 2 groups of data**Group 3 Group 2 216, 224, 239, 213, 242,259, 214, 237, 217, 258,218, 234, 211, 276, 223,245, 212, 234, 264, 257, 278, 210, • 186, 213, 245, 110, 236,364, 160, 375, 210, 114, 326, 441, 11, 242, 259, 514, 35, 119, 268, 208, 534, 11 Exercise Calculate the range the standard deviation for groups 3 and 2**Measures of dispersion (Inter quartile Range)**Inter-quartile Range**Measures of dispersion (Standard deviation)**33% Standard deviation