Measures of Central Tendency

9 Grade 7 Mathematics questions on Measures of Central Tendency, with worked marking schemes. 9 questions are available on this topic in full.

1. Question 1

   3 marks

   The mean of five numbers is 12. Four of the numbers are 8, 15, 10 and 14. Find the fifth number.

   (3 marks)

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2. Question 2

   1 mark

   Find the median: 3, 7, 2, 9, 5, 8, 1

   A. 7

   B. 3

   C. 9

   D. 5

   (1 mark)

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3. Question 3

   1 mark

   The mode of 4, 7, 2, 4, 9, 4, 7, 2 is:

   A. 4

   B. 9

   C. 2

   D. 7

   (1 mark)

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4. Question 4

   4 marks

   The marks of 10 students are: 45, 67, 52, 78, 60, 72, 55, 83, 48, 70. Find the mean and median.

   (4 marks)

   Marking scheme

   The mean is the total divided by how many values there are. Adding the ten marks: $45+67+52+78+60+72+55+83+48+70=630$. (1)

   Mean $=\frac{630}{10}=63$. (1)

   The median is the middle value, so first put the marks in order: $45,48,52,55,60,67,70,72,78,83$. (1)

   With an even count of $10$ there is no single middle, so average the $5$th and $6$th: $\frac{60+67}{2}=63.5$. (1)

   Final answer: mean $63$, median $63.5$.

5. Question 5

   3 marks

   The mean of five numbers is 12. Four of the numbers are 8, 15, 10 and 14. Find the fifth number.

   (3 marks)

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6. Question 6

   1 mark

   The range of 15, 22, 8, 31, 19 is:

   A. 23

   B. 19

   C. 31

   D. 8

   (1 mark)

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7. Question 7

   3 marks

   A frequency table shows: Score 5(3), 6(5), 7(8), 8(4). Find the mean.

   (3 marks)

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8. Question 8

   3 marks

   The mean of 8 numbers is 25. Two numbers (30 and 20) are removed. Find the new mean.

   (3 marks)

   Marking scheme

   The mean is the total divided by how many, so the total of the $8$ numbers is $8\times 25=200$. (1)

   Removing $30$ and $20$ takes $50$ off the total: $200-50=150$, and leaves $8-2=6$ numbers. (1)

   The new mean is $\frac{150}{6}=25$. (1)

   Final answer: $25$. It is unchanged because the two numbers removed averaged $25$ themselves.

9. Question 9

   1 mark

   The mean of 5 numbers is 12. Four are 8, 15, 10, 14. Find the fifth.

   A. 12

   B. 15

   C. 11

   D. 13

   (1 mark)

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