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Statistics questions for IPMAT, with solutions

10 free Statistics practice questions for IPMAT Indore, Rohtak and JIPMAT, each with the answer and a full worked solution. No sign-in. Try each one first, then open the solution. The lessons for this chapter are in Statistics on Learn.

1. Question 1Type the answerWritten by IPMATwayMean, Median and Mode

   The mean of $10$ observations is $12$. If each observation is doubled and then decreased by $3$, the mean of the new observations is

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   Answer: 21

   If every $x$ becomes $2x-3$, the mean becomes $2\bar x-3$.

2. Question 2Type the answerWritten by IPMATwayMean, Median and Mode

   If the mean of the numbers $a$, $a+2$, $a+4$, $a+6$ and $a+8$ is $20$, their median is

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   Answer: 20

   $5a+20=100\Rightarrow a=16$; the numbers are $16,18,20,22,24$ with median $20$.

3. Question 3Type the answerWritten by IPMATwayMean, Median and Mode

   In a group of $20$ students, $3$ scored $40$, $5$ scored $50$, $7$ scored $60$ and $5$ scored $70$. The median score is

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   Answer: 60

   Cumulative frequencies locate both middle positions in the $60$ group.

4. Question 4Type the answerWritten by IPMATwayRange, Variance and Deviation

   The standard deviation of $20$ items is $10$. If each item is decreased by $1$, the standard deviation of the new items is

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   Answer: 10

   Shifting all data by a constant does not change the spread.

5. Question 5Type the answerWritten by IPMATwayRange, Variance and Deviation

   The variance of a set of observations is $16$. If every observation is multiplied by $3$, the variance of the new set is

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   Answer: 144

   SD scales by $3$ (from $4$ to $12$), variance by $9$.

6. Question 6Type the answerWritten by IPMATwayMean, Median and Mode

   For three real numbers, the sum of the maximum and the minimum is $40$ and the median exceeds the mean by $-2$ (that is, the mean exceeds the median by $2$). The median of the three numbers is

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   Answer: 17

   Sum $=40+m$; set mean minus median equal to $2$ and solve.

7. Question 7Type the answerWritten by IPMATwayMean, Median and Mode

   The mean of $11$ numbers is $50$. If the mean of the first six numbers is $48$ and that of the last six numbers is $54$, the sixth number is

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   Answer: 62

   The two groups of six overlap in the sixth number, which is therefore counted twice in the combined sums.

8. Question 8Type the answerWritten by IPMATwayMean, Median and Mode

   The mean of $25$ observations is $40$. It was found that an observation $64$ had been wrongly included; after removing it, the mean of the remaining observations is

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   Answer: 39

   Remove the value from the total and divide by $24$.

9. Question 9Type the answerWritten by IPMATwayMean, Median and Mode

   The mean of $100$ observations is $50$. If the mean of the first $60$ observations is $44$, the mean of the remaining $40$ observations is

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   Answer: 59

   Remaining total divided by the remaining count.

10. Question 10Type the answerWritten by IPMATwayMean, Median and Mode

    The sum of the deviations of $15$ observations from the value $40$ is $30$. The mean of the observations is

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    Answer: 42

    The mean equals the assumed value plus the mean deviation from it: $40+30/15$.