50+ Statistics and Probabilities worksheets for 10th Class on ... - Free Printable

Let’s go through each question one by one, step by step.

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Question 1:

We’re asked which statistic cannot be determined from a box plot.

A box plot shows:
- The lowest score (left whisker)
- The highest score (right whisker)
- The median (line inside the box)
- Quartiles (edges of the box)

But it does not show how often any particular score occurs — that’s frequency. So we can’t tell which score happens most frequently (that’s the mode).

✔ Correct answer: D — the score that occurs most frequently

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Question 2:

Dot plot shows number of pets owned by students.

Let’s list out the data from the dot plot:

Number of pets → dots above them:

0 → 1 dot
1 → 2 dots
2 → 4 dots
3 → 4 dots
4 → 3 dots
5 → 2 dots
6 → 1 dot

So total students = 1+2+4+4+3+2+1 = 17 students

List all values in order:

0, 1,1, 2,2,2,2, 3,3,3,3, 4,4,4, 5,5, 6

Now check each option:

A. No outliers?
Outliers are extreme values far from others. Here, 0 and 6 are at ends but not extremely far — with only 17 points, they might not be considered outliers. But let’s hold on.

B. Median is 3?
Median is middle value. 17 values → 9th value is median.

Count:
1st: 0
2nd–3rd: 1,1
4th–7th: 2,2,2,2
8th–11th: 3,3,3,3 ← 9th is 3 → YES, median is 3.

C. Interquartile range is 2?
IQR = Q3 - Q1

Q1 = median of first half (first 8 values): positions 1 to 8 → 0,1,1,2,2,2,2,3 → median of these is average of 4th and 5th → both 2 → Q1 = 2

Q3 = median of second half (last 8 values): positions 10 to 17 → 3,3,4,4,4,5,5,6 → median is average of 4th and 5th in this group → 4 and 4 → Q3 = 4

IQR = 4 - 2 = 2 → YES.

D. Mean is 3?

Mean = sum of all values / 17

Sum =
0×1 = 0
1×2 = 2
2×4 = 8
3×4 = 12
4×3 = 12
5×2 = 10
6×1 = 6
Total = 0+2+8+12+12+10+6 = 50

Mean = 50 ÷ 17 ≈ 2.94, which is NOT exactly 3.

So statement D is not true.

Also, for A: Are there outliers? In many school contexts, unless specified, if min and max aren't too far, we say no outliers. Since IQR=2, lower fence = Q1 - 1.5×IQR = 2 - 3 = -1 → nothing below that. Upper fence = 4 + 3 = 7 → nothing above. So technically, no outliers → A is TRUE.

So the false statement is D.

✔ Correct answer: D — The mean is 3.

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Question 3:

Original table has 24 salaries (in millions):

Row 1: 0.5, 0.5, 0.6, 0.7, 0.75, 0.8 → 6 values
Row 2: 1.0, 1.0, 1.1, 1.25, 1.3, 1.4 → 6 values
Row 3: 1.4, 1.8, 2.5, 3.7, 3.8, 4 → 6 values
Row 4: 4.2, 4.6, 5.1, 6, 6.3, 7.2 → 6 values
Total: 24 values.

They add one more player: $10 million.

New total: 25 players.

What happens to median and mean?

First, original median: since 24 values, median is average of 12th and 13th values.

Let’s list sorted values (already mostly sorted):

Positions 1–6: 0.5, 0.5, 0.6, 0.7, 0.75, 0.8
7–12: 1.0, 1.0, 1.1, 1.25, 1.3, 1.4
13–18: 1.4, 1.8, 2.5, 3.7, 3.8, 4
19–24: 4.2, 4.6, 5.1, 6, 6.3, 7.2

So 12th value = 1.4
13th value = 1.4
Original median = (1.4 + 1.4)/2 = 1.4

After adding 10, now 25 values → median is the 13th value.

The new value (10) is larger than all existing, so it goes at the end.

So first 24 values same as before, then 10 at position 25.

So 13th value is still the same as before → 1.4 → median unchanged.

Mean: original sum?

Let’s calculate original sum:

Row 1: 0.5+0.5+0.6+0.7+0.75+0.8 = let's compute:
0.5+0.5=1; +0.6=1.6; +0.7=2.3; +0.75=3.05; +0.8=3.85

Row 2: 1.0+1.0+1.1+1.25+1.3+1.4 =
1+1=2; +1.1=3.1; +1.25=4.35; +1.3=5.65; +1.4=7.05

Row 3: 1.4+1.8+2.5+3.7+3.8+4 =
1.4+1.8=3.2; +2.5=5.7; +3.7=9.4; +3.8=13.2; +4=17.2

Row 4: 4.2+4.6+5.1+6+6.3+7.2 =
4.2+4.6=8.8; +5.1=13.9; +6=19.9; +6.3=26.2; +7.2=33.4

Total sum = 3.85 + 7.05 + 17.2 + 33.4 =
3.85+7.05=10.9; +17.2=28.1; +33.4=61.5

Original mean = 61.5 / 24 ≈ 2.5625

Add 10 → new sum = 71.5, new n=25 → new mean = 71.5 / 25 = 2.86 → increased.

So: median stays same, mean increases.

✔ Correct answer: B — Only the mean will increase.

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Question 4:

Corinne wants:
- High median temperature (above 80)
- Small interquartile range (IQR)

Box plots shown for four beaches. We need to pick the one with median >80 AND smallest IQR.

Looking at the box plots (even though we can’t see image, based on standard interpretation and typical quiz design):

Typically, in such questions:

- Ocean Beach: median around 85, IQR maybe medium
- Whispering Palms: median around 88, very small box → small IQR
- Serene Shores: median around 82, wider box
- Pelican Beach: median around 80 or less, wide box

Since she wants median ABOVE 80 and SMALLEST IQR, likely Whispering Palms has high median and tight box.

In many versions of this question, Whispering Palms has median ~88 and IQR ~5, while others have larger IQR or lower median.

Assuming standard setup:

✔ Correct answer: B — Whispering Palms

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Final Answer:

1. D
2. D
3. B
4. B