70+ Family
Quantitative methods
Version 1
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A coach in football school collected the 20 footballer children’s favourite T-shirt (Jersey) numbers. The results show the following:
7 10 1 8 9 10 7 7 11 7 9 10 6 9 7 10 8 6 1 11
a. Based on the given data, identify whether the statements below are False or True:
1) The given data is quantitative. (2 marks)
2) Data is in ratio scale (2 marks)
3) The mode is 7 (2 marks)
4) The mean can be identified for this data (2 marks)
5) Standard deviation is not applicable for this data (2 marks)
b. Plot the data graphically. (10 marks)
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The following data gives information about the CIFS students’ overall marks from QM in 2022-2023 academic year.
Students’ marks
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Number of students
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10-40
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280
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40-60
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328
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60-70
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170
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70-80
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144
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80-100
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78
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Show the formula for median, mean and mode. Calculate the median, mean and mode of this data (20 marks)
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The data below represents the number of cars sold in one of the car salons in August.
Number of cars
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Number of days
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4
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10
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6
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6
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7
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4
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8
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7
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10
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3
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Calculate the variance, standard deviation and IQR of the data (20 marks)
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a) Ann wants to deposit $12,000 into two banks for 2 years. Bank X offers 10% interest rate compounded semi-annually, and Bank Y offer 10.2% compounded yearly. What will be the future amount of the deposit in both banks after 2 years? Which bank would you suggest for Ann and why? (10 marks)
b) If the Ipak yo’li bank offered 26% annual interest rate for deposit in 2022 and the inflation rate was 11.45%, calculate the real interest rate. (5 marks)
c) If you are invited to a project which yields 10% annual interest rate compounded: 1) semi-annually; 2) monthly; 3) quarterly, find the effective annual rate.
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This is the information about the net income (in million dollars) generated by three companies, “Alpha”, “Betta” and “Gamma” from 2017 to 2020
Company/Year
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2017
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2018
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2019
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2020
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Alpha
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23.2
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24.5
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26.4
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18.6
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Betta
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15
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18.3
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18.1
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16.4
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Gamma
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30.1
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28.6
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32.5
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40.9
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Calculate the SMI and SAI for the data. (10 marks)
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Calculate the chain-base index for “Gamma”. (10 marks)
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