SL 06 Statistics for Univariate Data (Revision - GDC)

If the mean of the six numbers 8, 4, 6, 9, 7 and x is 7, find the inter-quartile range of the six numbers.

• 2

• 3

• 5

• 8

For the four numbers x - 3, x - 4, x + 2, x + 5, which of the following must be true?

I. The median is x - 1.

II. The mean is x.

III. The range is 8.

• I only

• II only

• I and III only

• II and III only

{x - 1, x - 2, x + 3, x + 4} and {x - 5, x - 6, x + 7, x + 8} are two groups of numbers. Which of the following is/are true?

I. The two groups of numbers have the same mean.

II. The two groups of numbers have the same inter-quartile range.

III. The two groups of numbers have the same range.

• I only

• II only

• I and III only

• II and III only

Which of the following box-and-whisker diagrams can represent the following set of data?

3, 2, 4, 6, 4, 6, 5, 8, 10, 12

• 
• 
• 
• 

The box-and-whisker diagram shows the distribution of the weights (in kg) of a group of students.

From the diagram, which of the following is/are true?

I. The weight of the lightest student is 35 kg.

II. The inter-quartile range of the distribution is 20 kg.

III. At least half of the students are heavier than 65 kg.

• I and II only

• I and III only

• II and III only

• I, II and III

The box-and-whisker diagram shows the marks distribution of 40 participants in a preliminary test.

Which of the following statements must be true?

I.  The mean of the test marks is 9.

II. At most 10 participants get 8 marks or below.

III. At least 11 participants get 10 marks.

• I only

• III only

• I and II only

• II and III only

If the mean of the data set {27, 2a – 1, 13, 18, a + 3, 30} is 26, find the standard deviation of the data set.

• 3

• 22

• 90

Which of the following statements is incorrect?

• Standard deviation takes into account of all the data.

• Inter-quartile range is affected by extreme values.

• Variance is a measure of dispersion.

• Median is a measure of central tendency.

The standard deviation of a set of data is k. If each datum is decreased by 3, find the standard deviation of the new set of data.

• k

• k - 3

• 3k

The standard deviation of a set of numbers is 9. Each number of the set is multiplied by 3 and then 8 is subtracted from each resulting number to form a new set of numbers. Find the variance of the new set of numbers.

• 33

• 235

• 361

• 729