Data and probability · Ages 14–15
Measures of central tendency worksheet
Covers: Mean, median and mode, Finding an unknown from an average, Averages of grouped data, Choosing the mean, median or mode, How changing the data changes the averages, Weighted mean, Weighted mean word problems
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Measures of central tendency 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.The stem-and-leaf diagram shows the ages (in years) of a hiking group's members. What is the median age?
Answer:
2.The four numbers 14, 20, x and 7 have a mean of 13. x =
Answer:
3.9 data have a mean of 22. One more is put in, and the mean of the 10 becomes 22 + 1. What was put in?
Answer:
4.The table is the cumulative frequency table of how many minutes 20 members of a gym spend on a workout (classes on the left, cumulative frequencies on the right). What is the estimated mean workout time, in minutes?
Answer:
5.Five flats have floor areas of 33, 96, 31, 36 and 34 m². By how many m² does the mean exceed the median?
Answer:
6.10 data have a mean of 27. Each value has 4 added, then is multiplied by 3. What is the new mean?
Answer:
7.A café's rating counts taste as 30% and service as 70%. It scores 87 for taste and 95 for service. What is its overall rating?
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8.In a dance troupe the numbers of men and women are in the ratio 3 : 2; the men's mean height is 152 cm and the women's 150 cm. What is the whole troupe's mean height, in cm?
Answer:
Part B: Choose, or true or false (2 marks each)
9.A website gained 20, 13, 21, 10, 18, 15 new members on six days. The mean of these data is greater than the median.
True or false?
Answer:
10.The table shows 25 families' grocery spending in a week ($, classes on the left, families on the right). The estimated mean spending is $47.
True or false?
Answer:
11.An ice-cream shop asked 155 customers for their favourite flavour. Which measure can describe the centre of these data?
- A. Any of the three
- B. Only the mode
- C. Only the median
- D. Only the mean
Choose the right answer
Answer:
12.6 data have a mean of 33. The value 31 is put in. What happens to the mean?
- A. It stays the same
- B. It can't be told
- C. It falls
- D. It rises
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.The table shows how many passengers each car in a car park carried (passengers on the left, cars on the right). What is the mode of the number of passengers?
Working:
Answer:
14.A dance troupe's 20 members have a mean weight of 65 kg. 4 members, with a mean weight of 53 kg, leave. What is the mean weight of the other 16, in kg?
Working:
Answer:
15.The table shows what each of 24 customers spent ($) at a snack shop one day (classes on the left, customers on the right). Using the class marks, about how many dollars did all the customers spend that day?
Working:
Answer:
16.Five flats in a block sold last month, for $730,000, $3,960,000, $820,000, $700,000 and $770,000, one of them a special penthouse. An estate agent wants a figure for a typical price. Which should it be?
- A. The mean of the highest and lowest, $2,330,000
- B. The top price, $3,960,000
- C. The mean, $1,396,000
- D. The median, $770,000
Choose the right answer
Working:
Answer:
17.A city's highest temperatures over 22 days average 18°C. Each day's is changed to Fahrenheit (°F = 1.8 × °C + 32). What is the mean in °F?
Working:
Answer:
18.Two hotels on a travel site: hotel A scores 67 for location and 79 for breakfast; hotel B 61 and 90. The site's overall score gives location a weight of 4 and breakfast 1. Which hotel has the higher overall score?
- A. Only the plain means can tell
- B. Hotel A
- C. Hotel B
- D. They are equal
Choose the right answer
Working:
Answer:
Show the answers and working
Measures of central tendency worksheet: Answers and working
Part A: Working out and filling in
1. 50.5 years
A stem-and-leaf diagram is already in order: count the 14 values, and the median sits at place (14 + 1) ÷ 2: 50.5.
2. 11
The sum = 13 × 4 = 52, so x = 52 − 14 − 20 − 7 = 11.
3. 32
The old sum is 9 × 22 = 198; the new 10 × (22 + 1) = 230; so 230 − 198 = 32 went in.
4. 42.25 minutes
First subtract neighbouring cumulative frequencies to get the frequencies back, 4, 3, 5, 4, 4; the class marks are 32, 37, 42, 47, 52: Σ(class mark × frequency) = 845, and 845 ÷ 20 = 42.25 minutes.
5. 12 m²
Mean 230 ÷ 5 = 46; the median is the middle one, 34; 12 m² apart: the very large 96 pulls the mean up.
6. 93
In order: adding 4 makes the mean 27 + 4 = 31; times 3: 31 × 3 = 93.
7. 92.6 points
The weights are percentages making 100%, so no dividing: 87 × 30% + 95 × 70% = 92.6.
8. 151.2 cm
The actual numbers aren't needed: the men are 3 parts and the women 2, so weight by the parts: (3 × 152 + 2 × 150) ÷ (3 + 2) = 756 ÷ 5 = 151.2 cm.
Part B: Choose, or true or false
9. False
Mean = 97 ÷ 6 = 976; in order, the median is the mean of the 3rd and 4th, 16.5.
10. False
With the class marks: Σ(class mark × frequency) ÷ 25 = 49.
11. B. Only the mode
Flavours are categories (qualitative data): all you can do is see which comes most often, the mode.
12. C. It falls
Compare 31 with the old mean 33: above it, the mean rises; below, it falls; equal, it stays.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 0
The mode is the value with the highest frequency: 12 cars carried 0 passengers.
14. 68 kg
The whole troupe 20 × 65 = 1300 kg, those leaving 4 × 53 = 212 kg: (1300 − 212) ÷ 16 = 68 kg.
15. 1768 dollars
Each class mark stands for every customer in its class: Σ(class mark × frequency) = $1,768.
16. D. The median, $770,000
With an extreme value, use the median: the middle one in order is $770,000.
17. 64.4°F
Every value is multiplied by 1.8 and has 32 added, so the mean too: 1.8 × 18 + 32 = 64.4.
18. B. Hotel A
A 69.4, B 66.8: location weighs more, so the better-placed hotel wins; the plain means would say the opposite.
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