Question

(a) the grouped frequency table shows the number of houses on different streets.

number of houses	frequency
6 to 10	9
11 to 15	14
16 to 20	8
21 to 25	7

(i) how many streets have between 6 and 10 houses?
(ii) what is the most common number of houses on a street?
(iii) how many streets have 16 or more houses on them?
(iv) what was the total number of streets surveyed?
(c) the grouped frequency table shows the weight w of some dogs at a veterinary centre.

weight (kg)	frequency
5 < w ≤ 10	4
10 < w ≤ 15	15
15 < w ≤ 20	23
20 < w ≤ 25	5

(i) how many dogs weighed 10 kg or less?
(ii) how many dogs were weighed in total?
(iii) what fraction of the dogs weigh 15 kg to 20 kg?
(iv) dea says \over 50% of dogs weighed more than 15 kg.\ is she correct?

Explanation:

Step1: Find number of streets with 6 - 10 houses

Look at the frequency for the 6 - 10 houses group in the first table. The frequency is 9.

Step2: Find the most common number of houses

The group with the highest frequency in the first table is 11 - 15 with a frequency of 14. But we are asked for a single - value mode in a grouped data, which is not straightforward. However, if we consider the group with the highest frequency, we can say the most common group is 11 - 15.

Step3: Find number of streets with 16 or more houses

Add the frequencies of the 16 - 20 and 21 - 25 groups in the first table. $8 + 7=15$.

Step4: Find total number of streets surveyed

Add all the frequencies in the first table. $2+9 + 14+8+7=40$.

Step5: Find number of dogs weighing 10 kg or less

Add the frequencies of the $0\lt w\leq5$ and $5\lt w\leq10$ groups in the second table. $3 + 4=7$.

Step6: Find total number of dogs weighed

Add all the frequencies in the second table. $3+4 + 15+23+5=50$.

Step7: Find fraction of dogs weighing 15 - 20 kg

The frequency of dogs weighing 15 - 20 kg is 23. The fraction is $\frac{23}{50}$.

Step8: Check Dea's statement

The number of dogs weighing more than 15 kg is the sum of the frequencies of the $15\lt w\leq20$ and $20\lt w\leq25$ groups, which is $23 + 5=28$. The total number of dogs is 50. The percentage of dogs weighing more than 15 kg is $\frac{28}{50}\times100\% = 56\%$. So Dea is correct.

Answer:

(i) 9
(ii) The group 11 - 15 (highest - frequency group)
(iii) 15
(iv) 40
(c)(i) 7
(c)(ii) 50
(c)(iii) $\frac{23}{50}$
(c)(iv) Yes