## Part (i)
**Answer:**
Median = 3.32 kg

Q1 (= 6.5th value) = 2.83  Q3 (= 19.5th value) = 3.71

Inter-quartile range = 3.71 – 2.83 = 0.88

**Marks:** B1 | B1 | B1 | [3]

**Guidance:**
- B1: For Q1 or Q3
- B1: For IQR dep on both quartiles correct
- B1: For reasonably linear scale shown
- For Q1 allow 2.82 to 2.84
- For Q3 allow 3.70 to 3.72
- If no quartiles given allow B0B1 for IQR in range 0.86 to 0.90
- Dep on attempt at box and whisker plot with at least a box and one whisker. Condone lack of label

## Part (ii)
[Box and whisker plot diagram]

**Marks:** G1 | G1 | G1 | G1 | [3]

**Guidance:**
- G1: For reasonably linear scale shown
- G1: For boxes in approximately correct positions, with median just to right of centre
- G1: For whiskers in approximately correct positions in proportion to the box
- G1: For labels. All correct labels for 'Hit' and 'Miss', 'H' and 'M' etc. Condone omission of First, Second, Third
- Do not award unless RH whisker significantly shorter than LH whisker. Allow LH whisker going to 2.5 and outlier marked at 1.39

## Part (iii)
**Answer:**
Lower limit: $2.83 - (1.5 \times 0.88) = 1.51$

Upper limit: $3.71 + (1.5 \times 0.88) = 5.03$

Exactly one baby weighs less than 1.51 kg and none weigh over 5.03 kg so there is exactly one outlier.

**Marks:** B1 | B1 | E1* | [4]

**Guidance:**
- B1: For 1.51 FT
- B1: For 5.03 FT
- E1*: Dep on their 1.51 and 5.03. Any use of median ± 1.5 × IQR scores B0 B0 E0. No marks for ± 2 or 3 × IQR. In this part FT their values from (i)or (ii) if sensibly obtained but not from location ie 6.5, 19.5. Do not penalise over-specification as not the final answer. Do not allow unless FT leads to upper limit above 4.34 and lower limit between 1.39 and 2.50

## Part (iv)
**Answer:**
Median = 3.5 kg

Q1 = 50th value = 3.12    Q3 = 150th value = 3.84

Inter-quartile range = 3.84 – 3.12 = 0.72

**Marks:** B1 | B1 | B1 | [3]

**Guidance:**
- B1: For Q1 or Q3
- B1: For IQR FT their quartiles
- B1: For reasonably linear scale shown
- For Q1 allow 3.11 to 3.13
- For Q3 allow 3.83 to 3.85
- Dep on both quartiles correct
- If no quartiles given allow B0B1 for IQR in range 0.70 to 0.74

## Part (v)
**Answer:**
Female babies have lower weight than male babies on the whole

Female babies have higher weight variation than male babies

**Marks:** E1 FT | E1 FT | [2]

**Guidance:**
- E1 FT: Allow 'on average' or similar in place of 'on the whole'
- E1 FT: Allow 'more spread' or similar but not 'higher range'. Condone less consistent
- Do not allow lower median, but SC1 for both lower median and higher IQR, making clear which is which

## Part (vi)
**Answer:**
Male babies must weigh more than 4.34 kg

Approx 10 male babies weigh more than this.

$$\text{Probability} = \frac{10}{200} \times \frac{9}{199} = \frac{90}{39800} = \frac{9}{3980} = 0.00226$$

Or:
$$\frac{9}{200} \times \frac{8}{199} = \frac{72}{39800} = 0.00181$$

Or:
$$\frac{8}{200} \times \frac{7}{199} = \frac{56}{39800} = \frac{7}{4975} = 0.00141$$

**Marks:** M1* | M1* dep | A1 | [3]

**Guidance:**
- M1*: For 10 or 9 or 8
- M1*: For first fraction multiplied by any other different fraction (Not a binomial probability)
- A1: CAO. Allow their answer to min of 2 sf. SC1 for n/200 × (n-1)/199

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