# Question 1:

## Part (iii) - Histogram

| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequency density table: $125 \leq x \leq 140$: fd = 1.67; $140 < x \leq 145$: fd = 5.80; $145 < x \leq 150$: fd = 4.80; $150 < x \leq 160$: fd = 1.80; $160 < x \leq 170$: fd = 0.40 | M1 | For fd's - at least 3 correct. Accept any suitable unit for fd such as freq per cm. Correct to at least 1dp; allow 1.66 but not 1.6 for first fd. M1 can also be gained from freq per 10: 16.7, 58, 48, 18, 4 (at least 3 correct) or freq per 5: 8.35, 29, 24, 9, 2 for all correct |
| All fd's correct | A1 | If fd not explicitly given, M1A1 can be gained from all heights correct (within one square) on histogram |
| Linear scales on both axes and label on vertical axis | G1 | Label on vertical axis IN RELATION to first M1 mark, i.e. fd or frequency density or if relevant freq/10 etc (NOT eg fd/10). Allow scale given as $\text{fd} \times 10$ or similar. Accept f/w or f/cw. Can also be gained from an accurate key. G0 if correct label but not fd's |
| Width of bars | W1 | Must be drawn at 125, 140 etc NOT 124.5 or 125.5 etc. NO GAPS ALLOWED. Must have linear scale. No inequality labels on their own such as $125 \leq S < 140$ etc but allow if a clear horizontal linear scale is also given. Ignore horizontal label |
| Height of bars | H1 | Height of bars must be linear vertical scale. FT of heights dep on at least 3 heights correct and all must agree with their fds. If fds not given and at least 3 heights correct then max M1A0G1W1H0. Allow restart with correct heights if given fd wrong (for last three marks only) |
| **Total [5]** | | |

## Part (iv)

| Answer | Marks | Guidance |
|--------|-------|----------|
| 4 boys; $0.6 \times 15$ | M1 | For $0.6 \times 15$. Or $45 \times 0.2 = 9$ (number of squares and 0.2 per square) |
| $= 9$ girls | A1 | For 9 girls |
| So 5 more girls | A1 | cao |
| **Total [3]** | | |

## Part (v)

| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequencies and midpoints for girls: Height midpoints: 132.5, 142.5, 147.5, 155, 167.5; Frequencies: 18, 23, 31, 19, 9 | B1 | For at least three frequencies correct |
| Midpoints as above | B1 | At least three midpoints correct. No further marks if not using midpoints |
| $\text{mean} = \frac{(132.5 \times 18)+(142.5 \times 23)+(147.5 \times 31)+(155 \times 19)+(167.5 \times 9)}{100}$ | M1 | For attempt at $\sum xf$. For sight of at least 3 $xf$ pairs |
| $= \frac{2385 + 3277.5 + 4572.5 + 2945 + 1507.5}{100}$ | M1* dep on M1 | For division by 100 |
| $= 146.9$ (Exact answer 146.875) | A1 | Allow answer 146.9 or 147 but not 150. NB Accept answers seen without working (from calculator). Use of 'not quite right' midpoints such as 132.49 or 132.51 etc can get B1B0M1M1A0. NB Watch for over-specification |
| **Total [5]** | | |

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