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Standard Deviation, SM-Bank 015

Rhonda and her friends were surveyed about the number of concerts they have been to in the last 12 months.

Their responses are as follows:

  1. Determine the median number of concerts from this data set.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to one decimal place.   (1 mark)

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Standard Deviation, SM-Bank 014

Albert teaches Physics and sets his class a mid-term exam.

The results are summarised in the Stem and Leaf plot drawn below.
 

  1. Determine the median test score of the data set.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to two decimal places.   (1 mark)

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Standard Deviation, SM-Bank 012

Seven 40-year old males are asked how many children they have in a survey.

The results are summarised in the histogram drawn below.
 

  1. Determine the mean number of children of the group surveyed, giving your answer to two decimal places.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to two decimal places.   (1 mark)

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Standard Deviation, SM-Bank 009

Isa Guha recorded the number of sixes hit in the first nine games of the Women's Big Bash Cricket League over two seasons.

The results are recorded in the two dot plots below.
  

  1. Determine the standard deviation of the results in Season 1, giving your answer correct to one decimal place.   (2 marks)

  2. Without using calculations, explain which data set will have the highest standard deviation.  (2 marks)

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Standard Deviation, SM-Bank 008

In a cricket test match, a scorebook recorded the number of runs scored by England's top six batsman.

The scores are summarised in the Stem and Leaf plot below.
 

Determine the standard deviation of the scores, giving your answer correct to one decimal place.   (2 marks)

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Standard Deviation, SM-Bank 007

Ms Arnott has seven students in her Ethics class. The results of the most recent exam, completed by the whole class, is summarised in the Stem and Leaf plot below.
 

Determine the standard deviation of the exam results, giving your answer correct to one decimal place.   (2 marks)

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Standard Deviation, SM-Bank 006

Seven players in two basketball teams, the Swifties and the Chiefs, recorded how many 3-point baskets they had shot in the last season.

The results are recorded in the two Stem and Leaf plots below.
 

  1. Determine the standard deviation of the Swifties' results, giving your answer correct to one decimal place.   (2 marks)

  2. Without using calculations, explain which data set will have the smallest standard deviation.  (2 marks)

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Standard Deviation, SM-Bank 005

9 students completed two quizzes and the results were summarised in the dot plot diagrams below.
 

  1. Determine the median value of the results of Quiz A.   (1 mark)

  2. Calculate the standard deviation of Quiz A and Quiz B, giving your answers correct to one decimal place.  (2 marks)

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Standard Deviation, SM-Bank 004

Two data sets are represented in the dot plot diagrams below.
 

  1. Calculate the standard deviation of Data Set B, giving your answer correct to one decimal place.   (1 mark)

  2. Without using calculations, explain which data set has the highest standard deviation.  (2 marks)

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Standard Deviation, SM-Bank 003

In a small business, the seven employees earn the following wages per week:

  1.  Calculate the standard deviation for this set of data, giving your answer to one decimal place.  (1 mark)

  2.  Each employee receives a $20 pay increase.

     

     Explain the effect that this increase will this have on the standard deviation?  (2 marks)

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Standard Deviation, SM-Bank 002

Ali’s class sits a Geography test and the results are recorded below.

The mean for the test was 68.5. 

  1. Calculate the standard deviation for the test. Give your answer correct to one decimal place.    (2 marks)

  2. Explain whether the mean of the test is greater than or less than the median of the test.    (1 mark)

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♦ Mean mark (a) 39%.

 
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Standard Deviation, SM-Bank 001

The ages of nine students were recorded in the table below.
 

 

  1. What is the standard deviation, correct to two decimal places?   (2 marks)

  2. Briefly explain what is meant by the term standard deviation.   (1 mark)

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Box-Plots and 5-Number Summary, SM-Bank 016

Ellyse recorded the number of wickets she took in the first seven games of the cricket season, which are as follows:

  1. Complete the 5-number summary table of Ellyse's results below.   (2 marks)

  1. Draw a box plot, using the number line below for reference, that displays Ellyse's results.   (2 marks)
     

  1. Describe the skew of Ellyse's results.   (1 mark)

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Box Plots and 5-Number Summary, SM-Bank 015

Eli sat 22 Maths quizzes throughout year 8 and her results were recorded in the 5-number summary below.

  1. Using the number line below as reference, draw a box plot that displays Eli's results.   (2 marks)
     

  1. Describe the skew of Eli's results.   (1 mark)

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Box Plots and 5-Number Summary, SM-Bank 014

The test results in English and Mathematics for a class were recorded and displayed in the box plots.
 

  1. What is the interquartile range for English?   (1 mark)

  2. Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of their centres and spread.   (3 marks)

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♦ Mean mark (ii) 35%
COMMENT: The best answers use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

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Box Plots and 5-Number Summary, SM-Bank 013

Terry and Kim each sat twenty class tests. Terry’s results on the tests are displayed in the box plot shown in part (i).

  1. Kim’s  5-number summary for the tests is  67,  69,  71,  73,  75.

     

    Draw a box plot to display Kim’s results below that of Terry’s results.   (1 mark)
     
       

  2. What percentage of Terry’s results were below 69?     (1 mark)

  3. Describe the skew of Kim's results.   (1 mark)

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Box Plots and 5-Number, SM-Bank 011

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 010

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 009

Yoyo was practicing his cello for an orchestra audition and the data set below records the number of hours he practiced each day over a 10-day period.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 008

Matt records the number of times he takes his dog Max for a walk each month. The data set below records the months January to August.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 005

Le Bron plays basketball and records the number of free throws he shoots in the first nine games of the season.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 004

Robert records the total goals scored in each of the first 11 matches of his favourite soccer team.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Simple Interest, SMB-023

Jevin has a bank account that pays him simple interest.

The bank statement below shows the transactions on Jevin’s account for the month of July.
  

  1. What amount, in dollars, did Jevin deposit in cash on 11 July?  (1 mark)

Interest for this account is calculated on the minimum monthly balance at a rate of 3.0% per annum.

  1. Calculate the interest for July, correct to the nearest cent.  (2 marks)

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Simple Interest, SMB-022

The transaction details for a savings account for the month of August 2014 are shown in the table below.

The table is incomplete.
  

 

Simple interest is calculated and paid monthly on the minimum balance for that month.

Calculate the annual simple interest rate paid on this account, correct to two decimal places.   (4 marks)

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Simple Interest, SMB-021

The graph below shows the growth in value of a $1000 investment over a period of four years.
 

A different amount of money is invested under the same investment conditions for eight years.

In total, the amount of interest earned on this investment is $600.

Calculate the amount of money invested.   (3 marks)

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Simple Interest, SMB-020

Chardie invests a sum of money in an account paying simple interest at a rate of 5.25% per annum.

No withdrawals or deposits are made into the account and over 4 years and the total value of Chardie's investment grows to .

Calculate the sum of money Chardie originally invested.   (3 marks)

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Simple Interest, SMB-019

A sum of money is invested in an account paying simple interest at a rate of 5.0% per annum.

No withdrawals or deposits are made into the account and over 3 years, with the total interest earned on the investment being $120.

Calculate the sum of money originally invested. (2 marks)

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Simple Interest, SMB-016

Kate and Amberley are Swifties and want to travel to Melbourne to go to a Tay-Tay concert.

It will cost them a total of $13 000 for tickets, accommodation and transport.

They currently have $12 500 and can invest this amount for 9 months.

What is the minimum simple interest rate, correct to 1 decimal place, at which they can invest their money to reach their goal of $13 000?   (3 marks)

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Simple Interest, SMB-015

Carissa borrowed $4000 to buy new surfboards.

She did not make any monthly repayments and repaid the loan in full 2 years later with a lump sum of $4400.

Determine the annual simple interest rate that Carissa was charged.   (2 marks)

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Simple Interest, SMB-014

Steffi borrowed $8600 to buy a new car.

She did not make any monthly repayments but instead repaid the loan in full 2 years later with a lump sum of $10 062.

Determine the annual simple interest rate that Steffi was charged.   (2 marks)

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Simple Interest, SMB-009 MC

Albert borrowed $2000 off his brother Sid so he could attend the rugby league Magic Round in Brisbane.

He did not make any monthly repayments but instead repaid the loan in full 12 months later with a lump sum of $2350.

What was the annual simple interest rate Sid charged Albert?

  1. 3.5%
  2. 17.5%
  3. 23.5%
  4. 35.0%
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Simple Interest, SMB-008

Sandy borrowed $7 000 for an overseas trip.

She did not make any monthly repayments but instead repaid the loan in full at the end of three years with a lump sum of $8800.

Calculate the annual simple interest rate was she charged?   (2 marks)

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Simple Interest, SMB-005

Johnno lives overseas and needs $6000 for his planned trip to Parramatta Stadium to watch Junior Paolo play.

If he invests $5600 for 15 months at a simple interest rate of 6.5% per annum, determine if will get to see the big fella play. Show your working.  (2 marks)

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Simple Interest, SMB-004

Clancy estimates that he will need $7800 for his planned trip to visit the The Stockman's Hall of Fame in Longreach.

If he invests $7000 for 18 months at a simple interest rate of 6% per annum, will he reach his goal of $7800? Show your working.   (2 marks)

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Financial Maths, SMB-027

The cash price of a large refrigerator is $2000.

A customer buys the refrigerator under a hire-purchase agreement.

She does not pay a deposit and will pay $55 per month for four years.

  1. Calculate the total amount, in dollars, the customer will pay.  (1 mark)

  2. Find the total interest the customer will pay over four years.  (1 mark)

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Financial Maths, SMB-026

Shaun decides to buy a new sound system on a hire-purchase plan.

The sound system is priced at $3500.

Shaun pays a 15% deposit and monthly repayments for five years.

If Shaun's total purchase price after paying the last instalment is $4425, calculate his monthly repayment.   (3 marks)

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Financial Maths, SMB-025

Brad investigated the cost of buying a $720 washing machine under a hire purchase agreement.

A 25% deposit is required and the balance will be paid in 24 equal monthly repayments of $27.90.

Calculate the amount of interest Brad pays on this purchase.   (3 marks)

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