Deck 8: Mode and Other Measures of Location

Question 1

If you wish to calculate the average (proportional) increase in the price of bread over the last five years which of the following statistics would give you the most useful figure?

A) Geometric Mean
B) Arithmetic Mean
C) Harmonic Mean
D) You can use any of these measures

Answer 1

Geometric Mean

Question 2

Data on the average monthly spend of 180 mobile phone customers shows that the modal class is '$40 to $50' (f=53); the previous and following classes had frequencies of 24 and 46 respectively. Estimate the mode for this data (2 decimal places).

A) 45.00
B) 48.36
C) 47.96
D) 46.34

Answer 2

48.36

Question 3

Over the last four years, the economy of Kazakhstan has grown by 4.6%, 6.5% and 3.8%. Using the geometric mean, estimate the average yearly growth (2 decimal places).

A) 4.82%
B) 4.96%
C) 4.97%
D) 5.21%

Answer 3

4.96%

Question 4

Which of the following statements about the mode is NOT true?

A) It has no natural measure of dispersion to partner with, limiting its usefulness
B) The mode is usually easy to calculate and to understand
C) Not all data sets will have a modal value
D) The mode is heavily affected by extreme values in the data set

Question 5

The Chamber of Commerce is conducting research into the length of time that retailers have been in their current premises. They collect data and then present it in a grouped frequency distribution. The modal class is '4 and up to 6 years' (f=8); the previous class had a frequency of 4; the following class had a frequency of 2. Estimate the mode for this data (1 decimal place).

A) 5.3
B) 4.8
C) 5.5
D) 4.9

Question 6

A courier company calculates the fuel consumption of four mopeds over the same route as 62 km/l; 55 km/l; 59 km/l and 49 km/l. Using the harmonic mean, calculate the average fuel consumption for these vehicles (2 decimal places).

A) 54.39
B) 57.00
C) 55.81
D) 56.25

Question 7

Which option is the best definition of the mode?

A) The sum of values divided by the number of data points
B) The most frequently occurring value in the data set
C) The middle value when all data points are arranged in order
D) The average of the highest and lowest data points

Question 8

In a moderately skewed distribution, which of the following statements is NOT true?

A) The modal value will lie under the 'hump' of the distribution
B) We expect the median to lie between the mean and the mode, but closer to the mean
C) Knowing the values for any two of the measures of dispersion allows you to estimate the other one
D) The mean will always fall towards the 'humped' end of the distribution

Question 9

Which of the following datasets is particularly well suited to using the mode to describe the 'average'?

A) Changes to the cost of a key component
B) Number of people attending a series of concerts
C) Popularity of cars by colour
D) Weights of sacks of carrots

Question 10

Patrice runs a small cafe in Lyon. He notes down the number of people selecting flavours of crepes. Which flavour is the mode for this data [flavour(frequency)]? Sugar(15); Chocolate(23); Chocolate and Banana (38); Raspberry Jam(11)

A) Sugar
B) Chocolate
C) Chocolate and Banana
D) Raspberry Jam