Question

1. maximum mark: 6

the table shows the number of bicycles owned by 50 households.

number of bicycles per household	frequency number of households	cumulative frequency
1	7	10
2	12	22
3	14	36
4	4	40
5	t	w
6	2	50

a. write down the value of
i. t 1
ii. w 1
b. indicate with a tick (✔) whether the following statements are true or false. 4

statement	true	false
the median number of bicycles per household is 3
the 25th percentile is 1 bicycle per household
there are 10 households with at most 1 bicycle

Explanation:

Step1: Calculate t (sum to 50)

$t = 50 - (3+7+12+14+4+2) = 50 - 42 = 8$

Step2: Calculate w (cumulative frequency)

$w = 40 + t = 40 + 8 = 48$

Step3: Check statement 1

3 households have 0 bicycles, so "Every household owns at least 1 bicycle" is False.

Step4: Find median position

Median position: $\frac{50}{2} = 25$. The 25th value falls in the row with 3 bicycles (cumulative frequency 36 ≥25), so median is 3: True.

Step5: Find 25th percentile position

25th percentile position: $0.25 \times 50 = 12.5$. The 13th value falls in the row with 2 bicycles (cumulative frequency 22 ≥12.5), so 25th percentile is 2: statement is False.

Step6: Count households with ≤1 bicycle

Households with 0 or 1 bicycle: $3+7=10$, so statement is True.

Answer:

a.
i. $t = 8$
ii. $w = 48$

b.

Statement	True	False
The median number of bicycles per household is 3	✔️
The 25th percentile is 1 bicycle per household		✔️
There are 10 households with at most 1 bicycle	✔️