PLEASE SOLVE THESE QUESTIONS LAID OUT BY MR.CHIRANJEEVI:
Q1. 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.
Q2. Find the mean of the first 10 natural numbers.
Q3. Find the value of y from the following observations if these are already arranged in ascending order. The Median is 63.
Q4. 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.
Q5. Find the mode of the following items.
Q. 6: Consider the following distribution of daily wages of 50 workers of a factory.
Daily wages (in Rs.) 100-120 120-140 140-160 160-180 180-200
Number of workers 12 14 8 6 10
Find the mean daily wages of the workers of the factory by using an appropriate method.
Q7. Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute was recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
Number of heart beats per minute 65-68 68-71 71-74 74-77 77-80 80-83 83-86
Number of women 2 4 3 8 7 4 2
Q8 . The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint : Sx-1 = S49 – Sx ]
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Answers
Q1. The given mean of 10 numbers = 15
So, Mean of 10 numbers = sum of observations/ no. of observations
15 = sum of observations / 10
Sum of observations of 10 numbers = 150
Similarly, Mean of 20 numbers = sum of observations/ no. of observations
11 = sum of observations / 20
Sum of observations of 20 numbers = 220
Hence, Mean of 32 numbers = (sum 10 numbers+sum of 20 numbers +sum of last two numbers)/ no. of observations
Mean of 32 numbers = (150 +220 + 20 ) / 32 = 390 /32 = 12.188
q2. 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
q3. 20, 24, 42, y , y +2, 73, 75, 80, 99
Solution:
As the number of observations made is odd, so the median will be the middle term, i.e. y+2. Therefore,
y + 2 = 63
y = 63 -2 = 61
q4. 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=20×60=1200
Also
x+125=20×y=20y
Next, Subtract 125−25=20y−1200
20y=1300
y=65
q5. 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 the maximum number of times.
So, the mode is = 5
q6. f we arrange his marks in ascending order
19, 25, 27, 30, 30, 30
As we can see, 30 occurs a maximum number of times. So, The mode is 30.
these are my answers. hope this helps