Question 1

Which measurement of a data set gives information about whether data is distributed symmetrically?&#10;A) Location&#10;B) Dispersion&#10;C) Skewness&#10;D) Reliability

Accepted Answer

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. If the data is distributed symmetrically, the skewness will be close to zero. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values, while negative skewness indicates a tail extending towards more negative values.

Question 2

Calculate the mean deviation for the following set of data: 2, 8, 3, 1, 5, 6, 3&#10;A) 2&#10;B) 4&#10;C) 3&#10;D) 5

Accepted Answer

The mean of the data set is 4. The deviations from the mean are 2, 4, 1, 3, 1, 2, 1. The mean deviation is the average of these absolute deviations, which is 2.

Question 3

Which of these statements relating to skewness is NOT true?&#10;A) The direction of the skew is determined by the long tail of the distribution&#10;B) We expect salaries to have a left skew&#10;C) The direction of skew can be seen by comparing the mean and mode&#10;D) The size of the difference between mean and mode gives an indication of how skewed the data is

Accepted Answer

Salaries are typically right-skewed because there are a few individuals with very high incomes that pull the mean to the right, while most people have lower incomes, resulting in a distribution with a long tail to the right.

Question 4

Which of these statements about the range IS true?&#10;A) It is often used in advanced statistical analysis&#10;B) It is not affected by extreme high or low values&#10;C) It is easy to calculate and understand&#10;D) It cannot be easily charted

Accepted Answer

The range, defined as the difference between the highest and lowest values in a dataset, is indeed easy to calculate and understand, making it accessible for basic statistical analysis.

Question 5

A corner shop makes a note of the number of shopping bags used by customers during the course of one day. The following frequency distribution is produced [number of bags(frequency)]: 0(8); 1(26); 2(24); 3(6); 4(1). Calculate the mean deviation (2 decimal places).

A) 1.48
B) 0.63
C) 1.25
D) 0.75

Accepted Answer

The answer of A corner shop makes a note of...

Question 6

Which measurement of a data set gives information about how spread out the data is?&#10;A) Location&#10;B) Dispersion&#10;C) Skewness&#10;D) Reliability

Accepted Answer

Dispersion is a statistical measure that describes the spread or distribution of a set of data points. It includes measures like range, variance, and standard deviation, which help to understand how much the data varies from the average.

Question 7

Which base for measuring the spread of data is associated with the median?&#10;A) Range&#10;B) Standard Deviation&#10;C) Quartile Deviation&#10;D) Mean Deviation

Accepted Answer

Quartile Deviation, also known as the interquartile range, is associated with the median as it measures the spread of the middle 50% of a dataset around the median.

Question 8

A bookshop records how many copies of a Statistics textbook are sold each day for a week. The results are: 4, 5, 1, 2, 0, 8, 5. What is the range of this set of data?&#10;A) 5&#10;B) 3.6&#10;C) 8&#10;D) 4

Accepted Answer

The range of a set of data is the difference between the highest and lowest values. In this case, the highest number of books sold in a day is 8 and the lowest is 0, so the range is 8 - 0 = 8.

Question 9

Which of the following statements about the mean deviation is NOT true?&#10;A) The mean deviation is useful for comparing data sets that are similar&#10;B) The mean deviation is easy to handle theoretically and commonly used in further analysis&#10;C) It can be awkward to calculate if the mean is not a whole number&#10;D) The mean deviation must always be calculated using absolute value of values in the data set

Accepted Answer

The mean deviation is not as easy to handle theoretically or commonly used in further analysis as other measures of variability, such as the standard deviation. This is because it does not have the same mathematical properties that make the standard deviation useful in further statistical analysis.

Question 10

When calculating a mean deviation for a grouped frequency distribution which value should be used in the calculation?&#10;A) Lower bound&#10;B) Upper bound&#10;C) Midpoint&#10;D) Width

Accepted Answer

The midpoint of each class interval is used in the calculation of mean deviation for a grouped frequency distribution because it represents the central value of each interval, providing a more accurate estimate of the mean deviation than the lower or upper bounds or the width of the intervals.

Deck 9: Measures of Dispersion and Skewness