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The scores of 15 students in an examination were recorded as 10,5,8,16,18,20,8,10,16,20,18,11,16,14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change?
  • a)
    Mean and median
  • b)
    Median and mode
  • c)
    Mode only
  • d)
    Mean and mode
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The scores of 15 students in an examination were recorded as 10,5,8,16...
Recorded data are:
10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12
Let us arrange the following data in ascending order to find out the median and mode, i.e.:
5, 8, 8, 10, 10, 11, 12, 14, 16, 16, 16, 18, 18, 20, 20
Total number of observation = 15
As we know,
Mean = ∑x/n

= 202/15
Median = value of  observation
∴ Median =8th observation = 14
From above observation 16 occurs maximum number of times.
∴ Mode =16
According to question,
One of the values is wrongly written as 16 instead of 18.
= 5, 8, 8, 10, 10, 11, 12, 14, 16, 16, 18, 18, 18, 20, 20
 Mean = ∑x/n

= 204/15
Median = value of  observation
Median = 8th  observation = 14
From the above observation 18 occurs the maximum number of times.
∴ Mode = 18
We can see that the mean and mode are changed.
Hence, the correct option is (D).
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The scores of 15 students in an examination were recorded as 10,5,8,16,18,20,8,10,16,20,18,11,16,14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change?a)Mean and medianb)Median and modec)Mode onlyd)Mean and modeCorrect answer is option 'D'. Can you explain this answer?
Question Description
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