US 9015 APPLY KNOWLEDGE OF STATISTICS AND PROBABILITY …

Portfolio of Evidence: Public Administration NQF 4: SAQA ID: 57824 US 9015

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Public Administration – US 9015 – Issue 3 – 01-01-2021

MATHEMATICAL LITERACY

US 9015 APPLY KNOWLEDGE OF STATISTICS AND PROBABILITY TO CRITICALLY INTERROGATE AND EFFECTIVELY COMMUNICATE FINDINGS ON

LIFE RELATED PROBLEMS; NQF LEVEL 5, 6 CREDITS

FORMATIVE ASSESSMENT

Learner Name: Learner ID #: Learner Student Number:

Answer the following questions in the space provided below. (the number in brackets is merely a weighting of

how much should be answered)

ACTIVITY 1 Identify each of the following statistics as either descriptive or inferential: (8) 1) In 2001, 23,8% of Asian households in South Africa owned a Television set

2) Households with children under the age of 18 years are more likely to have access to the Internet,

(62%0, than families with no children, (53%)

3) Graham Pollock’s lifetime batting average is 122

4) The average Grade 10 English score at a local high school in 2004 was 33%


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ACTIVITY 2

Consider the following table from Stats SA.

a) What does column 2 represent? (2)

b) What does column 5 represent? (2)

c) Which column represents the number of males living in non-urban areas? (2)


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d) If you wanted to find the total number of people, 16 years and older, living in a certain province, which

column would you look in? (2)

e) How many males, 16 years and older, live in urban areas in Kwa-Zulu-Natal? (2)

ACTIVITY 3-1

Every year millions of man days are lost because of people striking. A man day is one work day for one person. In other words, if 20 people strike for one day, 20 man days are lost. If 20 people strike for 2 days, 40 man days are lost. Look at this table of man days lost because of strikes:

1) Draw a bar graph to represent the data in the table. Label the axes of your graph. (20)


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ACTIVITY 3-2

The Human Resources Manager of a company employing 200 workers conducts a survey to investigate whether there is a relationship between the age of workers and the number of days they are absent per year. He takes a sample of 15 files and records the age and the number of days absent of the workers in the sample. He then plots the results of the survey on the following scatter graph:

1) Do you think the department would decide that there is a correlation between the number of days

absent and the age of workers? If yes, describe the correlation (positive or negative?) and explain. (12)


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2) Use your ruler to draw a line of best fit. (5)

3) Using your line of best fit, estimate: i) How many days a 35 year-old worker can be expected to be absent in a year. (3)

ii) The age of a worker who is likely to be absent for 3 days in a year. (3)

4) How can this kind of data be contaminated? How can the survey results be biased? (10)

5) What is the major assumption of the Human Resources Manager in the above survey? (5)


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ACTIVITY 4 1. The following data give the number of daily and Sunday newspapers published in each of the 13

western states during 2000: 7, 16, 92, 29, 6, 12, 11, 8, 18, 19, 6, 24, 9

a) Calculate the mean, median, standard deviation and interquartile range for these data. (12)

b) What type of data is this? (2)

ACTIVITY 5 What is the meaning of the following terms?

a) Parameter


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b) Variable

c) Difference

d) Statistics

e) Constant

f) Product

g) Sample

h) Measurable

i) Quotient


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j) Population

k) Sum

l) Ratio

12 X 2 = (24) ACTIVITY 6 1) What is the formula for Empirical Probability (5)

ACTIVITY 7

In a pack of cards, there are 52 cards. There are 4 suits: diamonds, hearts, spades and Clubs. Each suit has a King, a Queen, a Jack and an Ace. It also has cards for 2, 3, 4, 5, 6, 7, 8, 9 and 10. If the pack has been shuffled so that the cards are in no particular order, and you select one card from the pack without looking, what is the probability of selecting:

a) a Queen

b) a red Queen

c) a Jack of Hearts


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d) a Jack of Hearts or Diamonds

e) any club

f) a six or a seven

g) a black six

h) a picture card (Jack, Queen or King)

3 X 8 = 24

ACTIVITY 8

If Event A = rolling a total of 2, 3, 4, or 5 with 2 dice, we need to define the sample space for this experiment, which is shown in the table below:

{1, 1} {2, 1} {3, 1} {4, 1} {5, 1} {6, 1}

{1, 2} {2, 2} {3, 2} {4, 2} {5, 2} {6, 2}

{1, 3} {2, 3} {3, 3} {4, 3} {5, 3} {6, 3}

{1, 4} {2, 4} {3, 4} {4, 4} {5, 4} {6, 4}

{1, 5} {2, 5} {3, 5} {4, 5} {5, 5} {6, 5} {1,6} {2, 6} {3, 6} {4, 6} {5, 6} {6, 6}

There are 36 total outcomes for this experiment, each with the same chance of occurring. The occurrences that correspond to Event A are underlined. There is a total of 10 occurrences. Calculate P[A]


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(10)

ACTIVITY 9 The following table shows the outcomes of their last 20 matches:

Warm Up Time Lisa Wins (A) Gregory wins (A’) Total

Less than 10 min (B)

4 9 13

10 min or more (B’) 5 2 7

Total 9 11 20

The events of interest are:

Event A: Lisa wins the tennis match Event B: warm up time is less than 10 minutes Event A’: Gregory wins the tennis match Event B’: Warm up time is 10 minutes or more

i) Calculate P[A], P[B], P[A’] , P[B’], P[A / B] , P[A / B’], (6 X 3 = 18)


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SUMMATIVE ASSESSMENTS

TAKE NOTE

The assessment instruments included in this assessment pack are all summative assessment instruments and are to

be read in conjunction with the formative assessment instruments contained in the learner workbook. Both formative

(workbook) and summative assessments are to be retained as part of the learner’s portfolio of evidence.

MATHEMATICS IN BUSINESS

QUESTION 1 The last four semesters an instructor taught Intermediate Algebra, the following numbers of people passed the class.

17 19 4 20 Which of the following conclusions can be obtained from purely descriptive measures and which can be obtained by inferential methods? a) The last four semesters the instructor taught Intermediate Algebra, an average of 15 people passed the class.

(8) b) The next time the instructor teaches Intermediate Algebra, we can expect approximately 15 people

to pass the class.

(5)


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c) This instructor will never pass more than 20 people in an Intermediate Algebra class.

(5) d) The last four semesters the instructor taught Intermediate Algebra, no more than 20 people passed the class.

(8) e) Only 5 people passed one semester because the instructor was in a bad mood the entire semester.

(5)


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f) The instructor passed 20 people the last time he taught the class to keep the administration off of his

back for poor results.

(5) g) The instructor passes so few people in his Intermediate Algebra classes because he doesn't like

teaching that class.

(5) QUESTION 2 The following table illustrates the products are sold in Vuyo’s Shebeen and the number of customers who purchased these products in a single day:

Product # of Customers Relative Frequency

Percentage

Simba Chips 9 9/30 30%

Lemonade 13 13/30 43%

Lion Larger 6 6/30 20%

Cigarettes 2 2/30 7%

Total 30

Can you illustrate the above table as a Pie Chart


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(12) QUESTION 3 The table below represents Vuyo’s daily expenses for the period 1 January to 6 January 2004:

Date Total Expenses (in Rands)

1st 375

2nd 514

3rd 834

4th 603

5th 882

6th 468

Can you illustrate the above table as a bar chart? (12)


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QUESTION 4 1) What is the probability of rolling a 3 on a die (plural, dice).

(3)

QUESTION 5 5.1. Look at the graph below, and then answer the questions that follow.

a. What was Mabel’s highest pulse rate?

(2)

b. What was Albert’s highest pulse rate?

(2)

c. What was Mabel’s lowest pulse rate?

(2)

d. What was Albert’s lowest pulse rate?

(2)


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e. By referring to the graph, describe what happens to Albert’s heart rate during exercise.

(4)

5.2. Look at the graph below, and then answer the questions that follow.

a. Which fertilizer was the most effective?

(2)

b. Which fertilizer was the least effective?

(2)

c. Calculate the average growth of all the fertilizers. Show your calculations below.


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(8)

PERSONAL NARRATIVE

Answer the following questions based on your experience during the completion of this module. Discuss what you did well and what you would like to do differently.

What went well? What would I do differently?

1 I was able to identify and solve problems effectively throughout the various activities

completed in this module.

2 I was able to understand how different workplace activities have an impact on each other.

3 I was able to use new technology effectively in my daily tasks that I carried out.

4 I was able to communicate effectively with my team members and supervisors.


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5 I was able to complete all my work in an organized and efficient manner.

6 Additional Comments

Learner Name: Signature

Facilitator Name: Signature

Date


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FOR STUDENT This is to verify that the above work is my own / authentic. Learner Name: __________________________ Learner Student No:__________________ Learner Signature: ________________________ Date: _____________________________ FOR FACILITATOR This is to verify that the learner has completed all the above and is awaiting final assessment / moderation. File Checked:

Date Facilitator Name Facilitator Signature


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Basic Conditions of Employment Act, 1997

Record of Time Worked

Employee Name: ________________________________________________________

Employee Surname: ______________________________________________________

Employee ID Number: ____________________________________________________

Employee Signature: _____________________________________________________

Employer Name: _________________________________________________________

Employer Signature: ______________________________________________________

Year: 2021

Month: _______________________________________

Total hours worked / productive capacity made available during the month: 160 hours

Work completed:

Time spent on training including classroom training and/or digital learning as well as

study and revision time;

X

Time spent on completing work and digital work tasks (including availability for work); X

Time spent on compiling assessments (formative and summative) for your PoE; X

Time spent on task preparation & research X

Time spent travelling to and from location for task completion X

Documents

US 9015 APPLY KNOWLEDGE OF STATISTICS AND PROBABILITY …