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Fluency · Pack B

7.6 Statistics

Answer each question. Show working where needed.

Bronze

  1. Find the mode of: 4, 6, 4, 8, 6, 4, 2. Justify by stating how many times it appears compared to all other values.

  2. Find the median of: 9, 3, 7, 1, 5. Explain what you had to do before finding the middle value and why.

  3. Three numbers have a mean of 6. Two of the numbers are 3 and 7. Find the third number and justify using the definition of mean.

  4. Find the range of: 20, 7, 15, 2, 11. Explain what the range tells us about the spread of the data.

  5. A bar chart shows books read: Fiction 20, Non-fiction 9, Comics 7. A student says "Fiction is more than double Non-fiction." Is this correct? Justify.

  6. A frequency table shows favourite colours: Red = 10, Blue = 7, Green = 9, Yellow = 4. (a) How many students were surveyed? (b) Is "favourite colour" categorical or numerical data? Justify.

  7. A shoe-size frequency table shows: Size 5: 6; Size 6: 11; Size 7: 4; Size 8: 1 students. State the mode and explain why it is called the modal size.

  8. Find the median of: 8, 2, 14, 6, 10, 4. Explain why you average the two middle values instead of picking just one.

  9. A pie chart shows how 40 students travel to school: Walking = 20, Bus = 12, Car = 8. What fraction walk? Justify that the fractions for all groups must add to 1.

  10. A bar chart is drawn for: Mon = 5, Tue = 10, Wed = 15, Thu = 5. A student wants the vertical axis to go up in steps of 3. Explain why this is a poor choice and suggest a better scale step. Justify.

Silver

  1. A frequency table shows scores out of 10: Score 5: 5 students; Score 7: 4 students; Score 9: 1 students. Find the mean score.

  2. Find the median of this data set: 22, 6, 18, 4, 30, 12, 8, 26, 14, 20, 10.

  3. Two classes sit a spelling test. Class A scores: 5, 7, 6, 8, 4. Class B scores: 2, 9, 8, 7, 4. Compare the means and ranges of the two classes.

  4. A survey of 40 people found 15 prefer comedy films. What angle (in degrees) should the comedy sector be in a pie chart?

  5. A two-way table shows student choices. Year 7: Swimming 12, Tennis 18, Total 30. Year 8: Swimming 15, Tennis 5, Total 20. How many students play tennis altogether?

  6. The mean of four numbers is 10. Three of them are 7, 12, 9. Find the fourth number.

  7. A pie chart for 48 students has a sector of 90° for "Football". How many students chose Football?

  8. For the data set 5, 2, 5, 8, 2, 5, 6, 8, find (a) the mode and (b) the median.

  9. Five plants are measured (cm): 8.2, 11.5, 9.8, 12.1, 10.4. Find the mean height, rounding to 1 decimal place.

  10. A bar chart shows daily visitors to a café over 5 days: Mon 30, Tue 70, Wed 60, Thu 50, Fri 40. Calculate the mean number of daily visitors.

Gold

  1. The mean of 6 test scores is 72. 5 of the scores are 60, 75, 80, 68, 73. Find the missing score.

  2. A pie chart has a sector of 72°. (a) What fraction of the data does it represent? (b) What percentage?

  3. Team A sprint times (s): 9.8, 10.4, 10.2, 9.6, 10.0. Team B sprint times (s): 8.9, 11.7, 10.3, 9.1, 10.0. Compare the two distributions using the mean and range.

  4. 8 friends share a total of 64 sweets equally. Then 24 more sweets are added and shared equally among the same group. How many sweets does each person have now?

  5. Eight students score: 2, 3, 3, 4, 4, 4, 5, 30. (a) Find the mean, median, and mode. (b) Which average best represents the data? Explain.

  6. A survey of 80 people found: Category A = 30, Category B = 20, Category C = 30. Calculate the angle for each sector to draw a pie chart.

  7. The mean of seven numbers is 15. Six of the numbers have a sum of 89. Write and solve an equation to find the seventh number.

  8. A pie chart shows that 45% of 80 students chose Science as their favourite subject. How many students is that?

  9. A company has 8 employees. The 2 managers each earn £90000; the remaining 6 staff each earn £15000. (a) Calculate the actual mean salary. (b) Explain why the mean might be misleading as a "typical" salary.

  10. A data set has 5 whole numbers. The mode is 4, the range is 10, and the mean is 6. Write one possible data set.

Platinum

  1. Five positive integers have mean 9, median 8, and range 10. List one possible set of numbers.

  2. Daily temperatures (°C) for one week: −4, 1, −2, 6, −5, 3, −1. Find the mean and range.

  3. A market stall records daily profit (+) or loss (−) in £ over 5 days: 60, −25, 40, −15, −10. Find the mean daily profit/loss.

  4. A student has sat 5 assessments with a current mean of 60. She wants her overall mean to be 65 after a total of 8 assessments. What total must she score across the remaining 3 assessments?

  5. Two archers each shoot 6 arrows. Archer A distances from bullseye (cm): 4, 6, 5, 7, 4, 4. Archer B: 1, 10, 2, 9, 1, 7. Compare using mean and range, and state which archer you would pick for a competition.

  6. A class of 50 students chose a sport. Results: Football = 20, Tennis = 10, Swimming = 15, Other = 5. Calculate the angle and percentage for each sector.

  7. The sum of 15 data values is 225. Without dividing, use prime factorisation to check whether the mean will be a whole number. Then calculate the mean.

  8. A pie chart shows how a school spends its budget of £150000. Teaching staff = 50%, Resources = 25%, Premises = 15%, Other = 10%. (a) Calculate the amount spent on each category. (b) What angle represents Premises in the pie chart?

  9. Lengths of 40 leaves are grouped: 0–4 cm: 8 leaves; 4–8 cm: 22 leaves; 8–12 cm: 10 leaves. Use midpoints to estimate the mean length.

  10. A data set is: $x$, 5, 11, $2x$, 9. The mean of the data set is 8. Form an equation and solve it to find $x$.