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STATISTICS: Cumulative Frequency

NAME: ………………………………………………………….

1. The grouped frequency table shows information about the number of hours spent travelling by each of 60 commuters in one week.

|Number of hours spent travelling (t) |Frequency |

|0 < t ≤ 5 |0 |

| 5 < t ≤ 10 |14 |

|10 < t ≤ 15 |21 |

|15 < t ≤ 20 |15 |

|20 < t ≤ 25 |7 |

|25 < t ≤ 30 |3 |

a) Write down the modal class interval.

……………………………………………………………………………………………………………………

………………………………………………………………………………………………………………[1]

b) Work out an estimate for the mean number of hours spent travelling by the commuters that week.

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

…………………………………………………………………………………………………………… [4]

c) Which class interval contains the median?

……………………………………………………………………………………………………………………

…………………………………………………………………………………………………………… [1]

d) Complete the cumulative frequency table.

|Number of hours spent travelling (t) |Cumulative |

| |Frequency |

|0 < t ≤ 5 |  |

| 0 < t ≤ 10 |  |

| 0 < t ≤ 15 |  |

| 0 < t ≤ 20 |  |

| 0 < t ≤ 25 |  |

| 0 < t ≤ 30 |  |

[1]

e) On the grid below, draw a cumulative frequency graph for the table.

[2]

(f) Use your graph to find an estimate for the median.

…………………………………………………………………………………………………hours. [1]

g) Use your graph to find an estimate for the interquartile range of the

number of hours spent travelling by the commuters that week.

Show your method clearly.

……………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………..

………………………………………………………………………………………………..hours. [3]

Name:……………………………………..

2. Bob carried out a survey on the number of hours spent on homework a week. He asked 100 students in his school.

His results are shown in the table below.

|Hours (t) |Frequency |  |Cumulative |

| | | |Frequency |

| 0 < t ≤ 2 | 3 |t ≤ 2 |  |

| 2 < t ≤ 4 | 7 |t ≤ 4 |  |

| 4 < t ≤ 6 | 13 |t ≤ 6 |  |

| 6 < t ≤ 8 | 25 |t ≤ 8 |  |

| 8 < t ≤ 10 | 32 | t ≤ 10 |  |

| 10 < t ≤ 12 | 12 | t ≤ 12 |  |

| 12 < t ≤ 14 | 6 | t ≤ 14 |  |

| 14 < t ≤ 16 | 2 | t ≤ 16 |  |

a) Complete the cumulative frequency table for the 100 students.

b) Draw the cumulative frequency diagram on the grid below.

(c) Use your graph to find the median time spent on homework by these 100 students.

……………………………………………………………………………………………………hours.

d) Use your graph to work out an estimate for the interquartile range.

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………hours.

(e) Use your graph to estimate how many of these 100 students did more than 9 hours homework in a week.

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………students.

3. 200 pupils sat an exam. The cumulative frequency curve shows the marks they obtained.

Use the graph to find:

(a) (i) the median mark. ……………………………………………………………………

ii) the lower quartile. ……………………………………..…………………………..

iii) the upper quartile. ………………………………………………………………….

iv) The interquartile range. ………………………………………………………...

(b) If the pass mark was 64 marks, estimate how many pupils passed.

……………………………………………………………………………………………………………………

Name:……………………………………………………….

4. The lifespans of 100 domestic cats were recorded. The results are shown in this table.

Lifespan (years) | ................
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