## Statistics

1.Making a frequency table.

A frequency table is a table showing a record of raw data arranged in preparation for analysis and interpretation to give meaningful information.

It's constructed by arranging collected data in ascending order of magnitude with their corresponding frequencies.

1.Making a frequency table.

A frequency table is a table showing a record of
raw data arranged in preparation for analysis and interpretation to give
meaningful information.

It's constructed by arranging collected data in ascending order of
magnitude with their corresponding frequencies.

Example 1

The following data shows the number of goals
scored by a certain team during a football premiership league matches

0,0,1,1,2,1,1,0,3,4,4,3,2,2,5,6,4,6,4,1,1,1,4,5,5.

Make a frequency table showing the distribution above.

To draw a frequency table.

Step 1:

Construct a table with three columns. The first column to read the
number of goals(x). write down all the data values in ascending order of
magnitude i.e.(0-6)

Step 2:

The second column to read tally, then place a tally mark at the
appropriate place in the column for every data value.

When the fifth tally is reached, draw a line across the first four as
shown
,

Continue this process until all data values in the list are tallied.

Step 3:

Count the number of tally marks for each data value and write it in
the third column as frequency.

Solution

Grouped Data

Example 2

The following data shows the distribution of
marks out of 50 in a mathematics test for 20 students.

2,7,12,11,13,14,14,4,18,19,20,15,12,23,22,32,34,31,38,37.

Makes a grouped frequency table for the above data using a class
interval of 5.

Solution

Measures of central tendency: mean, median
and mode.

The mean, Mode and median are values about which
the distribution of a set of data is considered to be roughly balanced.

Mean

This is the sum of data values divided by the
number of data values. The mean can be obtained for grouped or ungrouped
data.

Example

The following are ages of college students.
Calculate their mean age 27, 28, 31, 30, 32, 35, 28, 30, 29

Solution

Grouped data

Example

The table below shows the distribution of
average marks out of 50 for thirty physics students in ngombini school.

Calculate the mean mark for the thirty students.

Solution

First make a frequency table as shown below.

Median

The median of a set of data values is the middle
values of the set of data when it has been arranged in ascending order.

Example

37, 25, 27, 22, 28, 29, 26, 24, 25

Find the median of this set of data.

Solution

Arrange the data values in ascending order

22, 24, 25, 25, 26, 27, 28, 29, 37

Since the data values are 9, the fifth value is the middle value.

Therefore the median of the set of data is 26.

The number of the values n, in the data set = 9.

Mode

The mode is the most frequent occurring value in
the data.

Example

Find the mode of the following set of data

38, 34, 38, 35, 32, 38, 39.

Solution

The mode is 38 since it occurs most often.

Note

It's possible for a set of data to have more
than one mode.

**STATISTICS**

Statistics is a very vital branch of
mathematics as it involves gathering of raw data, recording, analysis
and interpretation of data, into meaningfull information, which helps us
to make proper judgment in life.

**The Assumed Mean**

When the number of values in a set of data is large, the assumed mean method is used. The assumed mean is an expected value of the mean also known as the working mean, usually denoted as A. The assumed mean does not need to be one of the values given.

Estimate by calculation:

1.The median

2.The lower and upper quartiles

Solution

For one to estimate the median and the two quartiles, one must create a
cumulative frequency table with lower and upper class boundary column as
shown.

The Median

For us to calculate the median we must first
of all identify the median class, and since we have 100 data values the
middle value must lie at the 1/2 (N +1)value (refer to background) i.e.
it must lie at the 1/2(100+150).5th
value in the cumulative frequency column.

Therefore the median class should be the one having 59.5-69.5 class
boundaries

The median (Q2) using the formula

where

L = Lower class boundary of the median class.

N =Total frequency of the distribution.

Cfa=
Cumulative frequency above the median class.

fm=
Frequency of the median class.

i= Class interval of the median class.

The lower quartile (Q1)

Identify the quartile class as you did with the
median class above.

Calculate the lower quartile (Q1)
using the formula

Where

L= Lower class boundary of the Q1 class.

N= Total frequency of the distribution.

Cfa = Cumulative frequency above the Q1
class.

fQ1= Frequency of the Q1
class.

i= Class interval of the Q1 class.

In the case above:

L=39.5

N=100

Cfa= 24

fQ1 = 12

i = 10

For the Upper Quartile (Q3)

Identify the upper quartile class (Q3)
and highlight it.

Calculate the upper quartile Q3
using the formula

where

L= Lower class boundary of the Q3 class.

N= Total frequency of the distribution.

Cfa = Cumulative frequency above the Q3
class.

fQ3= Frequency of the Q3
class.

i= Class interval of the Q3 class.

In the case above:

L=69.5

N=100

Cfa= 68

fQ3 = 15

i = 10

**NB:**The difference between the upper
quartile (Q3) and the lower quartile (Q1)is
called the interquartile range.

Therefore, in the case above the interquartile range is given by

Interquartile range =Q3-
Q1

= 74.17 - 40.33

= 33.84

Half of the interquartile range is also known as the semi-interquartile range or the quartile deviation, i.e. semi-interquartile range (quartile deviation)

Use of Ogive/ Cumulative Frequency Curve.

An ogive/ cumulative frequency curve is obtained
by plotting cumulative frequency values against the upper class
boundaries.

The curve can be used to estimate the median, the lower quartile and the
upper quartile.

Example

The table below represents mass of sugar in kg
consumed in a college per day.

Draw an ogive (cumulative frequency curve) and use it to find:

1.The median.

2.The lower quartile3.

3.The upper quartile.

4.The interquartile range.

Solution

Construct a table showing the boundaries of the
classes and the cumulative frequencies as below

Plot the cumulative frequency against the upper class boundaries to get the cumulative frequency curve shown below

.

1.The median

Q2
= (1/2 x 60)th
value. i.e. 30th value

From the graph the 30th value is 26.5

2.The lower quartile

Q1
= (1/4 x 60)th
value. i.e 15th
value.From the graph the 15th
value is 24.

3.The upper quartile

Q3
= (3/4 x 60)th
value. i.e 45th
value.From the graph the 45th
value is 28.25

4.The interquartile range = Q3 - Q1 = 28.25 - 24 = 4.25

Example 1

One hundred students were asked to estimate the
distance between their dormitories and their classes in meters. Their
results were shown as in the table below.

Solution

Using steps 1 to 5 in II above and taking 38 to
be the assumed mean, the deviation ,d is given by x-A=d.

Example 2

The height of 50 tree seedlings in a tree nursery in cm were recorded as in the table below. Using a suitable assumed mean estimate the mean to the nearest cm.

Solution

Prepare a frequency table and obtain the
midpoint(x) of each class. Follow steps 1 to 5 as previously explained.

Making a cumulative frequency table

Cumulative frequency table is made by adding a
cumulative frequency column to a frequency table.

Cumulative frequency is the gradual increase of frequencies as a result
of subsequent addition.

Example.

The table below shows the distribution of masses
in kg of 35 people. Make a cummulative frequency table.

Solution

Estimating the median and the quartiles

a) Calculation

Median is the value that divides a distribution
of data values into two equal parts.

Quartiles (Q) are the values that divide a distribution into four equal
parts. Thus the lower quartile(Q1)
is the value below which lies the 25% (1/4) of the distribution and the
upper quartile(Q3)
is the value below which lies the 75% (3/4) of the distribution.

Example

The table below shows the speed of 100 public
service vehicles during a police check.

.

Statistics

## e-Content

Buy e-Content Digital CD covers all the topics for a particular class per year. One CDs costs 1200/-

click to play video

Purchase Online and have the CD sent to your nearest Parcel Service. Pay the amount to Patrick 0721806317 by M-PESA then provide your address for delivery of the Parcel.. Ask for clarification if in doubt,

Statistics

###### Candidate benefit from our quick revision booklets which are comprehensive and how to tackle examination question methods

###### We have an enourmous data quiz bank of past papers ranging from 1995 - 2017

KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination. KCSE mock past papers serves as a good motivation as well as revision material for the major exam the Kenya certificate of secondary education (KCSE). Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE . Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective

#### MOCK Past Papers

As a student, you will have access to the most important resources that can help you understand what is required for you to sit and pass your KCSE examination and proceed to secondary school or gain entry to University admission respectively.

#### KCSE ONLINE

Similar

More

Similar

KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination.

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective

Ask for clarification if in doubt, vitae dignissim est posuere id.

Statistics

sit amet congue Mock Past Papers, give you an actual exam situation in readiness for your forthcoming national examination from the Kenya National Examination Council KNEC

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien.

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien.

Statistics

As a supplementary to coursework content our e-library for digitized multimedia CDs while enhance and ensure that you never missed that important concept during the normal class lessons. It is a Do it Yourself Project..

Candidates who would want their papers remarked should request for the same within a month after release of the results. Those who will miss out on their results are advised to check with their respective school heads and not with the examination council

For Best results INSTALL Adobe Flash Player Version 16 to play the interactive content in your computer. Test the link below to find out if you have Adobe Flash in your computer.