Statistics is one of the crucial topics of Maths. It is an important topic for Board exams for class 10(CBSE). Apart from studying and practicing problems on statistics from NCERT, students shall also practice these important questions.
Solving these important questions of class 10 maths chapter 14 will help you prepare for CBSE board exams too.
Question1. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.
Solution: The given mean of 10 numbers = 15
So, Mean = sum of observations/ no. of observations
15 = sum of observations / 10
Sum of observations of 10 numbers = 150
Similarly, Mean = sum of observations/ no. of observations
11 = sum of observations / 20
Sum of observations of 20 numbers = 220
Hence, Mean = sum of observations/ no. of observations
Mean of 32 numbers = (150 +220 + 20 ) / 10 = 390 /32
Question 2. Find the mean of the first 10 natural numbers.
Solution: The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Mean = (1 +2 +3 +4 +5+ 6+ 7+ 8+ 9+10) / 10 = 55/10 =5.5
Also check – Probability and Statistics Concepts and Statistics Class 10 Notes
Question 3. Find the value of y from the following observations if these are already arranged in ascending order. The Median is 63.
20, 24, 42, y , y +2, 73, 75, 80, 99
Solution:
As the number of observations made are odd, so the median will be the mean of 5th and 6th term.
Y + 2 = 63
Y = 63 -1 = 61
Question 4 While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. Find the correct mean.
Solution:
Let y be the sum of observation of 19 (20 – 1) numbers leaving 125,
So, y + 25 = 20 * 60 = 1200 (Mean = sum of observations/ no. of observations)
As we know
x+25=20Ã—60=1200
Also
x+125=20Ã—y=20y
Next, Subtract 125âˆ’25=20yâˆ’1200
20y=1300
y=65
Question 5. Find the mode of the following items.
0, 5, 5, 1, 6, 4, 3, 0, 2, 5, 5, 6
Solution: On arranging the items in ascending order, we get:
0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 6, 6
As we can see 5 occurs maximum number of times.
So, the mode is = 6
Question 6. A student scored the following marks in 6 subjects:
30, 19, 25, 30, 27, 30
Find his modal score.
Solution: If we arrange his marks in ascending order
19, 25, 27, 30, 30, 30
As we can see, 30 occurs maximum number of times. So, The mode is 30.
Question 7.The daily minimum steps climbed by a man during a week were as under:
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
34 |
31 |
27 |
32 |
23 |
28 |
Find the mean steps
Solution: Number of steps climbed in a week : 35, 30, 27, 32, 23, 28.
So, we get,
Mean = sum of observation (steps) / total no of observations
= (35+30+27+32+23+28) / 7
= 175/7 = 25
Question 8 : If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18 , 1, a, b is 50. What is the value of b?
Solution:
Mean = sum of observations / no. of observations
15 = (2 + 6 + 7 +a)/4
15 = (15 + a) / 4
15 * 4 = 15 + a
60 – 15 = a
a = 45
Similarly, Mean = sum of observations / no. of observations
50 = (18 + 6 + 1 +a + b)/4
50 = (18 + 6 + 1 +45 + b)/4
50 = (170 + b)/5
250 = 170 + b
b = 250 – 170 = 80
So, The value of b = 80.
Question 9: The mean of the frequency distribution are 28 and 16 respectively. Find the median.
Solution:
3 x median = (mode + 2 mean)
3 x 26 = (29 +2 mean)
78 – 29 = 2 mean
2mean = 49
Mean = 49/2 = 24.5
Question 10. The cumulative frequency table is useful in determining the ____________?
Solution: Median