Statistics is one of the crucial topics of Maths. It is an important topic for Board exams for class 9(CBSE). Apart from studying and practicing problems on statistics from NCERT, students shall also practice these important questions.
Solving these important questions of class 9 maths chapter 14 will help you prepare for CBSE board exams too.
Question 1. Give three examples of data which you can get from your day-to-day life.
Solution:
Here are the three examples which are related to our day-to-day life :
- Number of boys in the sports team.
- Electricity bills of last one year.
- Number of students appearing for board exams from your school.
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.
- Make a frequency distribution table for the above data.
- Which is the most common height and which is the rarest height among these students?
Solution: The required frequency distribution table is
Height |
Tally Marks |
Students |
3.5 |
II |
2 |
4 |
IIII |
4 |
4.2 |
II |
2 |
4.5 |
II |
2 |
4.6 |
I |
1 |
4.7 |
I |
1 |
5 |
III |
3 |
5.3 |
I |
1 |
5.5 |
IIII |
4 |
Total |
20 |
Question 3: The number of family members in 10 flats of a society are
2, 4, 3, 4, 2, 0, 3, 5, 1, 6.
Find the mean number of family members per flat.
Solution:
Number of family members in 10 flats -2, 4, 3, 3, 1, 0, 2, 4, 1, 5.
So, we get,
Mean = sum of observation/ total no of observations
Mean = (2 + 4+ 3 + 3 + 1 + 0 + 2 + 4 + 1 + 5) / 10
Mean = 25/10 = 2.5
Also check – Probability and Statistics Concepts and Statistics Class 10 Notes
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.
Solution:
Number of coupons issued in a week : 105, 216, 322, 167, 273, 405 and 346.
So, we get,
Mean = sum of observation/ total no of observations
Mean = 106+ 215+ 323+166+273+405+346/ 7 = 346/7
Mean = 262
Question 5.The daily minimum questions solved by a student during a week were as under:
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
35 |
30 |
27 |
32 |
23 |
28 |
Find the mean questions
Solution: .
Number of questions solved in a week : 35, 30, 27, 32, 23, 28.
So, we get,
Mean = sum of observation/ total no of observations = (35+30+27+32+23+28) / 7 = 175/7 = 25
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.
Solution:
Mean = sum of observation/ total no of observations
13 = (y + y + 1+ y + 4+ y + 6+ y + 8+ y + 5) / 6
13 = (6y + 24)/6
(13 * 6) = 6y +24
(13 * 6) – 24 = 6y
(13 * 6) – 6 * 4 = 6y
6(13 – 4) = 6y
Y = 9
Question 7. In the above question, Find the mean of all the observations?
Solution:
The six given observations are
y, y + 1, y + 4, y + 6, y + 8, y + 5.
If we put the value of y (found in previous question), the observation values will be
9, 10, 13, 15, 17, 14
Mean = sum of observation/ total no of observations = (9+10+13+15+17+14) / 6 = 78/6 = 13
Question 8. 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.
Solution:
The mean score of 34 students = 46.5
Sum of the scores of 34 students = (46.5 * 34) = 1581
Change or increase in the mean score when the score of a new boy is added = 0.5
So, the new mean = (46.5 +0.5) = 47
So, let the score of new boy be y.
So, (sum of scores of 34 students + score of new boy) / 35 = 47
(1581+ y)/ 35 = 47
1581 + y = 1645
Y = 1645 – 1581 = 64
Question 9.The Number of books issued to 15 students in a class are:
25, 19, 24, 23, 29, 31, 19, 20, 22, 26, 17, 35, 21.
Find the median no. of books for the above data.
Solution:
Let’s arrange the data given in ascending order – 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29,31,35.
n= 13, so itâ€™s an odd number
Median = (n+1) / 2 observations
= (13+1)/ 2 = (14/2)^{th} observation = 7th observation = 23
Question 10.The weight (in kg) of 7 students of a class are 44, 52, 55, 60, 50, 49, 45.
Find the median weight.
Solution:
Let’s arrange the data given in ascending order – 44, 45, 49, 50, 52, 55, 60.
n= 7, so itâ€™s an odd number
Median = (n+1) / 2 observations
= (7+1)/ 2 = (8/2)^{th} observation = 4th observation = 50 kgs