Question

Question 1. Give three examples of data which you can get from your day-to-day life.

Question 2. The height of 20 students of class V are noted as follows

4, 4.5, 5, 5.5, 4, 4, 4.5, 5, 5.5, 4, 3.5, 3.5, 4.2, 4.6, 4.2, 4.7, 5.5, 5.3, 5, 5.5.

i)Make a frequency distribution table for the above data.
ii)Which is the most common height and which is the rarest height among these students?

Question 3: The number of family members in 10 flats of society are

2, 4, 3, 3, 1,0,2,4,1,5.

Find the mean number of family members per flat.

Question 4.The following is the list of number of coupons issued in a school canteen during a week:

105, 216, 322, 167, 273, 405 and 346.

Find the average no. of coupons issued per day.

Question 6.If the mean of six observations y, y + 1, y + 4, y + 6, y + 8, y + 5 is 13, find the value of y.

Question 7. The mean weight of a class of 34 students is 46.5 kg. If the weight of the new boy is included, the mean is rises by 500 g. Find the weight of the new boy.

Class 9 ​

Answer 1

Step-by-step explanation:

$\sf\underline\orange{Question-1:-}$

Three examples of data which we can get from our day to day life are:

• Temperature of a city
• Weight of students
• Cricket scores

$\sf\underline\orange{Question-2:-}$

(i) The frequency distribution for the data is given in the attachment. Please refer it!

(ii) The most common heights are 4 and 5.5. Since, number of students mostly have 4 and 5.5 as their height, 4 and 5.5 are the common heights.

The rarest heights are 4.6, 4.7 and 5.3, since lesser number of students have this measure of height.

$\sf\underline\orange{Question-3:-}$

From the given data, we can observe that:

$\tt{\implies Number\:of\:observations = 10}$

$\tt{\implies Sum\:of\:observations = 2+4+3+3+1+0+2+4+1+5}$

$\tt{\implies Sum\:of\:observations = 25}$

To find the mean, we use the formula:

$\tt{\implies Mean = \dfrac{Sum\:of\:observations}{Number\:of\: observations}}$

$\tt{\implies Mean = \dfrac{25}{10}}$

$\tt{\implies Mean = 2.5}$

Hence, the mean number of family members per flat is 2.5

$\sf\underline\orange{Question-4:-}$

From the given data,

$\tt{\implies Total\:number\:of\:coupons = 105+216+322+167+273+405+346}$

$\tt{\implies Total\:number\:of\:coupons = 1834}$

We know that, there are 7 days in a week.

$\tt{\implies Average\:number\:of\:coupons = \dfrac{Total\:number\:of\:coupons}{Total\:number\:of\:days\:in\:a\:week}}$

$\tt{\implies Average\:number\:of\:coupons = \dfrac{1834}{7}}$

$\tt{\implies Average\:number\:of\:coupons = 262}$

Hence, the average number of coupons is 262.

$\sf\underline\orange{Question-5:-}$

$\tt{\implies Mean = \dfrac{Sum\:of\:observations}{Number\:of\: observations}}$

$\tt{\implies 13 = \dfrac{y+y+1+y+4+y+6+y+8+y+5}{6}}$

$\tt{\implies 13 = \dfrac{6y+24}{6}}$

$\tt{\implies 6y+24 = 13 \times 6}$

$\tt{\implies 6y+24 = 78}$

$\tt{\implies 6(y+4) = 78}$

$\tt{\implies y+4 = \dfrac{78}{6}}$

$\tt{\implies y+4 = 13}$

$\tt{\implies y = 13-4}$

$\tt{\implies y = 9}$

Hence, the value of y is 9.

$\sf\underline\orange{Question-6:-}$

We are given that,

⟹ Mean weight of 34 students = 46.5kg

Therefore,

⟹ Total weight = 34 × 46.5

⟹ Total weight = 1581kg

We know that 500g is also the same as 0.5kg.

⟹ Mean weight of 34 students and teacher = 46.5 + 0.5

⟹ Mean weight of 34 students and teacher = 47kg

⟹ Total weight of 34 students and teacher = 47×35

⟹ Total weight of 34 students and teacher = 1645kg

The weight of the teacher can be calculated by:

⟹ Weight of the teacher = Total weight of 34 students and teacher - Total weight

⟹ Weight of the teacher = 1645-1581

⟹ Weight of the teacher = 64kg

Hence, the weight of the teacher is 64kg.

Answer 2

Step-by-step explanation:

Q-1:-

1. calculate the daily income of a shop during a month.

2.compare heights of boys and girls.

3.weather report and cricket match schedules from news channels or papers.

Q-2:-

See the above attachment

Taking inclusive classes of length 1 unit

0-1,1-2,2-3,3-4,4-5,5-6

Total frequency = 20

Using tally marks

Q-3:-

Given observations are 2, 4, 3, 3, 1,0,2,4,1,5.

Sum of all observations

= 2+4+3+3+1+0+2+4+1+5=25

Number of observations = 10

Mean = Sum of all observations/Number of all observations

=> Mean = 25/10

Mean = 2.5

Q:4-

Given observations are

105, 216, 322, 167, 273, 405 and 346.

Sum of all observations =

105+216+322+167+273+405+346= 1834

Number of observations = 7

Average = Sum of all observations/Number of all observations

=>Average = 1834/7

Average = 267

the average no. of coupons issued per day = 267

Q-6:-

If the mean of six observations y, y + 1, y + 4, y + 6, y + 8, y + 5 is 13

Sum of all observations =

y+y+1+y+4+y+6+y+8+y+5=6y+24

Number of all observations = 6

Mean= Sum of all observations/Number of all observations

=> (6y+24)/6 = 13

=>6(y+4)/6 = 13

=> y+4 = 13

=>y = 13-4

=>y = 9

The value of y = 9

Q-7:-

The mean weight of a class of 34 students =

46.5 kg.

Mean= Sum of all observations/Number of all observations

Sum of the weights of all students

= 34×46.5kg

=1581 kg

the weight of the new boy is included

Then number of students = 34+1=35

Then the mean is rises by 500 g.

New mean = 46.5kg +500 g =47 kg

Sum of the weights of all students

=47×35=1645 kg

weight of the new boy

=Sum of 35 students weight - Sum of 34 students weight

= 1645-1581

=64 kg

Weight of the boy who included newly = 64 kg