Calculate five yearly moving averages of the number of students in a college from the following data and plot them on a graph paper: Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 No. of students 332 317 357 392 402 405 510 427 405 438

Given, Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 No. of students 332 317 357 392 402 405 510 427 405 438 The first 5 -yearly moving average is 332 + 317 + 357 + 392 + 402 5 = 1800 5 = 360 and is placed against 3 rd year i.e, 1983 . The second 5 -yearly moving average is 317 + 357 + 392 + 402 + 405 5 = 1873 5 = 374 . 6 and is placed against 4 th year i.e, 1984 . The third 5 -yearly moving average is 357 + 392 + 402 + 405 + 510 5 = 2066 5 = 413 . 2 and is placed against 5 th year i.e, 1985 . The fourth 5 -yearly moving average is 392 + 402 + 405 + 510 + 427 5 = 2136 5 = 427 . 2 and is placed against 6 th year i.e, 1986 . The fifth 5 -yearly moving average is 402 + 405 + 510 + 427 + 405 5 = 2149 5 = 429 . 8 and is placed against 7 th year i.e, 1987 . The sixth 5 -yearly moving average is 405 + 510 + 427 + 405 + 438 5 = 2185 5 = 437 and is placed against 8 th year i.e, 1988 . Thus, the 5 -yearly moving average are 360 , 374 . 6 , 413 . 2 , 427 . 2 , 429 . 8 and 437 which are represented as the dotted line and the actual figures by regular line in the graph below:

The number of traffic offences committed in a certain city over a period of 3 years is given in the following table: Jan-March April-June July-Sept. Oct.-Dec 2000 74 56 48 69 2001 83 52 49 81 2002 94 60 48 79 Draw a graph illustrating these figures. Calculate suitable moving averages and plot them on the same graph. Comment on the result.

The given number of traffic offences for 200 , 2001 and 2002 are in four time periods. So, the period is even which indicates that we have to determine centred moving averages. The first quarterly moving average is 74 + 56 + 48 + 69 4 = 247 4 = 61 . 75 . The second quarterly moving average is 56 + 48 + 69 + 83 4 = 256 4 = 64 . Similarly, the third, fourth, fifth, sixth, seventh, eighth and ninth quarterly moving averages are 48 + 69 + 83 + 52 4 = 252 4 = 6 3 , 69 + 83 + 52 + 49 4 = 253 4 = 6 3 . 25 , 83 + 52 + 49 + 81 4 = 265 4 = 66 . 25 , 52 + 49 + 81 + 94 4 = 276 4 = 69 , 49 + 81 + 94 + 60 4 = 284 4 = 71 , 81 + 94 + 60 + 48 4 = 283 4 = 70 . 75 and 94 + 60 + 48 + 79 4 = 281 4 = 70 . 25 respectively. Now, The first quarterly centre moving average is 61 . 75 + 64 2 = 62 . 875 . The second quarterly centre moving average is 64 + 63 2 = 63 . 5 Similarly, the third, fourth, fifth, sixth, seventh and eighth quarterly centre moving averages are 63 + 63 . 25 2 = 63 . 125 , 63 . 25 + 66 . 25 2 = 64 . 75 , 66 . 25 + 69 2 = 67 . 625 , 66 . 25 + 69 2 = 67 . 625 , 69 + 71 2 = 70 , 71 + 70 . 75 2 = 70 . 875 and 70 . 75 + 70 . 25 2 = 70 . 500 respectively . Thus, the quarterly moving average are 62 . 875 , 63 . 5 , 63 . 125 , 64 . 75 , 67 . 625 , 70 , 70 . 875 and 70 . 5 which are represented as the dotted line and the actual figures by regular line in the graph below: The graph shows a long term increasing trend may be due to increase in the number of vehicles.

M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST

Attempt the practice questions on Chapter 3: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 2 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST with Hints & Solutions

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 2

The table shows the average prices $(in ₹)$ of coffee, sugar and milk in $2009 and 2010$ , and the weights used to calculate the cost of making a cup of coffee:

	Cost in $2009$ $(per kg)$	Cost in $2010 (per kg)$	Weights
Sugar	$3$	$7$	$3$
Milk	$3$	$3.50$	$4$
Coffee	$90$	$120$	$2$

Calculate, correct to one decimal place, the index number for the cost of a cup of coffee in $2010$ using weighted price relatives.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 2

The table shows the average prices $(in ₹)$ of coffee, sugar and milk in $2009 and 2010$ , and the weights used to calculate the cost of making a cup of coffee:

	Cost in $2009$ $(per kg)$	Cost in $2010 (per kg)$	Weights
Sugar	$3$	$7$	$3$
Milk	$3$	$3.50$	$4$
Coffee	$90$	$120$	$2$

Calculate, correct to one decimal place, the index number for the cost of a cup of coffee in $2010$ using weighted aggregates taking the index number for $2009 to be 100$ in each case.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 3

From the following data, compute price index by applying weighted average of price relatives method using arithmetic mean up to one decimal place:

Commodity	$p_{0} (₹)$	$q_{0}$	$p_{1} (₹)$
Sugar	$9.00$	$20 kg$	$15.00$
Flour	$5.00$	$40 kg$	$10.00$
Milk	$6.00$	$10 lt$	$15.00$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 4

Due to change in prices, the cost of living index for the working class in a city rose to $225 in April from 180 in March 2003$ . The index of food became $252 from 198$ , that of clothing from $185 to 205$ , that of fuel and lighting from $175 to 195$ and that of miscellaneous from $138 to 212$ . The index of rent, however remained unchanged at $150$ . Find the weights of all the groups if the weights of clothing, fuel and lighting, and rent were the same.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 5

The following data relate to the pay of workers employed at a factory.

Types of worker	Rate of pay $(₹ / h o u r)$	Average number of hours worked per week		Number of workers employed
		June	November
Skilled	$6.50$	$37$	$38.5$	$26$
Semi-Skilled	$5.10$	$38.5$	$39.5$	$14$
Unskilled	$3.50$	$40.5$	$40$	$42$

Calculate a weighted aggregate index of average weekly pay for November $(June = 100)$ , using the number of workers employed as a weighting factor.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 6

Calculate five yearly moving averages of the number of students in a college from the following data and plot them on a graph paper:

Year	$1981$	$1982$	$1983$	$1984$	$1985$	$1986$	$1987$	$1988$	$1989$	$1990$
No. of students	$332$	$317$	$357$	$392$	$402$	$405$	$510$	$427$	$405$	$438$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>CHAPTER TEST>Q 7

The number of traffic offences committed in a certain city over a period of $3$ years is given in the following table:

	Jan-March	April-June	July-Sept.	Oct.-Dec
$2000$	$74$	$56$	$48$	$69$
$2001$	$83$	$52$	$49$	$81$
$2002$	$94$	$60$	$48$	$79$

Draw a graph illustrating these figures. Calculate suitable moving averages and plot them on the same graph. Comment on the result.

M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST

Questions from M L Aggarwal Solutions for Chapter: Index Numbers and Moving Averages, Exercise 3: CHAPTER TEST with Hints & Solutions

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