The production of cement by a firm in years 1 to 9 is given below: Year 1 2 3 4 5 6 7 8 9 Production (Tonnes) 4 5 5 6 7 8 9 8 10 Calculate the trend values for the above series by the 3 -yearly moving average method .

Given, Year 1 2 3 4 5 6 7 8 9 Production (Tonnes) 4 5 5 6 7 8 9 8 10 The first 3 -year moving average is 4 + 5 + 5 3 = 14 3 = 4 . 6 6 ¯ = 4 . 67 and is placed against 2 nd year i.e, 2 . The second 3 -year moving average is 5 + 5 + 6 3 = 16 3 = 5 . 33 and is placed against 3 rd year i.e, 3 . The third 3 -year moving average is 5 + 6 + 7 3 = 18 3 = 6 and is placed against 4 th year i.e, 4 . The fourth 3 -year moving average is 6 + 7 + 8 3 = 21 3 = 7 and is placed against 5 th year i.e, 5 . The fifth 3 -year moving average is 7 + 8 + 9 3 = 24 3 = 8 and is placed against 6 th year i.e, 6 . The sixth 3 -year moving average is 8 + 9 + 8 3 = 25 3 = 8 . 33 and is placed against 7 th year i.e, 7 . The seventh 3 -year moving average is 9 + 8 + 10 3 = 27 3 = 9 and is placed against 8 th year i.e, 8 . Thus, the trend values for the above series by the 3 -year moving average are 4 . 67 , 5 . 33 , 6 , 7 , 8 , 8 . 33 and 9 .

Consider the following data: Dates in the month of April 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Number of units sold 2 5 0 12 13 25 45 13 31 18 11 2 3 1 Calculate three days moving averages and display these and the original figures on the same graph.

Given, Dates in the month of April 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Number of units sold 2 5 0 12 13 25 45 13 31 18 11 2 3 1 The first 3 -day moving average is 2 + 5 + 0 3 = 7 3 = 2 . 33 and is placed against 2 nd day i.e, 13 . The second 3 -day moving average is 5 + 0 + 12 3 = 17 3 = 5 . 6 6 ¯ = 5 . 67 and is placed against 3 rd day i.e, 14 . The third 3 -day moving average is 0 + 12 + 13 3 = 25 3 = 8 . 33 and is placed against 4 th day i.e, 15 . The fourth 3 -day moving average is 12 + 13 + 25 3 = 50 3 = 16 . 6 6 ¯ = 16 . 67 and is placed against 5 th day i.e, 16 . The fifth 3 -day moving average is 13 + 25 + 45 3 = 83 3 = 27 . 6 6 ¯ = 27 . 67 and is placed against 6 th day i.e, 17 . The sixth 3 -day moving average is 25 + 45 + 13 3 = 83 3 = 27 . 6 6 ¯ = 27 . 67 and is placed against 7 th day i.e, 18 . The seventh 3 -day moving average is 45 + 13 + 31 3 = 89 3 = 29 . 6 6 ¯ = 29 . 67 and is placed against 8 th day i.e, 19 . The eighth 3 -day moving average is 13 + 31 + 18 3 = 62 3 = 20 . 6 6 ¯ = 20 . 67 and is placed against 9 th day i.e, 20 . The ninth 3 -day moving average is 31 + 18 + 11 3 = 60 3 = 20 and is placed against 10 th day i.e, 21 . The tenth 3 -day moving average is 18 + 11 + 2 3 = 31 3 = 10 . 33 and is placed against 11 th day i.e, 22 . The eleventh 3 -day moving average is 11 + 2 + 3 3 = 16 3 = 5 . 33 and is placed against 12 th day i.e, 23 . The twelfth 3 -day moving average is 2 + 3 + 1 3 = 6 3 = 2 and is placed against 13 th day i.e, 24 . Thus, the 3 -day moving average are 2 . 33 , 5 . 67 , 8 . 33 , 16 . 67 , 27 . 67 , 27 . 67 , 29 . 67 , 20 . 67 , 20 , 10 . 33 , 5 . 33 and 2 which are graphically represented as below: The moving averages are shown by dotted line and the actual figures are shown by regular line.

In an influenza epidemic the number of cases diagnosed were Date ( March) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Numbers 2 0 5 12 20 27 46 30 31 18 11 5 0 1 Calculate three days moving averages and display these and the original figures on the same graph.

Given, Date ( March) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Numbers 2 0 5 12 20 27 46 30 31 18 11 5 0 1 The first 3 -day moving average is 2 + 0 + 5 3 = 7 3 = 2 . 33 and is placed against 2 nd day i.e, 2 . The second 3 -day moving average is 0 + 5 + 12 3 = 17 3 = 5 . 6 6 ¯ = 5 . 67 and is placed against 3 rd day i.e, 3 . The third 3 -day moving average is 5 + 12 + 20 3 = 37 3 = 12 . 33 and is placed against 4 th day i.e, 4 . The fourth 3 -day moving average is 12 + 20 + 27 3 = 59 3 = 19 . 6 6 ¯ = 19 . 67 and is placed against 5 th day i.e, 5 . The fifth 3 -day moving average is 20 + 27 + 46 3 = 93 3 = 31 and is placed against 6 th day i.e, 6 . The sixth 3 -day moving average is 27 + 46 + 30 3 = 103 3 = 34 . 33 and is placed against 7 th day i.e, 7 . The seventh 3 -day moving average is 46 + 30 + 31 3 = 107 3 = 35 . 6 6 ¯ = 35 . 67 and is placed against 8 th day i.e, 8 . The eighth 3 -day moving average is 30 + 31 + 18 3 = 79 3 = 26 . 33 and is placed against 9 th day i.e, 9 . The ninth 3 -day moving average is 31 + 18 + 11 3 = 60 3 = 20 and is placed against 10 th day i.e, 10 . The tenth 3 -day moving average is 18 + 11 + 5 3 = 34 3 = 14 . 6 6 ¯ = 14 . 67 and is placed against 11 th day i.e, 11 . The eleventh 3 -day moving average is 11 + 5 + 0 3 = 16 3 = 5 . 33 and is placed against 12 th day i.e, 12 . The twelfth 3 -day moving average is 5 + 0 + 1 3 = 6 3 = 2 and is placed against 13 th day i.e, 13 . Thus, the 3 -day moving average are 2 . 33 , 5 . 67 , 12 . 33 , 19 . 67 , 31 , 34 . 33 , 35 . 67 , 26 . 33 , 20 , 14 . 67 , 5 . 33 and 2 which is graphically represented as below: The moving averages are shown by dotted line and the actual figures are shown by regular line.

Calculate five yearly moving averages of the number of students who have studied in a school given below: Year 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 No. of students 442 427 467 502 512 515 520 527 515 541

Given, Year 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 No. of students 442 427 467 502 512 515 520 527 515 541 The first 5 -yearly moving average is 442 + 427 + 467 + 502 + 512 5 = 2350 5 = 470 and is placed against 3 rd year i.e, 1995 . The second 5 -yearly moving average is 427 + 467 + 502 + 512 + 515 5 = 2423 5 = 484 . 6 and is placed against 4 th year i.e, 1996 . The third 5 -yearly moving average is 467 + 502 + 512 + 515 + 520 5 = 2516 5 = 503 . 2 and is placed against 5 th year i.e, 1997 . The fourth 5 -yearly moving average is 502 + 512 + 515 + 520 + 527 5 = 2576 5 = 515 . 2 and is placed against 6 th year i.e, 1998 . The fifth 5 -yearly moving average is 512 + 515 + 520 + 527 + 515 5 = 2589 5 = 517 . 8 and is placed against 7 th year i.e, 1999 . The sixth 5 -yearly moving average is 515 + 520 + 527 + 515 + 541 5 = 2618 5 = 523 . 6 and is placed against 8 th year i.e, 2000 . Thus, the 5 -yearly moving average are 470 , 484 . 6 , 503 . 2 , 515 . 2 , 517 . 8 and 523 . 6 .

Calculate five yearly moving averages of the number of students who have studied in a school given below: Year Production (in tonnes) 1986 351 1987 366 1988 361 1989 362 1990 400 1991 419 1992 410 1993 420 1994 450 1995 500

The first 5 -yearly moving average is 351 + 366 + 361 + 362 + 400 5 = 1840 5 = 368 and is placed against 3 rd year i.e, 1988 . The second 5 -yearly moving average is 366 + 361 + 362 + 400 + 419 5 = 1908 5 = 381 . 6 and is placed against 4 th year i.e, 1989 . The third 5 -yearly moving average is 361 + 362 + 400 + 419 + 410 5 = 1952 5 = 390 . 4 and is placed against 5 th year i.e, 1990 . The fourth 5 -yearly moving average is 362 + 400 + 419 + 410 + 420 5 = 2011 5 = 402 . 2 and is placed against 6 th year i.e, 1991 . The fifth 5 -yearly moving average is 400 + 419 + 410 + 420 + 450 5 = 2099 5 = 419 . 8 and is placed against 7 th year i.e, 1992 . The sixth 5 -yearly moving average is 419 + 410 + 420 + 450 + 500 5 = 2199 5 = 439 . 8 and is placed against 8 th year i.e, 1993 . Thus, the 5 -yearly moving average are 368 , 381 . 6 , 390 . 4 , 402 . 2 , 419 . 8 and 439 . 8 .

Daily absence from a school during three weeks is recorded as follows: Monday Tuesday Wednesday Thursday Friday Week 1 23 28 21 33 40 Week 2 38 52 43 58 63 Week 3 52 54 61 51 51 Draw a graph, illustrating these figures. Calculate 5 day moving averages and plot them on the same graph.

The given data can be rearranged in the following way: Days Number of Absence Week 1 Monday 23 Tuesday 28 Wednesday 21 Thursday 33 Friday 40 Week 3 Monday 38 Tuesday 52 Wednesday 43 Thursday 58 Friday 63 Week 3 Monday 52 Tuesday 54 Wednesday 61 Thursday 51 Friday 51 The first 5 -day moving average is 23 + 28 + 21 + 33 + 40 5 = 145 5 = 29 and is placed against 3 rd day of 1 st week i.e, Wednesday. The second 5 -day moving average is 28 + 21 + 33 + 40 + 38 5 = 160 5 = 32 and is placed against 4 th day of 1 st week i.e, Thursday. The third 5 -day moving average is 21 + 33 + 40 + 38 + 52 5 = 184 5 = 36 . 8 and is placed against 5 th day of 1 st week i.e, Friday. The fourth 5 -day moving average is 33 + 40 + 38 + 52 + 43 5 = 206 5 = 41 . 2 and is placed against 1 st day of week 2 i.e, Monday. The fifth 5 -day moving average is 40 + 38 + 52 + 43 + 58 5 = 231 5 = 46 . 2 and is placed against 2 nd day of week 2 i.e, Tuesday. The sixth 5 -day moving average is 38 + 52 + 43 + 58 + 63 5 = 274 5 = 54 . 8 and is placed against 3 rd day of week 2 i.e, Wednesday. The seventh 5 -day moving average is 52 + 43 + 58 + 63 + 52 5 = 268 5 = 53 . 6 and is placed against 4 th day of week 2 i.e, Thursday. The eighth 5 -day moving average is 43 + 58 + 63 + 52 + 54 5 = 270 5 = 54 and is placed against 5 th day of week 2 i.e, Friday. The ninth 5 -day moving average is 58 + 63 + 52 + 54 + 61 5 = 288 5 = 57 . 6 and is placed against 1 st day of week 3 i.e, Monday. The tenth 5 -day moving average is 63 + 52 + 54 + 61 + 51 5 = 281 5 = 56 . 2 and is placed against 2 nd day of week 3 i.e, Tuesday. The eleventh 5 -day moving average is 52 + 54 + 61 + 51 + 51 5 = 269 5 = 53 . 8 and is placed against 3 rd day of week 3 i.e, Wednesday. Thus, the 5 -day moving average are 29 , 32 , 36 . 8 , 41 . 2 , 46 . 2 , 54 . 8 , 53 . 6 , 54 , 57 . 6 , 56 . 2 and 53 . 8 which are graphically represented as below: The moving averages are shown by dotted line and the actual figures are shown by regular line.

The table given below shows that the daily attendance in thousands at a certain exhibition over a period of two weeks: Week 1 52 48 64 68 52 70 72 Week 2 55 47 61 65 58 75 81 Calculate seven day moving averages and illustrate these and original information on the same graph using the same scales.

The given data can be rearranged in the following way: Days Number of Absence Week 1 Monday 52 Tuesday 48 Wednesday 64 Thursday 68 Friday 52 Saturday 70 Sunday 72 Week 2 Monday 55 Tuesday 47 Wednesday 61 Thursday 65 Friday 58 Saturday 75 Sunday 81 The first 7 -day moving average is 52 + 48 + 64 + 68 + 52 + 70 + 72 7 = 426 7 = 60 . 8571 ≅ 60 . 86 and is placed against 4 th day of 1 st week i.e, Thursday. The second 7 -day moving average is 48 + 64 + 68 + 52 + 70 + 72 + 55 7 = 429 7 = 61 . 2857 ≅ 61 . 28 and is placed against 5 th day of 1 st week i.e, Friday. The third 7 -day moving average is 64 + 68 + 52 + 70 + 72 + 55 + 47 7 = 428 7 = 61 . 1428 ≅ 61 . 14 and is placed against 6 th day of 1 st week i.e, Saturday. The fourth 7 -day moving average is 68 + 52 + 70 + 72 + 55 + 47 + 61 7 = 425 7 = 60 . 7142 ≅ 60 . 71 and is placed against 7 th day of 1 st week i.e, Sunday. The fifth 7 -day moving average is 52 + 70 + 72 + 55 + 47 + 61 + 65 7 = 422 7 = 60 . 2857 ≅ 60 . 28 and is placed against 1 st day of 2 nd week i.e, Monday. The sixth 7 -day moving average is 70 + 72 + 55 + 47 + 61 + 65 + 58 7 = 428 7 = 61 . 1428 ≅ 61 . 14 and is placed against 2 nd day of 2 nd week i.e, Tuesday. The seventh 7 -day moving average is 72 + 55 + 47 + 61 + 65 + 58 + 75 7 = 433 7 = 61 . 8571 ≅ 61 . 86 and is placed against 3 rd day of 2 nd week i.e, Wednesday. The eighth 7 -day moving average is 55 + 47 + 61 + 65 + 58 + 75 + 81 7 = 442 7 = 63 . 1428 ≅ 63 . 14 and is placed against 4 th day of 2 nd week i.e, Thursday. Thus, the 7 -day moving average are 60 . 86 , 61 . 28 , 61 . 14 , 60 . 71 , 60 . 28 , 61 . 14 , 61 . 86 and 63 . 14 which are graphically represented as below: The moving averages are shown by dotted line and the actual figures are shown by regular line.

Calculate the3yearlymoving averages of the following data Year 1 2 3 4 5 6 7 Value 2 4 5 7 8 10 13

HARD

11th ICSE

IMPORTANT

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

The number of letters, in hundreds, posted in a certain city on each day of a week is given as follows: $35, 70, 36, 59, 62, 60, 71$ . Calculate the three-day moving averages and display these graphically.

MEDIUM

11th ICSE

IMPORTANT

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

The production of cement by a firm in years $1 to 9$ is given below:

Year	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Production (Tonnes)	$4$	$5$	$5$	$6$	$7$	$8$	$9$	$8$	$10$

Calculate the trend values for the above series by the $3 -yearly moving average method$ .

HARD

11th ICSE

IMPORTANT

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

Consider the following data:

Dates in the month of April	$12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$
Number of units sold	$2$	$5$	$0$	$12$	$13$	$25$	$45$	$13$	$31$	$18$	$11$	$2$	$3$	$1$

Calculate three days moving averages and display these and the original figures on the same graph.

HARD

11th ICSE

IMPORTANT

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

In an influenza epidemic the number of cases diagnosed were

Date (March)	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$
Numbers	$2$	$0$	$5$	$12$	$20$	$27$	$46$	$30$	$31$	$18$	$11$	$5$	$0$	$1$

Calculate three days moving averages and display these and the original figures on the same graph.

HARD

11th ICSE

IMPORTANT

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

Calculate five yearly moving averages of the number of students who have studied in a school given below:

Year	$1993$	$1994$	$1995$	$1996$	$1997$	$1998$	$1999$	$2000$	$2001$	$2002$
No. of students	$442$	$427$	$467$	$502$	$512$	$515$	$520$	$527$	$515$	$541$

HARD

11th ICSE

IMPORTANT

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

Calculate five yearly moving averages of the number of students who have studied in a school given below:

Year	Production (in tonnes)
$1986$	$351$
$1987$	$366$
$1988$	$361$
$1989$	$362$
$1990$	$400$
$1991$	$419$
$1992$	$410$
$1993$	$420$
$1994$	$450$
$1995$	$500$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>EXERCISE>Q 8

Daily absence from a school during three weeks is recorded as follows:

	Monday	Tuesday	Wednesday	Thursday	Friday
Week $1$	$23$	$28$	$21$	$33$	$40$
Week $2$	$38$	$52$	$43$	$58$	$63$
Week $3$	$52$	$54$	$61$	$51$	$51$

Draw a graph, illustrating these figures. Calculate 5 day moving averages and plot them on the same graph.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 3 - Index Numbers and Moving Averages>EXERCISE>Q 9

The table given below shows that the daily attendance in thousands at a certain exhibition over a period of two weeks:

Week $1$	$52$	$48$	$64$	$68$	$52$	$70$	$72$
Week $2$	$55$	$47$	$61$	$65$	$58$	$75$	$81$

Calculate seven day moving averages and illustrate these and original information on the same graph using the same scales.

Calculate the $3 -yearly$ moving averages of the following data:

Year $1$ $2$ $3$ $4$ $5$ $6$ $7$

Value $2$ $4$ $5$ $7$ $8$ $10$ $13$

Important Questions on Index Numbers and Moving Averages

Learn and Prepare for any exam you want !

Calculate the 3-yearly moving averages of the following data: Year 1 2 3 4 5 6 7 Value 2 4 5 7 8 10 13

Important Questions on Index Numbers and Moving Averages

Learn and Prepare for any exam you want !

Calculate the $3 -yearly$ moving averages of the following data:

Year $1$ $2$ $3$ $4$ $5$ $6$ $7$

Value $2$ $4$ $5$ $7$ $8$ $10$ $13$