Question 1

13, 24, 33, 47, 56, 68, 87&#10;-1) the arithmetic mean of the values above is:&#10;A) 46.9&#10;B) 47&#10;C) 46.857&#10;D) 46.86

Accepted Answer

A

Question 2

13, 24, 33, 47, 56, 68, 87&#10;-2) The median of the values above is:&#10;A) 56&#10;B) 33&#10;C) 47&#10;D) 68

Accepted Answer

The median is the middle value in a set of numbers arranged in order. To find the median, we first arrange the numbers in order: 13, 24, 33, 47, 56, 68, 87. The middle value is 47, which is the fourth number in the list. Therefore, the answer is C) 47.

Question 3

3) The mode of 9, 12, 13, 23, 13, 16, 18, 35, 14, 18, 18, 13 is:&#10;A) 13&#10;B) 18&#10;C) 13 or 18&#10;D) 13 and 18

Accepted Answer

The mode is the number that appears most frequently in a data set. In this case, both 13 and 18 appear three times, making them both modes of the data set.

Question 4

4) If the standard deviation of a data set is 4 then the variance is:&#10;A) 2&#10;B) 16&#10;C) 6&#10;D) 40

Accepted Answer

The variance is equal to the square of the standard deviation, therefore the variance is (4^2) = 16.

Question 5

5) What is the range of the scores:&#10;23 14 17 28 31 27&#10;A) 17&#10;B) 18&#10;C) 7&#10;D) 4

Accepted Answer

To find the range, we subtract the lowest score from the highest score. 
Highest score = 31 
Lowest score = 14 
Range = 31 - 14 = 17 
Therefore, the answer is B) 18 because range is equal to 17.

Question 6

6) A researcher records A if a car stopped at a red light, B if it crossed and C if it stopped only with difficulty. The data recorded are:&#10;A) At an interval level of measurement&#10;B) Ordinal data&#10;C) Categorical data&#10;D) At a ratio level of measurement

Accepted Answer

The data recorded are categorical because they are divided into distinct categories (A, B, C) rather than numerical values.

Question 7

7) Which of the following kinds of data can be treated as being at interval level?&#10;A) The gender of each participant&#10;B) Scores on a standardised measure of anxiety&#10;C) Songs ranked by a participant in order of preference&#10;D) The kind of physical activity each participant reports being engaged in

Accepted Answer

Scores on a standardized measure of anxiety can be treated as interval level data because they have equal intervals between each level of the scale and a meaningful zero point (i.e. absence of anxiety). None of the other options (gender, song preferences, physical activity) have a true zero point, and therefore cannot be treated as interval level data.

Question 8

8) Which of the following is true?&#10;A) The sample variance is almost always larger than the population variance&#10;B) The formula for standard deviation when it is used to estimate population variance uses just N on the bottom of the equation&#10;C) The formula for standard deviation when it is used to estimate population variance uses N -1 on the bottom of the equation&#10;D) The 'uncorrected' version of the standard deviation formula uses N -1 on the bottom of the equation

Accepted Answer

The formula for standard deviation when it is used to estimate population variance uses N -1 on the bottom of the equation. This is known as the 'corrected' version of the standard deviation formula, which accounts for the fact that when we calculate a sample standard deviation, we are estimating the population standard deviation based on a smaller number of observations. The 'uncorrected' version of the standard deviation formula uses just N on the bottom of the equation, and is used when we have complete data for the entire population. Choice A is incorrect because there is no general rule that the sample variance is larger than the population variance. It depends on the particular sample and population being compared. Choice B is incorrect because the formula for standard deviation when used to estimate population variance uses N -1 on the bottom of the equation, not just N. Choice D is partially correct, but does not specify that the formula using N -1 is the corrected version used to estimate population variance.

Question 9

9) Which of the following is true?&#10;A) Sample statistics are always a good indication of population parameters&#10;B) Population parameters can never be estimated from sample statistics&#10;C) Sample statistics can be used to estimate population parameters&#10;D) Population parameters can be used to estimate sample statistics

Accepted Answer

Sample statistics can be used to estimate population parameters through inferential statistics techniques such as hypothesis testing and confidence intervals. However, it is important to note that there is always some degree of uncertainty in these estimates and they should be interpreted with caution.

Question 10

10) A disadvantage of using the arithmetic mean to measure central tendency is that:&#10;A) It is not a very sensitive measure&#10;B) It is easily distorted by rogue scores&#10;C) It cannot be used in the estimation of population parameters&#10;D) It is less accurate than the median

Accepted Answer

The arithmetic mean is easily distorted by rogue scores or outliers, which can significantly affect the value of the measure. This makes it less robust compared to other measures of central tendency such as the median or mode.

Deck 13: Statistics Organising the Data