4MA0 Foundation June 2016 Paper 1 Q11
11 The table shows information about the number of visits each of 40 adults made to the gym last week.
| Number of visits to the gym | Frequency |
|---|---|
| 0 | 4 |
| 1 | 3 |
| 2 | 12 |
| 3 | 5 |
| 4 | 8 |
| 5 | 5 |
| 6 | 2 |
| 7 | 1 |
(a) Write down the mode of the number of visits to the gym. (1)
(b) Find the median of the number of visits to the gym. (2)
(c) Work out the mean of the number of visits to the gym. (3)
One of these adults is chosen at random.
(d) Write down the probability that this adult made more than 5 visits to the gym last week. (2)
| Scheme | Marks |
|---|---|
| 2 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (40 + 1) ÷ 2 (=20.5th) or 40 ÷ 2 (=20th) | M1 |
| 3 | A1 |
| (2) |
Notes
M1: or evidence of correct working by table or listing numbers to find median
| Scheme | Marks |
|---|---|
| 0×4 + 1×3 + 2×12 + 3×5 + 4×8 + 5×5 + 6×2 + 7×1 or (0) + 3 + 24 + 15 + 32 + 25 + 12 + 7 (=118) | M1 |
| “118” ÷ “40” | M1 |
| 2.95 | A1 |
| (3) |
Notes
M1: condone one error
M1: dep
NB. Allow a value other than 40 provided it has clearly come from the sum of the frequency column
A1: Accept 3 from 118 ÷ 40
SC: B2 for 3.05
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{40}\) oe | B2 |
| (2) |
Notes
B2: Award B1 for \(\dfrac{a}{40}\) with \(a \lt 40\) or \(\dfrac{3}{b}\) with \(b \gt 3\)