Mathematics
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Fluency · Pack A

7.6 Statistics

Answer each question. Show working where needed.

Bronze

  1. Find the mode of: 3, 7, 3, 9, 5, 3, 7. Justify by stating how many times it appears compared to all other values.

  2. Find the median of: 5, 2, 8, 1, 6. 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 4 and 10. Find the third number and justify using the definition of mean.

  4. Find the range of: 12, 5, 18, 9, 3. Explain what the range tells us about the spread of the data.

  5. A bar chart shows books read: Fiction 14, Non-fiction 9, Comics 5. A student says "Fiction is more than double Non-fiction." Is this correct? Justify.

  6. A frequency table shows favourite colours: Red = 8, Blue = 12, Green = 5, Yellow = 3. (a) How many students were surveyed? (b) Is "favourite colour" categorical or numerical data? Justify.

  7. A shoe-size frequency table shows: Size 4: 3; Size 5: 8; Size 6: 5; Size 7: 2 students. State the mode and explain why it is called the modal size.

  8. Find the median of: 3, 11, 7, 1, 9, 5. Explain why you average the two middle values instead of picking just one.

  9. A pie chart shows how 30 students travel to school: Walking = 10, Bus = 15, Car = 5. What fraction walk? Justify that the fractions for all groups must add to 1.

  10. A bar chart is drawn for: Mon = 4, Tue = 6, Wed = 2, Thu = 8. 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 6: 4 students; Score 8: 3 students; Score 10: 3 students. Find the mean score.

  2. Find the median of this data set: 14, 3, 21, 9, 17, 5, 11, 8, 25, 13, 7.

  3. Two classes sit a spelling test. Class A scores: 6, 8, 7, 9, 5. Class B scores: 4, 10, 6, 9, 1. Compare the means and ranges of the two classes.

  4. A survey of 30 people found 10 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 14, Tennis 11, Total 25. Year 8: Swimming 9, Tennis 16, Total 25. How many students play tennis altogether?

  6. The mean of four numbers is 8. Three of them are 5, 9, 6. Find the fourth number.

  7. A pie chart for 36 students has a sector of 120° for "Football". How many students chose Football?

  8. For the data set 4, 7, 4, 9, 4, 7, 3, 9, find (a) the mode and (b) the median.

  9. Five plants are measured (cm): 12.4, 9.7, 11.3, 10.6, 13.5. Find the mean height, rounding to 1 decimal place.

  10. A bar chart shows daily visitors to a café over 5 days: Mon 40, Tue 55, Wed 50, Thu 45, Fri 60. Calculate the mean number of daily visitors.

Gold

  1. The mean of 5 test scores is 78. 4 of the scores are 65, 80, 70, 90. Find the missing score.

  2. A pie chart has a sector of 90°. (a) What fraction of the data does it represent? (b) What percentage?

  3. Team A sprint times (s): 11.2, 12.4, 11.8, 13.0, 11.6. Team B sprint times (s): 10.5, 14.1, 11.9, 12.5, 11.0. Compare the two distributions using the mean and range.

  4. 6 friends share a total of 48 sweets equally. Then 12 more sweets are added and shared equally among the same group. How many sweets does each person have now?

  5. Eight students score: 5, 6, 6, 7, 7, 7, 8, 40. (a) Find the mean, median, and mode. (b) Which average best represents the data? Explain.

  6. A survey of 60 people found: Category A = 20, Category B = 25, Category C = 15. Calculate the angle for each sector to draw a pie chart.

  7. The mean of seven numbers is 12. Six of the numbers have a sum of 74. Write and solve an equation to find the seventh number.

  8. A pie chart shows that 35% of 60 students chose Science as their favourite subject. How many students is that?

  9. A company has 10 employees. The 2 managers each earn £100000; the remaining 8 staff each earn £20000. (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 6, the range is 8, and the mean is 7. Write one possible data set.

Platinum

  1. Five positive integers have mean 11, median 10, and range 6. List one possible set of numbers.

  2. Daily temperatures (°C) for one week: 3, −2, 0, 4, −1, 5, −3. Find the mean and range.

  3. A market stall records daily profit (+) or loss (−) in £ over 5 days: 35, −12, 48, −20, 9. Find the mean daily profit/loss.

  4. A student has sat 4 assessments with a current mean of 65. She wants her overall mean to be 70 after a total of 6 assessments. What total must she score across the remaining 2 assessments?

  5. Two archers each shoot 6 arrows. Archer A distances from bullseye (cm): 3, 5, 4, 6, 3, 3. Archer B: 2, 8, 1, 9, 2, 8. Compare using mean and range, and state which archer you would pick for a competition.

  6. A class of 40 students chose a sport. Results: Football = 16, Tennis = 8, Swimming = 10, Other = 6. Calculate the angle and percentage for each sector.

  7. The sum of 12 data values is 156. 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 £200000. Teaching staff = 60%, Resources = 20%, Premises = 15%, Other = 5%. (a) Calculate the amount spent on each category. (b) What angle represents Premises in the pie chart?

  9. Lengths of 30 leaves are grouped: 1–3 cm: 6 leaves; 3–5 cm: 14 leaves; 5–7 cm: 10 leaves. Use midpoints to estimate the mean length.

  10. A data set is: $x$, 8, 14, $2x$, 6. The mean of the data set is 11. Form an equation and solve it to find $x$.