Pearson Edexcel GCSE (9-1) · Statistics (1ST0)

Standard deviation (Higher tier): Practice Questions

4 multiple-choice questions marked as you go, and 3 written questions with worked solutions. All on Standard deviation (Higher tier).

7 questions15 marksFree, no account

Question 1

1 mark

A distribution of test scores has a mean of 65, a median of 72, and a mode of 80. Based on these measures of central tendency, what is the skewness of the distribution?

Question 2

1 mark

For a data set where the Lower Quartile (LQ) is 15 and the Upper Quartile (UQ) is 35, an outlier is defined as any value more than \(1.5 \times \text{IQR}\) above the UQ or below the LQ. Which of the following values would be considered a large outlier?

Question 3

1 mark

A set of data is displayed in a stem and leaf diagram. The leaf values for one stem are 2, 5, 5, 8, 9. What is the median of this specific row if the stem represents tens and the leaves represent units?

Question 4

1 mark

A histogram is drawn for grouped data with unequal class widths. The class \(10 < x \le 20\) has a frequency of 50. The class \(20 < x \le 50\) has a frequency of 60. What is the ratio of the frequency density of the first class to the frequency density of the second class?

Question 5

2 marks

A data set consists of the following values:
7, 12, 15, 18, 45.
Identify the outlier in this data set and suggest one reason why it might have occurred in the context of data cleaning.<\/p>

Write your answer out first, then check it against the worked solution.

Question 6

4 marks

A distribution of test scores has a mean of 62, a median of 55, and a mode of 48.
Determine the skewness<\/b> of this distribution and explain what this tells you about the spread of the data relative to the median.<\/p>

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

A health clinic tracks the recovery time (in days) of patients after a specific treatment. The data for 10 patients is shown below:

\(12, 15, 14, 18, 11, 45, 13, 16, 14, 17\)

(a) Identify the outlier in the data set by inspection.
(b) Calculate the median and the interquartile range (IQR) for these 10 patients.
(c) The clinic manager wants to summarize the 'typical' recovery time. Explain why the median might be a more appropriate average than the mean in this context, referring to the outlier identified in part (a).

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, graded as you go.

Practice More