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# Sts 102 by Adeosun Sakiru Abiodun

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My students second semester exam question for 2011/2012 session

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### Sts 102 by Adeosun Sakiru Abiodun

1. 1. ! "! # \$%&&\$%&\$ ( " ( ) " ) * ) ++ , * 2 QUESTION 1(a) (i) Define the term “Statistics”. (ii) Give three (3) examples each of quantitative data and qualitative data.(b) Differentiate between Primary data and Secondary data and cite one example each.(c) The following data represent the ages (in years) of people living in a housing estate in Abeokuta: 18 31 30 6 16 17 18 43 2 8 32 33 9 18 33 19 21 13 13 14 14 6 52 45 61 23 26 15 14 15 14 27 36 19 37 11 12 11 20 12 39 20 40 69 63 29 64 27 15 28 . (i) Present the above data in a frequency table showing: class interval, class boundary, class mark, tally, frequency and cumulative frequency in that order. Use your table to answer the following questions: (ii) How many people aged between 32 and 61? (iii) What is the probability that a person selected at random from the estate would age more than 51?(d) Make a stem plot for these data: 45, 59, 35, 41, 46, 21, 24, 33, 40, 45, 49, 53, 48, 54, 62, 36, 70, 58, 47, 11, 85. QUESTION 2(a)(i) The rate of inflation in five successive years in a certain country was 5%, 8%, 12%, 25% and 34%. What was the average rate of inflation per year? (ii) In a class of fifteen students, the Lecturer in charge of STS 102 pasted ten students’ scores in the Continuous Assessment Test as follows: 16, 20, 19, 21, 18, 20, 17, 22, 20, 17. Compute the arithmetic mean and standard deviation for these scores.(b) The length of a pole is measured as 20 metres to the nearest metre. Calculate the percentage error.(c) The table below shows the distribution of the waiting times for some customers in a certain petrol station in Gusau.Estimate:(i) Coefficient of variation
2. 2. (ii) Karl-Pearson’s coefficient of skewness for the given distribution(d) Calculate (measure of kurtosis based on moment) for the following data and comment on your result. X 0 1 2 3 4 F 5 10 15 20 25 QUESTION 3(a) If the voting age population (people of 18 years and above) in a country consists of 77650000 females and 62350000 males. What is the proportion of males?(b) Draw a Pie chart for the following data of production of sugar in quintals of various countries. Country Production of Sugar (in quintals) Cuba 62 Australia 47 India 35 Japan 16 Egypt 6(c) Find out the measure of skewness based on moments from the following series. Ages in years No. of persons 0 – 10 20 10 – 20 25 20 – 30 32 30 – 40 40 40 – 50 42 50 – 60 35 60 – 70 10 70 – 80 8(d) In two factories A and B located in the same industrial area, the average weekly wages (in Naira) and the standard deviations are as follows: Factory Averages Standard deviation No. of workers A 34.5 5 476 B 28.5 4.5 524 (i) Which factory A or B pays out a larger amount as weekly wages? (ii) Which factory A or B has greater variability in industrial wages? QUESTION 4(a) Construct price index number from the following data by applying (i) Laspeyre’s method (ii) Paashe’s method and (iii) Fisher’s ideal method and comments on your results.
3. 3. 2010 2011 Commodity Price Total value Price Total value A 2 16 4 20 B 5 60 6 60 C 4 60 5 60 D 2 36 4 80 (b) Price of a particular commodity in five successive years in two cities are given below: Price in city of Ibadan Price in city of Abeokuta 20 10 22 20 19 18 23 12 16 15 Which city has more stable prices?(c) The allotment of time in minutes per week for some of the university courses in second semester are as follows: Courses Minutes GNS 104 60 MTS 102 120 STS 102 180 ECO 102 120 BFN 108 120 PHS 192 140 Construct a bar chart to represent the above data.(d) The exact pension allowance paid (in Naira) to 30 workers of a company is given in the table below: Pension in N 25 30 35 40 45 50 No. of person 6 5 7 4 3 5 Calculate the arithmetic mean using an assumed mean method. QUESTION 5(a) Mention the three types of class intervals.(b) Calculate consumer price index by using Family Budget method for year 2011 with 2007 as base year from the following data: Items Weights Price in 2007 (N) Price in 2011 (N) Food 35 150 140 Rent 20 75 90 Clothing 10 25 30 Fuel &Lighting 15 50 60 Miscellaneous 20 60 80
4. 4. (c) Find the Bowley’s coefficient of skewness for the following series: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.(d) The six numbers 8, 8, 3, 7, 4, and X, have mean of 9. Find the value of X. QUESTION 6(a) State the goal of descriptive statistics.(b) List any six methods for collection of data.(c) From the following data, compute quantity indices by (i) Laspeyre’s method (ii) Paasche’s method (iii) Fisher’s ideal method. Commodity 2010 2011 Price Quantity Price Quantity X 10 10 12 15 Y 12 20 15 30 Z 15 15 17 20(d) Construct the consumer price index number for 1996 on the basis of 1993 from the following data using Aggregate expenditure method. Commodity Quantity Consumed Price in 1993 Price in 1996 Rice 100 8 12 Yam 25 6 7 Beans 10 5 8 Garri 20 15 18ADEOSUN S. A 28/06/12