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Statistics · 6.SP
Unit 6 Workbook — Statistics
Practice mean, median, mode, range, and the quartiles (Q1, Q3, IQR) — solve each problem here, check your answer, and reveal the steps.
Score: 0 / 18
🟢 Easy
E1 · Mean Find the mean (average) of the data: 4, 6, 8, 2.
💡 Hint
What two steps turn a whole list of values into one average?
Add them up: 4 + 6 + 8 + 2 = 20 → total
Divide by how many (4): 20 ÷ 4 → mean = total ÷ count
Mean = 5
Why: the mean shares the total out evenly — as if all four values were leveled to the same height.
E2 · Mode Find the mode (most common value): 3, 7, 7, 2, 5.
💡 Hint
Which value would you have to write down more than once?
Which value appears most often? → count repeats
7 appears twice; every other value appears once. → 7 is most common
Mode = 7
Why: the mode just reports the most frequent value, so it's the only average that also works for non-number data like favorite color.
E3 · Median Find the median (middle value): 9, 3, 6, 1, 8.
💡 Hint
What must you do to the list before you can pick its middle value?
Put them in order: 1, 3, 6, 8, 9 → always sort first
5 values → the middle one is the 3rd. → odd count
Median = 6
Why: once sorted, the median splits the data in half — as many values fall below it as above.
E4 · Range Find the range: 12, 5, 9, 20, 7. (range = max − min)
💡 Hint
Which two values — and only those two — does range depend on?
Largest = 20, smallest = 5 → find max and min
Range = 20 − 5 → max − min
Range = 15
Why: range captures the full width of the data in one number, but ignores everything between the extremes.
E5 · Mean Find the mean: 10, 10, 10, 10.
💡 Hint
If every value is the same, what could the average possibly be?
Sum = 40, count = 4 → 10 four times
40 ÷ 4 = 10 → all the same, so the mean is that value
Mean = 10
Why: when all values are identical, leveling them out changes nothing — so the mean is exactly that value.
E6 · Median (even) Find the median: 2, 4, 6, 8. (even count → average the two middle values)
💡 Hint
With four values there's no single middle — what do you do with the middle two?
Already in order: 2, 4, 6, 8 → 4 values, no single middle
Average the two middle ones: (4 + 6) ÷ 2 = 10 ÷ 2 → mean of 4 and 6
Median = 5
Why: the median lands exactly halfway between the two central values, so it need not be one of the data points.
🟡 Medium
M1 · Median (even) Find the median: 3, 5, 5, 7, 10, 12.
💡 Hint
After confirming the list is sorted, which two values straddle the center?
In order already: 3, 5, 5, 7, 10, 12 → 6 values
Two middle values are 5 and 7: (5 + 7) ÷ 2 = 12 ÷ 2 → average them
Median = 6
Why: averaging the middle pair places the median right between them — here, between 5 and 7.
M2 · Mean Find the mean: 4, 7, 9, 5. (answer as a decimal)
💡 Hint
Add everything first — then what number do you divide by?
Sum = 4 + 7 + 9 + 5 = 25 → total
25 ÷ 4 → divide by the 4 values
Mean = 6.25
Why: dividing the total by the count shares it equally, and the result can be a decimal — the mean needn't be a whole number.
M3 · Mode Find the mode: 8, 3, 8, 5, 8, 2.
💡 Hint
Which value appears more times than any other?
Count repeats: 8 appears three times. → more than any other
Mode = 8
Why: the mode is pure frequency counting — whichever value repeats most often wins, here 8 with three appearances.
M4 · Range Find the range: 14, 9, 21, 6, 18.
💡 Hint
Find the biggest and smallest values — then what do you do with them?
Max = 21, min = 6 → biggest and smallest
Range = 21 − 6 → max − min
Range = 15
Why: only the extremes matter for range; the in-between values don't change it at all.
M5 · Median (odd) Find the median: 11, 4, 7, 9, 2, 6, 8.
💡 Hint
What's the very first thing to do before you can locate the middle?
Sort: 2, 4, 6, 7, 8, 9, 11 → 7 values
The middle (4th) value is 7. → odd count
Median = 7
Why: sorting is essential — the median is about position in the ordered list, not the order the numbers were written.
M6 · Mean Find the mean: 6, 8, 10, 12, 14.
💡 Hint
Total them up, then divide by how many values there are.
Sum = 6 + 8 + 10 + 12 + 14 = 50 → total
50 ÷ 5 → 5 values
Mean = 10
Why: for an evenly spaced list, the mean lands right on the center value (10 here).
🔴 Hard
H1 · Q1 For the sorted data 2, 4, 5, 7, 8, 10, 12, 14, find the first quartile, Q1. (median of the lower half)
💡 Hint
Q1 is the median of which part of the data?
8 values → the median splits them into halves. → lower half: 2, 4, 5, 7
Q1 = median of 2, 4, 5, 7 = (4 + 5) ÷ 2 = 9 ÷ 2 → middle two of the lower half
Q1 = 4.5
Why: Q1 marks the boundary of the lowest quarter — it's simply the median of the bottom half of the data.
H2 · Q3 For the same data 2, 4, 5, 7, 8, 10, 12, 14, find the third quartile, Q3. (median of the upper half)
💡 Hint
Q3 is the median of which part of the data?
Upper half: 8, 10, 12, 14 → the top four values
Q3 = (10 + 12) ÷ 2 = 22 ÷ 2 → middle two of the upper half
Q3 = 11
Why: Q3 marks where the top quarter begins — it's the median of the upper half of the data.
H3 · IQR Using Q1 = 4.5 and Q3 = 11 from above, find the IQR (interquartile range). (IQR = Q3 − Q1)
💡 Hint
IQR measures the spread of the middle — which two values bound it, and what do you do with them?
IQR = Q3 − Q1 → spread of the middle 50%
IQR = 11 − 4.5 → subtract
IQR = 6.5
Why: subtracting Q1 from Q3 gives the width of the middle 50% of the data, ignoring extreme values at both ends.
H4 · Median (even) Find the median: 5, 9, 12, 3, 7, 15, 8, 10. (answer as a decimal)
💡 Hint
Sort first — then which two of the eight values sit in the middle?
Sort: 3, 5, 7, 8, 9, 10, 12, 15 → 8 values
Two middle values are 8 and 9: (8 + 9) ÷ 2 = 17 ÷ 2 → average them
Median = 8.5
Why: with 8 values the median is the average of the 4th and 5th, so always order the data before locating them.
H5 · Mean (decimals) Find the mean: 2.5, 3.5, 4, 6.
💡 Hint
Do decimals change the recipe for a mean at all?
Sum = 2.5 + 3.5 + 4 + 6 = 16 → total
16 ÷ 4 → 4 values
Mean = 4
Why: decimals follow the same rule as whole numbers — total them, then divide by the count.
H6 · IQR (odd count) For 1, 3, 5, 7, 9, 11, 13, find the IQR. (7 values: the median is 7 — leave it out of both halves)
💡 Hint
With 7 values, what happens to the median when you split the data into halves?
Median = 7 (the 4th value). → exclude it from the halves
Lower half: 1, 3, 5 → Q1 = 3 → middle of the lower half
Upper half: 9, 11, 13 → Q3 = 11 → middle of the upper half
IQR = Q3 − Q1 = 11 − 3 → subtract
IQR = 8
Why: with an odd count you leave the median out of both halves, so it belongs to neither quarter.
