From the data, given below, calculate the mean wage, correct to the nearest rupee. Category : A B C D E F Wages in Rs/day: 50 60 70 80 90 100 Number of workers 2 4 8 12 10 6 If the wages per day in each category are increased by 60 %. What is the new mean wage?

Wages x i Number of workers f i f i x i 50 2 100 60 4 240 70 8 560 80 12 960 90 10 900 100 6 600 Total 42 3360 x = Σ f x Σ f = 3360 42 = 80 if wages increased by 60 % , mean will also increased by 60 % Mean = 80 × 160 100 = 128

From the data, given below, calculate the mean wage, correct to the nearest rupee. Category : A B C D E F Wages in Rs/day: 50 60 70 80 90 100 Number of workers 2 4 8 12 10 6 If the number of workers in each category is doubled and the wages per day per worker are reduced by 40 %. What would be the new mean wage?

Wages x No. of workers f fx 50 2 100 60 4 240 70 8 560 80 12 960 90 10 900 100 6 600 Total 42 3360 x - = Σ f i x i Σ f i = 3360 42 = 80 No change in mean if wages are doubled . but if wages are reduced by 40 % New mean = 80 × 60 100 = 48

The contents of 100 match boxes were checked to determine the number of matches they contained. No. of matches: 35 36 37 38 39 40 41 No. of boxes : 6 10 18 25 21 12 8 Calculate, correct to one decimal place, the mean number of matches per box.

Number of matches x i Number of boxes f i f i x i 35 6 210 36 10 360 37 18 666 38 25 980 39 21 819 40 12 480 41 8 328 Total 100 3813 x - = Σ f i x i Σ f i = 3813 100 = 38 . 13

The contents of 100 match boxes were checked to determine the number of matches they contained. Number of matches: 35 36 37 38 39 40 41 Number of boxes: 6 10 18 25 21 12 8 Determine, how many extra matches would have to be added to the total contents of the 100 boxes to bring the mean up to exactly 39 matches?

Number of matches x i Number of boxes f i f i x i 35 6 210 36 10 360 37 18 666 38 25 980 39 21 819 40 12 480 41 8 328 Total 100 3813 x - = Σ f i x i Σ f i = 3813 100 = 38 . 13 2 nd case . mean = 39 Contents = 39 × 100 = 3900 Total match = 3813 Number of New matches be added 3900 - 3813 = 87

If the mean of the following distribution is 3 , find the value of p . x i 1 2 3 5 p + 4 f i 9 6 9 3 6

x i f i f i x i 1 9 9 2 6 12 3 9 27 5 3 15 p + 4 6 6 p + 24 Σ f i = 33 Σf i x i = 6 p + 87 Mean x - = Σ f i x i Σ f i = 3 = 6 p + 87 33 ⇒ 99 = 6 p + 87 ⇒ 6 p = 12 ⇒ p = 2

In the following table, ∑ f i = 200 and mean = 73 . Find the missing frequencies f 1 , and f 2 . x i 0 50 100 150 200 250 f i 46 f 1 f 2 25 10 5

x i f i f i x i 0 46 0 50 f 1 50 f 1 100 f 2 100 f 2 150 25 3750 200 10 2000 250 5 1250 Total 86 + f 1 + f 2 7000 + 50 f 1 + 100 f 2 Σ f i = 200 86 + f 1 + f 2 = 200 f 1 + f 2 = 114 - i Mean x - = Σ f i x i Σ f i 73 = 7000 + 50 f 1 + 100 f 2 200 7000 + 50 f 1 + 100 f 2 = 14600 50 f 1 + 100 f 2 = 7600 f 1 + 2 f 2 = 152 - ii Subtracting ii from i f 2 = 38 f 1 = 114 - 38 = 76 Hence , f 1 = 76 and f 2 = 38

Find the mean (correct to one place of decimal ) by using short-cut method . x 40 41 43 45 46 49 50 f 14 28 38 50 40 20 10

Assume mean = 45 = A x f d = x - A fd 40 14 - 5 - 70 41 28 - 4 - 112 43 38 - 2 - 76 45 50 0 0 46 40 1 40 49 20 4 80 50 10 5 50 total 200 - 88 Mean = A + Σ f d Σ f = 45 + - 88 200 = 1125 - 11 25 = 44 . 6

R K Bansal Solutions for Exercise 1: EXERCISE

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Concise Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 10

From the data, given below, calculate the mean wage, correct to the nearest rupee.

Category :	$A$	$B$	$C$	$D$	$E$	$F$
Wages in Rs/day:	$50$	$60$	$70$	$80$	$90$	$100$
Number of workers	$2$	$4$	$8$	$12$	$10$	$6$

If the wages per day in each category are increased by $60$ %. What is the new mean wage?

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 10

From the data, given below, calculate the mean wage, correct to the nearest rupee.

Category :	$A$	$B$	$C$	$D$	$E$	$F$
Wages in Rs/day:	$50$	$60$	$70$	$80$	$90$	$100$
Number of workers	$2$	$4$	$8$	$12$	$10$	$6$

If the number of workers in each category is doubled and the wages per day per worker are reduced by $40$ %. What would be the new mean wage?

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 11

The contents of $100$ match boxes were checked to determine the number of matches they contained.

No. of matches:	$35$	$36$	$37$	$38$	$39$	$40$	$41$
No. of boxes :	$6$	$10$	$18$	$25$	$21$	$12$	$8$

Calculate, correct to one decimal place, the mean number of matches per box.

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 11

The contents of $100$ match boxes were checked to determine the number of matches they contained.

Number of matches:	$35$	$36$	$37$	$38$	$39$	$40$	$41$
Number of boxes:	$6$	$10$	$18$	$25$	$21$	$12$	$8$

Determine, how many extra matches would have to be added to the total contents of the $100$ boxes to bring the mean up to exactly $39$ matches?

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 12

If the mean of the following distribution is $3$ , find the value of $p$ .

$x_{i}$	$1$	$2$	$3$	$5$	$p + 4$
$f_{i}$	$9$	$6$	$9$	$3$	$6$

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 13

In the following table, $\underset{}{\sum f_{i} = 200}$ and mean $= 73 .$ Find the missing frequencies $f_{1,}$ and $f_{2}$ .

$x_{i}$	$0$	$50$	$100$	$150$	$200$	$250$
$f_{i}$	$46$	$f_{1}$	$f_{2}$	$25$	$10$	$5$

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 14

Find the arithmetic mean ( correct to the nearest whole-number) by using step-deviation method.

$x$	$5$	$10$	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
$y$	$20$	$43$	$75$	$67$	$72$	$45$	$39$	$9$	$8$	$6$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 15

Find the mean (correct to one place of decimal ) by using short-cut method .

$x$	$40$	$41$	$43$	$45$	$46$	$49$	$50$
$f$	$14$	$28$	$38$	$50$	$40$	$20$	$10$

R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

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