Statistics · Guided Practice
Distributions
8 questions with answers and video solutions. Try each one before revealing the answer.
Describe the shape of this distribution.
Answer
The tail of high values stretches out to the right.
Describe the shape of this distribution.
Answer
The tail of low values stretches out to the left.
State the most appropriate measure of location and measure of spread.
Answer
Spread: the standard deviation.
These are appropriate because the distribution is symmetrical with no skew.
Describe the likely shape of this distribution.
Answer
Each face is equally likely, so all six bars should be roughly the same height, at about each.
State the most appropriate measure of location and measure of spread, and justify your answer.
Answer
Spread: the interquartile range.
The long tail of high values would drag the mean upwards and inflate the standard deviation, so both would misrepresent a typical value.
Answer
The tail of high values pulls the mean up, while the median stays near the bulk of the data.
(a) Describe the shape of the distribution.
(b) State which average the clinic should quote to describe a typical wait, and why.
Answer
(b) The median, because the few very long waits would pull the mean above what most patients actually experience.
You must refer to the spreadsheet file 'Q5 Radio.csv' for the data, and the word processing file 'Q5 Radio Answers.docx' when answering this question.
You must complete parts (a) (i) and (a) (iii) using appropriate statistical software.
You must include all output from statistical software, and your answers in the word processing file 'Q5 Radio Answers.docx'.
A radio station asks their listeners to report how many hours they are listening for one week in July.
(a)(i) Construct a histogram to summarise the data.
(a)(ii) Describe the distribution of the data shown in the histogram.
(a)(iii) Hence, generate and state the appropriate measure of location to summarise the data.
The data is then used to determine listening hours last summer.
(b) State one reason why the data might misrepresent the listening hours last summer.
Answer
(a)(i) Output from statistical software showing the generated histogram.
(a)(ii) Skewed (to the right)
(a)(iii) Median: 18.7 (hours)
(b) e.g., Extrapolation, self-recorded data, or not a random sample.