# Leaving Certificate Mathematics/Further Probability and Statistics

Leaving Cert - Paper2: Statistics

Calculate the mean, median and mode of:

a list of numbers.

Example: Question: A group of students scored the following marks in an exam: 50, 61, 46, 54, 46, 47,28, 46, 76, 98, 99, 21, 43. What was the mean, median and mode of the results? Solution:

The mean(x̄) = 50+61+46+54+46+47+28+46+76+98+99+21+43/13 =

When the number of members in a set is small, say ten or less, the data can be represented diagramatically without further analysis, by means of pictograms, bar charts, percentage componens bar charts or pie cahrts.

For sets having more than ten members, those members having similar values are grouped together in classes to form a frequency distribution. To assist in accurately counting members in the various classes, a tally diagram is used sometimes.

A frequency distribution is merely a table showing classes and their corresponding frequencies.

grouped data: a frequency distribution

Example:
Question
The mean of the numbers 1, 3, x, 8 is x.
Find the value of x.
Solution Mean = x.
${\displaystyle 1+3+x+8/4=x}$
${\displaystyle 12+x=4x.}$
${\displaystyle 12-3x}$
${\displaystyle x=4}$

Given the mean, calculate the frequency:

Calculate a weighted mean

Example:
Question
(a)Calculate the weighted mean of the results: 6, 10, 8, 4, given the respective weights: 2,3, 4, 1.
Soultion
weighted mean = (6x2)+(10x3)+(8x4)+(4x1)/2+3+4+1

Calculate the standard deviation of:

a list of numbers
a frequency distribution

Construct a histogram from a frequency distribution table

and vice versa

Draw an ogive

Using an ogive, estimate median, lower quartile, upper quartile and inter quartile range

Form a grouped frequency table