Data and probability · Ages 14–15
Choosing the mean, median or mode worksheet
Part of: Measures of central tendency
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Choosing the mean, median or mode worksheet
Data and probability · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Five flats have floor areas of 41, 117, 39, 46 and 42 m². By how many m² does the mean exceed the median?
Answer:
2.Five flats have floor areas of 38, 113, 35, 43 and 41 m². By how many m² does the mean exceed the median?
Answer:
3.A courier delivered 33, 23, 195, 21, 31, 27 parcels on six days, one of them during a big sale. With that extreme value taken out, the mean falls by and the median only by .
Fill in each blank
Answer:
4.A courier delivered 28, 19, 88, 16, 25, 22 parcels on six days, one of them during a big sale. With that extreme value taken out, the mean falls by and the median only by .
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
5.A small firm's five staff earn $17,000, $15,000, $181,000, $18,000 and $16,000 a month. Which figure best represents a typical member of staff's pay?
- A. The mean, $49,400
- B. The median, $17,000
- C. The highest pay, $181,000
- D. The lowest pay, $15,000
Choose the right answer
Answer:
6.A shoe shop is deciding which size to order most of next month. Which measure of last month's sizes sold should it look at?
- A. The median
- B. The largest size
- C. The mean
- D. The mode
Choose the right answer
Answer:
7.A small firm's five staff earn $21,000, $18,000, $178,000, $22,000 and $20,000 a month. Which figure best represents a typical member of staff's pay?
- A. The median, $21,000
- B. The mean, $51,800
- C. The highest pay, $178,000
- D. The lowest pay, $18,000
Choose the right answer
Answer:
8.An ice-cream shop asked 197 customers for their favourite flavour. Which measure can describe the centre of these data?
- A. Only the median
- B. Any of the three
- C. Only the mean
- D. Only the mode
Choose the right answer
Answer:
9.An ice-cream shop asked 47 customers for their favourite flavour. Which measure can describe the centre of these data?
- A. Only the mean
- B. Only the median
- C. Any of the three
- D. Only the mode
Choose the right answer
Answer:
10.A runner ran 22, 15, 52, 19, 16 km on five runs. The mean and median of these data are less than 2 km apart.
True or false?
Answer:
11.A runner ran 22, 16, 52, 20, 18 km on five runs. The mean and median of these data are less than 2 km apart.
True or false?
Answer:
12.A runner ran 26, 20, 66, 25, 22 km on five runs. The mean and median of these data are less than 2 km apart.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Five flats in a block sold last month, for $590,000, $3,590,000, $640,000, $560,000 and $620,000, one of them a special penthouse. An estate agent wants a figure for a typical price. Which should it be?
- A. The top price, $3,590,000
- B. The median, $620,000
- C. The mean of the highest and lowest, $2,075,000
- D. The mean, $1,200,000
Choose the right answer
Working:
Answer:
14.A small shop's seven people, the owner among them, earn $13,000, $18,000, $116,000, $13,000, $16,000, $13,000 and $14,000 a month. The owner says 'our mean pay is high'. By how many dollars does the mean exceed the median?
Working:
Answer:
15.A restaurant served 44, 43, 46, 44 and 44 lunch customers on five days. On the sixth a tour group came: 235 customers. With the sixth day in, the median number of customers is unchanged.
True or false?
Working:
Answer:
16.A clothes shop sold 29 T-shirts in size S last month, 5 in M, 7 in L and 20 in XL. Which size should it stock most of next month?
- A. XL
- B. S
- C. M
- D. L
Choose the right answer
Working:
Answer:
17.A small shop's seven people, the owner among them, earn $16,000, $17,000, $106,000, $15,000, $17,000, $15,000 and $17,000 a month. The owner says 'our mean pay is high'. By how many dollars does the mean exceed the median?
Working:
Answer:
18.A clothes shop sold 27 T-shirts in size S last month, 26 in M, 17 in L and 35 in XL. Which size should it stock most of next month?
- A. M
- B. L
- C. S
- D. XL
Choose the right answer
Working:
Answer:
Show the answers and working
Choosing the mean, median or mode worksheet: Answers and working
Part A: Working out and filling in
1. 15 m²
Mean 285 ÷ 5 = 57; the median is the middle one, 42; 15 m² apart: the very large 117 pulls the mean up.
2. 13 m²
Mean 270 ÷ 5 = 54; the median is the middle one, 41; 13 m² apart: the very large 113 pulls the mean up.
3. 28, 2
Six days: mean 55, median (27 + 31) ÷ 2 = 29. Without 195: mean 135 ÷ 5 = 27, median 27. The mean falls by 28, the median only by 2: an extreme value drags the mean a long way and barely moves the median, so with an extreme value the median stands for the typical day.
4. 11, 1.5
Six days: mean 33, median (22 + 25) ÷ 2 = 23.5. Without 88: mean 110 ÷ 5 = 22, median 22. The mean falls by 11, the median only by 1.5: an extreme value drags the mean a long way and barely moves the median, so with an extreme value the median stands for the typical day.
Part B: Choose, or true or false
5. B. The median, $17,000
With an extreme value ($181,000) the median isn't moved and best represents the typical case: the middle one in order is $17,000.
6. D. The mode
The mode is the value that comes most often: exactly the best-selling size.
7. A. The median, $21,000
With an extreme value ($178,000) the median isn't moved and best represents the typical case: the middle one in order is $21,000.
8. D. Only the mode
Flavours are categories (qualitative data): all you can do is see which comes most often, the mode.
9. D. Only the mode
Flavours are categories (qualitative data): all you can do is see which comes most often, the mode.
10. False
Mean 24.8, median 19: 5.8 km apart. An extreme value pulls the mean away from the median.
11. False
Mean 25.6, median 20: 5.6 km apart. An extreme value pulls the mean away from the median.
12. False
Mean 31.8, median 25: 6.8 km apart. An extreme value pulls the mean away from the median.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. B. The median, $620,000
With an extreme value, use the median: the middle one in order is $620,000.
14. 15,000 dollars
The mean is $29,000, the median (the 4th) $14,000: $15,000 apart, the owner's $116,000 pulling the mean up.
15. True
The old median is 44; for six days it is the mean of the 3rd and 4th, (44 + 44) ÷ 2 = 44. The extreme value only shifts the median's place.
16. B. S
Sizes are categories, so the mode: the one that sold most (29) is the answer.
17. 12,000 dollars
The mean is $29,000, the median (the 4th) $17,000: $12,000 apart, the owner's $106,000 pulling the mean up.
18. D. XL
Sizes are categories, so the mode: the one that sold most (35) is the answer.
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