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 diagrammatically without further analysis, by means of pictograms, bar charts, percentage componens bar charts or pie charts.
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
The mean of the numbers 1, 3, x, 8 is x.
Find the value of x.
Solution Mean = x.
Given the mean, calculate the frequency:
Calculate a weighted mean
(a)Calculate the weighted mean of the results: 6, 10, 8, 4, given the respective weights: 2,3, 4, 1.
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 interquartile range
Form a grouped frequency table