MCQ Questions

Question No. 1

Copy and complete the tables below by calculating the class boundaries and the midpoint for each class.

Answer :

a) Table a

b) Table b

c) Table c

Question No. 2

Is it possible to have a data set for which the variance and standard deviation are negative? Give a reason for your answer.

Answer :

Question No. 3

For each of the following data sets, calculate the mean, median, mode and range.

Answer :

a) {3, 5, 9, 12, 17, 21, 21, 26, 33}

b) {16, 41, 2, 28, 42, 59, 52, 46, 21, 52, 41, 54, 33, 15}

c) {0.3, 8.9, −5.9, −7.7, 9.6, 5.6, 8.4, 5, 5.5, 3.9, 3.6, −7.5, −0.1}

Question No. 4

A florist is delivering bunches of mixed flowers. Summarise this data in a frequency table and use your frequency table to calculate:

Answer :

a) frequency table

b) mean

c) median

d) mode

e) range

Question No. 5

An English teacher challenged her class to read at least five books over the school holidays. Summarise this data in a frequency table and use your frequency table to calculate:

Answer :

a) frequency table

b) mean

c) median

d) mode

e) range

Question No. 6

Copy and complete the table below by first calculating the mean and then calculating the deviation of each data value from the mean.

Answer :

Question No. 7

Given the following data set: {6, 0, −3, 1, 5, 4, −4, 3}.

Answer :

a) Calculate the mean.

b) Calculate the deviation of each data value from the mean. Display your results in a table with the following headings:

Question No. 8

A game warden recorded the number of baboons that she saw on ten successive days: 29, 14, 17, 25, 37, 16, 23, 28, 40, 31.

Answer :

a) Calculate the mean number of baboons.

b) Calculate the deviation of each number of baboons from the mean. Display your results in a table with the following headings:

Question No. 9

Copy and complete the table below, then calculate the variance of this data.

Answer :

Question No. 10

Given: the data set {2, 4, 6, 8, 10, 12}.

Answer :

a) Calculate the mean.

b) Calculate the variance of the data set. Use a table with the following headings:

Question No. 11

Given: the data set {−12, −7, −2, 0, 3, 6, 9, 10, 14, 28}.

Answer :

a) Calculate the mean.

b) Calculate the variance of the data set. Use a table with the following headings:

Question No. 12

Ten SS2 students were asked to make a note of the number of movies that they watched at the cinema during a given month. Their responses are listed below: 2, 4, 9, 0, 6, 3, 2, 1, 5, 0. Calculate the variance of this data. Show all your calculations.

Answer :

Question No. 13

Calculate the standard deviation, correct to two decimal places, if the variance is:

Answer :

a) 1.44

b) 32.75

c) 192.68

d) 4091.03

Question No. 14

Calculate the variance, correct to two decimal places, if the standard deviation is:

Answer :

a) 0.3

b) 1.09

c) 29.83

d) 508.15

Question No. 15

Calculate the standard deviation of the following data sets. Write your answers in simplified surd form.

Answer :

a) {1, 2, 3, 4, 5}

b) {14, 15, 16, 17, 18}

c) {2, 4, 6, 8, 10}

d) {100, 200, 300, 400, 500}

Question No. 16

Refer to your answers to question 3. What do you notice about the standard deviations of the following pairs of sets?

Answer :

a) {1, 2, 3, 4, 5} and {14, 15, 16, 17, 18}

b) {1, 2, 3, 4, 5} and {2, 4, 6, 8, 10}

c) {1, 2, 3, 4, 5} and {100, 200, 300, 400, 500}

Question No. 17

Is it possible to have a data set for which the variance and standard deviation are zero? Give a reason for your answer.

Answer :

Question No. 18

Use the same data as in the previous example on the temperature of cooled water. Summarise the data in a frequency table using the classes (−17, −13], (−12, −8], and so on.

Answer :

Question No. 19

The number of meals served daily at a school cafeteria over a period of 40 school days was as follows. Summarise this data in a frequency table using the classes 91−100, 101−110, and so on.

Answer :

Question No. 20

The masses of 56 papayas (in grams) were as follows. Summarise this data in a frequency table using the classes 700−799, 800−899, and so on.

Answer :

Question No. 21

The distances that some students travel every morning to get to school are as follows.

Answer :

a) Use this frequency table to estimate: (i) the mean, and (ii) the median of this data.

b) Find the modal class of this data.

c) Comment on possible values of the range for this data.

Question No. 22

A speed trap was set on an open road where the speed limit was 80 km/h. Several motorists were caught exceeding the speed limit. The speeds at which these motorists were travelling are shown in the table.

Answer :

a) Use this frequency table to estimate: (i) the mean, and (ii) the median of this data.

b) Find the modal class of this data.

c) Comment on possible values of the range for this data.

Question No. 23

Copy and complete the table below.

Answer :

Question No. 24

Copy and complete the table below, by calculating:

Answer :

a) the midpoint of each class

b) estimating the mean of each class

c) estimating the mean deviation of each class

Question No. 25

120 students sold raffle tickets to raise funds for a new piano for the school hall. Their ticket sales are summarised in the frequency table below.

Answer :

a) Estimate the mean number of tickets sold by each student.

b) Estimate the mean deviation of each class

Question No. 26

Copy and complete the table below, then estimate:

Answer :

a) the variance of this data

b) the standard deviation of this data

Question No. 27

Given the following frequency table, estimate:

Answer :

a) the mean of these masses

b) the variance of this data

c) the standard deviation of this data

Question No. 28

A class of SS2 students estimated the area (cm²) of their textbook covers. Their answers are summarised in the table below. Estimate:

Answer :

a) the mean of these areas

b) the variance of this data

c) the standard deviation of this data

Question No. 29

A class of 45 SS2 students wrote a Science test. Their marks out of 40 are listed below. The mean of these marks is 22.6 and the standard deviation is 6.45 (correct to two decimal places).

Answer :

a) How many marks lie within one standard deviation from the mean?

b) Identify the marks that lie outside one standard deviation from the mean.

c) If the pass mark was 40%, how many students failed the test?

d) The students who failed the test complained that the test was too difficult. Do you agree? Use the given statistics to support your answer.

Question No. 30

Volunteers worked at a polling station in two-hour shifts from 6 am to 6 pm. The numbers of voters (rounded to the nearest 100) who voted during each shift are shown in the table below.

Answer :

a) Estimate the variance of this data, correct to the nearest integer.

b) Estimate the standard deviation of this data, correct to the nearest integer.

c) Which shift(s) do not fall within one standard deviation from the mean?

d) Does the data suggest that the by-election took place on a normal working day, as opposed to a public holiday? Give reasons for your answer.

Question No. 31

The masses of eight dogs that were weighed at an animal shelter were as follows: 5 kg, 10 kg, 12 kg, 18 kg, 21 kg, 28 kg, 40 kg and 54 kg.

Answer :

a) Calculate the mean, variance and the standard deviation of these masses.

b) How many of these masses fall within one standard deviation from the mean?

Question No. 32

A class of Primary School Mathematics students worked in groups of five as they measured the same angle and compared their measurements.

Answer :

a) The standard deviation of the measurements of one group was 0°. How is this possible?

b) Another group was measuring an angle of 60°, but their mean measurement was 72°. Suggest what might have happened in this case. (Hint: Think about the sum of the five measurements.)

Question No. 33

Say whether or not each of the following sets of data is suitable for representation in a histogram. Give a reason each time.

Answer :

a) number of items in the pencil cases of a class of students

b) maximum daily temperatures for a month

c) favourite colours of a group of friends

d) marks scored by a class in a Mathematics exam

e) heights of out-patients at a clinic

Question No. 34

The masses and heights of some Nigerian dwarf goats are summarised in the tables below.

Answer :

a) How many goats are represented in each table?

b) Display the masses of these goats in a histogram.

c) Display the heights of these goats in a separate histogram.

Question No. 35

A small village has a population of 500 people. Their ages are given in this frequency table. Copy and complete the table by calculating the cumulative frequencies.

Answer :

Question No. 36

Draw up a new cumulative frequency table for the data in question 1, but use these class intervals: 0−20, 21−40, and so on.

Answer :

Question No. 37

Copy and complete the table and represent the cumulative frequencies in an ogive.

Answer :

Question No. 38

Students were asked to collect items to bring to school for recycling. The ogive below shows the results of this recycling effort.

Answer :

a) How many students took part in this recycling effort?

b) What was the maximum number of items that any one student brought to school?

c) Estimate Q2

d) Estimate Q1

e) Estimate Q3

f) If a student brought eight items to school for recycling, between which two quartiles will that student fall?

Question No. 39

The manager of a large taxi company analysed the distances that his taxis covered during one week. He presented his data in the ogive below.

Answer :

a) How many taxis operated during that week?

b) What was the maximum distance that any one taxi covered?

Question No. 40

Use the ogive from the previous example to answer the following questions.

Answer :

a) Estimate the value of P75 (the 75th percentile).

b) Into which percentile does a patient with a BMI of 31 fall?

Question No. 41

For a project on Statistics, a student interviewed 160 students in her school to find out how long it took them on average to get to school every morning. She rounded the answers off to the nearest minute and presented her data in this ogive.

Answer :

a) Estimate the values (to the nearest minute) of: (i) P10 (ii) P30 (iii) P50 (iv) P90

b) Name two other measures of dispersion that are equivalent to P50.

c) What does the value of P50 tell us in this situation?

d) If a student takes half an hour to get to school, into which percentile does he or she fall?

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