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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Statistics

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Find the mean of the data: $4, 6, 8, 10, 12.
     
  2. 2.
    Find the median of: $3, 6, 10, 14, 18.
     
  3. 3.
    Find the median of: $5, 8, 12, 15.
     
  4. 4.
    Find the mode of: $5, 7, 7, 8, 9, 7, 10.
     
  5. 5.
    Find the range of: $14, 22, 8, 18, 25, 10.
     
  6. 6.
    Find the mean of: $6, 9, 12, 15, 18.
     
  7. 7.
    Find the mode and the range of: $7, 7, 9, 10, 14.
     
  8. 8.
    A boxplot has lower quartile 12, median 18, and upper quartile 24. State (a) the IQR and (b) the median.
     
  9. 9.
    A stem-and-leaf plot shows 1 ∣ 2  5  91\,|\,2\;5\;9 and 2 ∣ 1  4  6  72\,|\,1\;4\;6\;7. How many values are there?
     
  10. 10.
    In a frequency table, value xx has frequency 2; value 3 has frequency 5; value 5 has frequency 3. Total frequency 10. Mean: x=?x = ? given mean is 4. (Find xx.)
     
SilverQuestions 11–20
  1. 11.
    Find the mean of: $1(4), 3(3), 5(3) (where format is "value(frequency)").
     
  2. 12.
    A data set has 25 values. What is the median position?
     
  3. 13.
    For the ordered data 3,5,8,9,11,13,15,17,20,find3, 5, 8, 9, 11, 13, 15, 17, 20, findQ_1andandQ_3$.
     
  4. 14.
    A data set has Q1=22Q_1 = 22 and Q3=41Q_3 = 41. Find the IQR.
     
  5. 15.
    For the data 2,4,5,7,9,11,12,15,18,findmin,2, 4, 5, 7, 9, 11, 12, 15, 18, find min,Q_1,median,, median,Q_3$, max.
     
  6. 16.
    Two boxplots are shown. Boxplot A: median 18, IQR 10. Boxplot B: median 22, IQR 6. Which group has more consistent values?
     
  7. 17.
    A test was sat by 20 students. Scores: 1(2), 2(5), 3(8), 4(3), 5(2). Find the mean.
     
  8. 18.
    From the frequency table, state the modal value: 1(4), 2(7), 3(10), 4(5), 5(4).
     
  9. 19.
    A data set {3,5,7,x,11}\{3, 5, 7, x, 11\} has mean 88. Find xx.
     
  10. 20.
    A boxplot has whiskers from 0 to 50, Q1=10Q_1 = 10, median 15, Q3=22Q_3 = 22. Is the distribution symmetric or skewed?
     
GoldQuestions 21–30
  1. 21.
    A cumulative frequency curve for 100 students has cf = 25 at score 12, cf = 50 at score 18, cf = 75 at score 23. State Q1Q_1, median, Q3Q_3.
     
  2. 22.
    For the cumulative frequency data: Q1=25Q_1 = 25, Q3=48Q_3 = 48. Find the IQR.
     
  3. 23.
    A grouped frequency table has: [0,10)[0, 10) freq 4; [10,20)[10, 20) freq 8; [20,30)[20, 30) freq 6; [30,40)[30, 40) freq 2. Estimate the mean.
     
  4. 24.
    A boxplot has Q1=20Q_1 = 20, Q3=40Q_3 = 40. Using the 1.5×IQR rule, determine if 75 is an outlier.
     
  5. 25.
    Group A has median 25, IQR 10. Group B has median 25, IQR 20. Compare the spreads.
     
  6. 26.
    From the cumulative frequency curve: at score = 30, cf = 75; at score = 40, cf = 95. How many students scored between 30 and 40?
     
  7. 27.
    A grouped table has total frequency 60, with cumulative frequencies at class boundaries: 8, 22, 45, 60. The median is in which class?
     
  8. 28.
    A data set has values 1, 2, 3, 4 with frequencies 4, xx, 6, 3. The mean is 2.5. Find xx.
     
  9. 29.
    A boxplot shows min 5, Q1Q_1 12, median 20, Q3Q_3 28, max 35. What percentage of data lies above Q3Q_3?
     
  10. 30.
    A data set has n=40n = 40 values with mean 22.522.5. Find the sum.
     
PlatinumQuestions 31–40
  1. 31.
    Class A has 25 students with mean test score 60. Class B has 15 students with mean 72. Find the combined mean.
     
  2. 32.
    Six values are {12,15,17,x,22,25}\{12, 15, 17, x, 22, 25\}. The median is 19. Find xx.
     
  3. 33.
    A cumulative frequency table on 200 values shows cf = 80 at score 50, cf = 120 at score 70. Estimate the score for the 60th percentile.
     
  4. 34.
    Group A: min 5, Q1Q_1 12, median 18, Q3Q_3 25, max 35. Group B: min 8, Q1Q_1 18, median 22, Q3Q_3 28, max 38. Make two comparisons.
     
  5. 35.
    A data set has Q1=15Q_1 = 15, Q3=35Q_3 = 35. Identify values from {3,10,22,50,70}\{3, 10, 22, 50, 70\} that are outliers.
     
  6. 36.
    In a test, the mean of 20 students is 72. After re-marking, two scores increased by 5 each. What is the new mean?
     
  7. 37.
    Grouped data: [0,10)[0, 10) freq 5; [10,20)[10, 20) freq 12; [20,30)[20, 30) freq 8; [30,50)[30, 50) freq 5. State the modal class and explain why frequency density matters here.
     
  8. 38.
    Two data sets both have mean 10. Set A has range 4; Set B has range 20. Which is more spread out?
     
  9. 39.
    A class of 1919 students has mean test score 7070. A new student joins with score 5050. Find the new mean (1 d.p.).
     
  10. 40.
    Five integers have mean 5, median 5, and mode 7. State a possible set of integers.