JEMIMAH WUGHANGA MWANDOE

8/7/2019 JEMIMAH WUGHANGA MWANDOE

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PRESBYTERIAN UNIVERSITY OF EAST AFRICA

SCHOOL OF BUSINESS ADMINISTRATION

UNIT CODE :

NAME:JEMIMAH MWANDOE

ADMISSION:N33/1102/02

TOPIC:

LECTURER:


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MEAN is defined as the sum of all values divided by the number of values.

That is

the sum of all values/

the number of values

fxn

mean is used to estimate the total or the sum of a group of valuesas: sum arithmetic mean * number of values.It is also used as an example of a measure of location or average which aims to

represent a set of data numerically.

INTERPRETATIONmean for an ungrouped data:

1. Find the arithmetic mean for the set of data 100,200,300,500

= 100+200+300+500/4 =275

interpretion: the average of the set of data is 275

mean for a grouped data:

2. below are profits made by certain companies:3.

Profits made Number of comn

Mid-pointx

fx

0-5000 10 2500 25000

5000-10000 60 7500 450000

10000-15000 50 12500 625000

15000-20000 40 17500 70000020000-25000 30 22500 675000

25000-30000 10 27500 275000

mean=fx/n =2975500/200 =14875the companies made an average profit of 14875


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advantages

1.its calculation best suits the development of advancedstatistical theories and calculations.

2.it can be calculated even if some values are unknown-ed.

advantages

1.poor representative value when used for descriptive

purposes only.

2.its size is affected by presence of extreme values.

MODE

is the value that occurs most often or equivalently has largest frequency.

USES1.used when a distribution has open ended classes.

2.used as an alternative to the mean or median when situation calls

for most popular value to represent some data.

INTERPRETATION1.mode of a set of data.

Car prices(kshs) Number of cars

200000 2

300000 4

600000 3

900000 1

The price of cars costing 300000 appears four times, mode is 300000meaning the typical price of cars is 300000kshs.

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2. mode for grouped data

weight Number of people

20-30 3

30-40 2

40-50 6

50-60 5

60-70 2

70-80 2

The modal class is at weight of 40-50

Mo=Oe+c(fm-fm-1)/2(fm-1-fm+1)

40+10(6-2)/18-2-5=48

therefore the typical weight of people is 48.

advantages

1.easy to understand2.not difficult to calculate3.its values are not influenced by presence of extreem values.

Disadvantages

1.Not used in advanced statistical work.2.It has no natural measure of dispersion to twin with where further

analysis is required.

3.It may not exist and if it does, may not have a unique value.4.Cannot be used to calculate the sum of the values.

MEDIANThe median of a set of data is the value of that item which lies exactly halfway


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along the set-arranged into size order.

USES:Used when certain end values of a set or distribution are difficult,expensive orimpossible to obtain,particularly appropriate to life data.Used when a distribution is skewed or when end values are not known.

INTERPRETATION:a) The median of a set of values

-1 3 2 4 8 6 5The middle value by visual inspection is 4.

b) Median of grouped data.

40 Students in a class measured their masses and recorded them to the nearestkg.

40, 48, 56, 52, 49, 57, 56, 52, 53, 48, 38, 39, 43, 47, 41, 60, 63, 59, 45, 51.

CLASS Yf cf

35-39 2 2

40-44 3 5

45-49 5 10

50-54 4 14

55-59 4 18

60-64 2 20

ADVANTAGES:1) Not affected by outliers as the mean and mode can be.


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2) An appropriate alternative to the mean when extreme values are present.3) May be determined or estimated if only the middle values are known.

DISADVANTAGES:

1) Cannot be used to determine the sum of a group of values.2) Calculation unsuitable for the development of advanced statistical

concept.3) Its exact value may be indeterminate if the values are widely dispersed

within range.

Range: This is the numerical difference between the smallest and the largestvalues of items in a set of distribution.

USES:

-Used in quality control purposes.-Variation in money rates.

-In weather forecasting.

INTERPRETATION:Students performed as follows in their end of course exam:-

57, 55, 62, 52, 54, 45, 57, 66.Range=66-45

=21=>The difference between the highest (66) and lowest (45) is 21.

ADVANTAGES:

1) It is a simple concept and easy to calculate.2) It shows the spread of results.

DISADVANTAGES:

1) Does not take into account any 'clustering' of results in a set of data.2) It is affected strongly by outliers.3) Has no natural partner in a measure of location and is not used in further

advanced statistical work.

INTERQUARTILE RANGE:

This is the difference between upper and lower quartile.

USES.a)used to summarize the extent of the spread of your data.


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ADVANTAGES.a)Its a good indicator of the spread in the center region of data .b)Relatively easy to compute .c)More resistant to extreme values than range.

DISADVANTAGES.a)Doesn't incorporate all of the data in the small

QUARTILE DEVIATIONIs defined as half the range of the middle items the difference between the lower and upper quartile.

USES.a)used in situations where extreme observations are thought to be un representative .b)used in interpretation of sedimentary rocks.

INTERPRETATION.Find the quartile deviation10,20,30,40,50,60,70,80,

AGE OF STUDENTS NUMBER OF STUDENTS C.F

3 3


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2 5

6 11

5 16

2 18

2 20

ADVANTAGESa)Not influenced by extremely high or extremely low scoresb)it is a relative measurement.c)simple to understand

DISADVANTAGES.a)unstable for small samples

VARIANCE.This is the mean of the square of the deviations from the mean .

USES.a)Used in exponential distribution

INTERPRETATION.The students performed as follows in their end course.

Students:85,32,55,87,24,78,49,38x-x :29 -24-1 31 32 22 7 -18448=568MEAN=56

VARIANCE=we square all deviations to get a positive value3d=841,576,961,1024,484,49,32


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variance =4260=532.58

ADVANTAGES.a)its less affected by outliersb)it is easy to locate

DISADVANTAGES.a)it is resistant to sampling

STANDARD DEVIATIONSThis is the root of the mean of the squares of deviation from the common mean of a set of values

standard deviation=variance

USESa)used to estimate the accuracy of the sample mean as an estimate of the population mean.b)used to measure the investments volatility in finance.c)used for assessing the degree of dispersion of value around its mean interpretationd)used by climatologists to help classify abnormal climatic conditions.

The table represents the distribution of marks of 40 students in a test.

MARKS

FREQUENCY

2 2 3 9 12 5 2 3 1

CLASS FREQUENCY

MIDPOINT fx d= d2 fd

2 5.5 11 -39.5 1560.25 3120.25

2 15.5 31 -29.5 870.5 1740.5

3 25.5 76.5 -19.5 380.25 1140.75

9 35.5 319.5 -9.5 90.25 812.25

12 45.5 546 0.5 0.25 3

5 55.5 277.5 10.5 110.25 551.25

2 65.5 131 20.5 420.25 840.5

3 75.5 226.5 30.5 930.25 2790.5

1 85.5 85.5 40.5 1640.25 1640.25

1 95.5 95.5 50.5 2550.25 2550.25


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ADVANTAGES.a)Can be used to convert scores calculated on different scales to scores on a standard scale.b)gives an accurate idea of its relative size or importance.c)can be regarded as truly representative of the data since all data values are taken into A|C in itscalculation.

DISADVANTAGES.a)loss of information on absolute levels.b)when the mean value is close to zero the coefficient of variation is sensitive to small changes in the meanlimiting its usefulness.c)resistant to sampling variationd)affected by extreme values.


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