2.13 Showing Data Summaries

What is the purpose of showing data summaries in statistics?

• To make data more complex

• To simplify and organise data

• To increase the amount of data

• To confuse the reader

Answer explanation

The purpose of showing data summaries in statistics is to simplify and organise data, making it easier to understand and interpret. This helps in identifying trends and patterns without overwhelming the reader with raw data.

Which of the following is a common method for summarising data?

• Pie chart

• Long paragraphs

• Random numbers

• Unstructured text

Answer explanation

A pie chart is a common method for summarising data as it visually represents proportions of a whole, making it easy to compare different categories. The other options do not effectively summarise data.

What is the median in a data set?

• The most frequently occurring value

• The middle value when data is ordered

• The sum of all values

• The smallest value

Answer explanation

The median is defined as the middle value of a data set when it is ordered. This means that half the values are below it and half are above it, making 'The middle value when data is ordered' the correct choice.

If a data set has the values 3, 7, 7, 2, 9, what is the mode?

• 3

• 7

• 2

• 9

Answer explanation

The mode is the value that appears most frequently in a data set. In the values 3, 7, 7, 2, 9, the number 7 appears twice, more than any other number, making it the mode.

What does the range of a data set represent?

• The average of the data

• The difference between the highest and lowest values

• The sum of all data points

• The number of data points

Answer explanation

The range of a data set is defined as the difference between the highest and lowest values. It provides a measure of how spread out the values are, making 'the difference between the highest and lowest values' the correct choice.

Which of the following is a measure of central tendency?

• Range

• Variance

• Mean

• Standard deviation

Answer explanation

The mean is a measure of central tendency that represents the average of a data set. In contrast, range, variance, and standard deviation are measures of dispersion, not central tendency.

If the mean of a data set is 10 and the sum of all data points is 50, how many data points are there?

• 4

• 5

• 6

• 7

Answer explanation

To find the number of data points, use the formula: Mean = Sum of data points / Number of data points. Here, 10 = 50 / x. Solving for x gives x = 50 / 10 = 5. Thus, there are 5 data points.

What is the purpose of a histogram?

• To display data in a tabular form

• To show the distribution of data

• To list data points

• To calculate the mean

Answer explanation

A histogram is used to show the distribution of data by representing the frequency of data points within specified ranges, allowing for easy visualization of patterns and trends in the dataset.

Which of the following is not a graphical representation of data?

• Bar chart

• Line graph

• Scatter plot

• Paragraph

Answer explanation

A paragraph is a text format and does not visually represent data like a bar chart, line graph, or scatter plot, which all display data graphically. Therefore, the correct answer is 'Paragraph'.

If a data set is skewed to the right, which of the following is true?

• The mean is less than the median

• The mean is greater than the median

• The mean is equal to the median

• The mode is greater than the mean

Answer explanation

In a right-skewed distribution, the tail on the right side is longer, pulling the mean higher than the median. Therefore, the mean is greater than the median.