View source for 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(x&#772;) = 50+61+46+54+46+47+28+46+76+98+99+21+43/13 = 

<p>When the number of members in a set is small, say ten or less, the data can be represented diagrammatically without further analysis, by means of pictograms, bar charts, percentage componens bar charts or pie charts. </p>
<p>For sets having more than ten members, those members having similar values are grouped together in <b>classes</b> to form a <b>frequency distribution</b>. To assist in accurately counting members in the various classes, a tally diagram is used sometimes.</p>
<p>A frequency distribution is merely a table showing classes and their corresponding frequencies.</p>

:: grouped data: a frequency distribution

'''Example:'''<br/>
'''Question'''<br/>
The mean of the numbers 1, 3, x, 8 is x. <br/>
Find the value of x. <br/>
'''Solution'''
Mean = x. <br/> <math>1+3+x+8/4 = x</math><br/>
<math>12+x = 4x.</math><br/>
<math>12- 3x</math><br/>
<math>x=4</math>

 

<s>Given the mean, calculate the frequency:</s>




Calculate a weighted mean

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


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 interquartile range


Form a grouped frequency table

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