Representing and Measuring Data

This page deals with one-variable statistics. You need to know how to represent the data in tables and diagrams (histograms, cumulative frequency graphs and box and whisker diagrams), as well measure the data using measures of central tendency (mean, median and mode) and dispersion (interquartile range, standard deviation and variance). It is not a difficult topic, but attention to detail is required. It is recommended that you work through the revision notes carefully.


Key Concepts

On this page, you should learn about

  • frequency distributions
  • histograms
  • cumulative frequency graphs
  • mean, median,mode
  • quartiles, percentiles
  • range, interquartile range, standard deviation and variance
  • box and whisker diagrams
  • outliers
  • the effect of constant changes to mean and standard deviation 

Summary

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Test Yourself

Here is a quiz about some definitions in statistics


START QUIZ!

Here is a quiz about boxplots, cumulative frequency and histograms


START QUIZ!

Here is a quiz about mean and standard deviation


START QUIZ!

Exam-style Questions

Question 1

During week 1, a group of 60 athletes were asked to record the amount of water, X litres, that they consumed in that week. Here are the results

\(\sum x=1470\)

\(\sum x^2=36\ 132.6\)

Calculate

a. the mean of X

b. the standard deviation of X

During week 2, as part of a programme to improve their performance, the athletes were instructed to drink 10% more water. Assuming that they do this, find for week 2

c. the new mean

d. the new standard deviation


Hint

Full Solution

 

Question 2

The graph below shows the scores in the SL Mathematics Analysis and Approaches for at Goodenough High School. There are 20 students, the minimum score was 2 and the mean score is 4.45

How many grade 4s and how many grade 7s were there?


Hint

Full Solution

Question 3

The cumulative frequency graph gives information about the lengths, in minutes, of 80 telephone calls.

a. Find the median length of a phone call

b. Find the interquartile range of the length of a phone call

c. Find the number of phone calls that were more than 10 minutes in length

d. The frequency table below shows the lengths of the 80 phone calls. Find values a, b and c.

e. These data contain some outliers. How many outliers are there?

f. Calculate an estimate of the mean length of a phone call


Hint

Full Solution

 

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