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प्रश्न
The mean of marks scored by 100 students was found to be 40, later on, it was discovered that a score of 53 was misread as 83. Find the correct mean.
उत्तर
Total number of students = 100
Initial mean = 40
We first calculate the total sum of marks based on the initial mean:
Total Sum of Marks = Mean × Number of Students
Total Sum of Marks = 40 × 100 = 4000
A score of 53 was mistakenly read as 83.
The error introduced an extra 83 − 53 = 30 marks to the total.
To correct the total, subtract this error:
Correct Total Sum = Initial Total Sum − 30
Correct Total Sum = 4000 − 30 = 3970
The correct mean is calculated by dividing the corrected total sum by the number of students:
Correct Mean = `"Correct total Sum"/"Number of Students"`
Correct Mean = `3970/100`
= 39.7
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संबंधित प्रश्न
Find the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks:
0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7 and 8.
In a case of 40 students, marks obtained by the students in a class test (out of 10) are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Number of students | 1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |
Calculate the following for the given distribution:
(i) Median
(ii) Mode
Find the mean of the following frequency distribution :
| Class | 101-110 | 111-120 | 121-130 | 131-140 | 141-150 | 151-160 |
| Frequency | 11 | 16 | 20 | 30 | 14 | 9 |
Find the mode of the following:
15, 17, 16, 17, 10, 12, 14, 16, 19, 12, 16, 15, 16
The marks obtained by 200 students in an examination are given below :
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No.of students | 5 | 10 | 11 | 20 | 27 | 38 | 40 | 29 | 14 | 6 |
Using a graph paper, draw an Ogive for the above distribution. Use your Ogive to estimate:
(i) the median;
(ii) the lower quartile;
(iii) the number of students who obtained more than 80% marks in the examination and
(iv) the number of students who did not pass, if the pass percentage was 35.
Use the scale as 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis.
Estimate the median, the lower quartile and the upper quartile of the following frequency distribution by drawing an ogive:
| Marks(more than) | 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |
| No. of students | 6 | 13 | 22 | 34 | 48 | 60 | 70 | 78 | 80 | 80 |
The mean of six numbers: x − 5, x − 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
Mean of 5 numbers is 20 and the mean of the other 5 numbers is 30. Find the mean of all the 10 numbers taken together.
Find the mean of: 3, 1, 5, 4, 4 and 7
Median is one of the observations in the data if number of observations is ______.
