Question

to the nearest tenth.

dot plot: number line 1–10, dots at 2 (1), 3 (2), 4 (3), 5 (4), 6 (3), 7 (2), 8 (1)

1. what is the mean of the data? ______
2. what is the median of the data? ______
3. circle the data values that fall within the mean absolute deviation.
4. which statements describe the distribution of the data in the box plot?

select all that apply.

box plot: number line 0–20 labeled \pairs of pants owned\

a) of the people surveyed, ( \frac{1}{2} ) own 7 to 13 pairs of pants.
b) of the people surveyed, ( \frac{1}{4} ) own 3 to 10 pairs of pants.
c) of the people surveyed, ( \frac{1}{2} ) own 13 to 18 pairs of pants.
d) of the people surveyed, ( \frac{1}{4} ) own 3 to 7 pairs of pants.
e) of the people surveyed, ( \frac{3}{4} ) own 10 to 18 pairs of pants.

twin model rocket desi

Explanation:

Question 13: Mean of the data

First, we count the number of data points (dots) at each value:

• At 2: 1 dot
• At 3: 2 dots
• At 4: 3 dots
• At 5: 4 dots
• At 6: 3 dots
• At 7: 2 dots
• At 8: 1 dot

Now, calculate the sum of (value × frequency):
$$(2×1) + (3×2) + (4×3) + (5×4) + (6×3) + (7×2) + (8×1)$$
$$= 2 + 6 + 12 + 20 + 18 + 14 + 8$$
$$= 80$$

Total number of data points: \(1 + 2 + 3 + 4 + 3 + 2 + 1 = 16\)

Mean = \(\frac{\text{Total Sum}}{\text{Number of Data Points}} = \frac{80}{16} = 5\)

Question 14: Median of the data

There are 16 data points (even number). The median is the average of the 8th and 9th values when sorted.

Sort the data by value (with frequencies):

• 2 (1), 3 (2), 4 (3), 5 (4), 6 (3), 7 (2), 8 (1)

Cumulative frequencies:

• After 2: 1
• After 3: \(1 + 2 = 3\)
• After 4: \(3 + 3 = 6\)
• After 5: \(6 + 4 = 10\)

The 8th and 9th values both fall in the "5" group (since cumulative frequency at 4 is 6, so 7th, 8th, 9th, 10th are 5). Thus, median = \(\frac{5 + 5}{2} = 5\)

Question 15: Mean Absolute Deviation (MAD)

First, calculate the deviation of each value from the mean (mean = 5):

• For 2: \(|2 - 5| = 3\), frequency 1: total deviation = \(3×1 = 3\)
• For 3: \(|3 - 5| = 2\), frequency 2: total deviation = \(2×2 = 4\)
• For 4: \(|4 - 5| = 1\), frequency 3: total deviation = \(1×3 = 3\)
• For 5: \(|5 - 5| = 0\), frequency 4: total deviation = \(0×4 = 0\)
• For 6: \(|6 - 5| = 1\), frequency 3: total deviation = \(1×3 = 3\)
• For 7: \(|7 - 5| = 2\), frequency 2: total deviation = \(2×2 = 4\)
• For 8: \(|8 - 5| = 3\), frequency 1: total deviation = \(3×1 = 3\)

Total absolute deviation: \(3 + 4 + 3 + 0 + 3 + 4 + 3 = 20\)

MAD = \(\frac{\text{Total Absolute Deviation}}{\text{Number of Data Points}} = \frac{20}{16} = 1.25\)

Values within \( \text{mean} \pm \text{MAD} \) (i.e., \(5 - 1.25 = 3.75\) to \(5 + 1.25 = 6.25\)):

• Values: 4, 5, 6 (since 3.75 ≤ 4, 5, 6 ≤ 6.25)
• Circle the dots at 4, 5, 6.

Question 16: Box Plot Interpretation

A box plot shows:

• Minimum (left whisker start)
• Q1 (25th percentile, left box edge)
• Median (line in box)
• Q3 (75th percentile, right box edge)
• Maximum (right whisker end)

From the plot:

• Minimum: ~3
• Q1: 7
• Median: 10
• Q3: 13
• Maximum: ~18

Interpret each option:

• A: \( \frac{1}{2} \) (50%) own 7–13 pairs. The box (Q1 to Q3) represents 50% of data. Q1=7, Q3=13 → Correct.
• B: \( \frac{1}{4} \) (25%) own 3–10 pairs. Q1=7, so 3–7 is left whisker (25%), 7–10 is part of the box. Incorrect.
• C: \( \frac{1}{2} \) own 13–18. The right whisker (Q3 to Max) is 25% (not 50%). Incorrect.
• D: \( \frac{1}{4} \) (25%) own 3–7 pairs. Left whisker (Min to Q1) is 25% (Min~3, Q1=7) → Correct.
• E: \( \frac{3}{4} \) own 10–18. Q2 (median) to Max: 50% (not 75%). Incorrect.

Answer:

s

1. \(\boldsymbol{5}\)
2. \(\boldsymbol{5}\)
3. Circle data values 4, 5, 6 (dots at 4, 5, 6).
4. Correct options: \(\boldsymbol{A, D}\)