Unit notes and practice questions

Grade 9 Mathematics unit 9: Statistics and Probability

Everything here is for unit 9 of the Grade 9 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.

3
Cards: 10
Practice questions on unit 9

What unit 9 covers

1.Statistical Data
2.Probability

Short notes for unit 9

The cards filed under this chapter on the Grade 9 Mathematics page. Open one at a time.

Arithmetic Mean of Raw DataFormula

\text{Mean} = \frac{x_1 + x_2 + \dots + x_n}{n}

\text{Mean} = \frac{x_1 + x_2 + \dots + x_n}{n}

$x_i$: Individual data value $none$
$n$: Total number of observations $none$

When you use it

Use when finding the average of an unorganized list of numerical values.

Watch out

Divide by the total count of values, not by the maximum value in the set.

Drafted from Grade 9 Mathematics, page 263 onwards, then checked twice before it went up

Mean from Frequency DistributionFormula

\text{Mean} = \frac{f_1 x_1 + f_2 x_2 + \dots + f_k x_k}{f_1 + f_2 + \dots + f_k}

\text{Mean} = \frac{f_1 x_1 + f_2 x_2 + \dots + f_k x_k}{f_1 + f_2 + \dots + f_k}

$x_i$: Data value or class score $none$
$f_i$: Frequency of the corresponding data value $none$

When you use it

Use when calculating the mean of data given in a frequency table.

Watch out

Divide by the sum of frequencies, not by the number of rows in the table.

Drafted from Grade 9 Mathematics, page 263 onwards, then checked twice before it went up

Properties of Mean under Linear ChangesReference tableAdd p · Subtract p · Multiply by nonzero p · +1

Change to each data value	Resulting Mean
Add $p$	$\text{Mean} + p$
Subtract $p$	$\text{Mean} - p$
Multiply by nonzero $p$	$p \cdot \text{Mean}$
Divide by nonzero $p$	$\frac{\text{Mean}}{p}$

When you use it

Use to quickly determine the new mean when every data value is changed by the same constant operation.

Watch out

The sum of deviations of all original values from their mean is always zero.

Drafted from Grade 9 Mathematics, page 263 onwards, then checked twice before it went up

Practice questions on unit 9

10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.

Question 1

Which of the following is an example of qualitative data?

A.Monthly income of a person in birr
B.Height of a student in centimeters
C.Religion of a person
D.Number of academic months in a year

Show the answer and why

Answer: C Religion of a person

Why

Qualitative data describes characteristics whose values are not numbers, such as religion, sex, or color.

Question 2

What type of data is a count involving whole integers that cannot be divided into smaller parts, such as the number of children in a school?

A.Continuous data
B.Discrete data
C.Qualitative data
D.Secondary data

Show the answer and why

Answer: B Discrete data

Why

Discrete data is a count that involves integers. Only whole numbers are possible, and the values cannot be subdivided into parts.

Question 3

In a standard histogram, which quantity is plotted along the vertical (y-axis)?

A.Frequency (f)
B.Variable or class interval (V)
C.Mean value
D.Median value

Show the answer and why

Answer: A Frequency (f)

Why

By definition, in a histogram the variable (V) is plotted on the x-axis and the frequency (f) is plotted on the y-axis.

Question 4

What is the mode of a set of data?

A.The sum of all values divided by the total count
B.The middle score when data is ordered by magnitude
C.The most frequent value in the data set
D.The difference between the highest and lowest values

Show the answer and why

Answer: C The most frequent value in the data set

Why

The mode is defined as the most frequent value in a set of data.

Question 5

Data that is collected directly by the researcher through surveys, interviews, or experiments to solve a specific problem is called:

A.Secondary data
B.Primary data
C.Census data
D.Continuous data

Show the answer and why

Answer: B Primary data

Why

Primary data is data generated directly by the researcher through their own surveys, interviews, or experiments.

Question 6

Seven students have the following number of exercise books: 5, 4, 6, 4, 3, 6, and 7. What is the mean number of exercise books?

Show the answer and why

Answer: B 5

Why

The mean is the sum divided by the count: (5 + 4 + 6 + 4 + 3 + 6 + 7) / 7 = 35 / 7 = 5.

Question 7

What is the median of the following set of 10 test scores?
14, 35, 45, 55, 55, 56, 56, 65, 87, 89

A.55.0
B.55.5
C.56.0
D.57.5

Show the answer and why

Answer: B 55.5

Why

For an even number of observations, take the average of the 5th and 6th scores: (55 + 56) / 2 = 55.5.

Question 8

A shopkeeper in Addis Ababa recorded the number of pencils bought by 10 customers as follows:
- 3 pencils: 2 customers
- 5 pencils: 2 customers
- 6 pencils: 4 customers
- 10 pencils: 2 customers
What is the mean number of pencils bought per customer?

Show the answer and why

Answer: B 6

Why

Multiply each value by its frequency and divide by the total frequency: (3*2 + 5*2 + 6*4 + 10*2) / 10 = (6 + 10 + 24 + 20) / 10 = 60 / 10 = 6.

Question 9

If x̄ is the arithmetic mean of n observations x₁, x₂, ..., x_n, what is the sum of the deviations from the mean: (x₁ - x̄) + (x₂ - x̄) + ... + (x_n - x̄)?

A.0
B.1
C.n
D.n * x̄

Show the answer and why

Answer: A 0

Why

According to Property 1 of the mean, the sum of the deviations of all observations from their arithmetic mean is always equal to 0.

Question 10

The mean of a set of numbers is 4. If each number is first multiplied by 3 and then increased by 1, what is the new mean?

A.12
B.13
C.15
D.16

Show the answer and why

Answer: B 13

Why

When every observation is multiplied by 3, the mean becomes 4 * 3 = 12. When 1 is then added to each observation, the new mean becomes 12 + 1 = 13.

The app holds 12 questions on this unit, marked as you go. These are the first 10.

The textbook pages for unit 9

The whole Grade 9 Mathematics textbook, free as a PDF.

Ministry of Education edition, English, 337 pages

Download the PDF

All Grade 9 Mathematics short notes

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