# Exam-style Questions: Representation of Data

**1.** The following raw data was obtained from the ages of 31 people asked in a cinema one Saturday afternoon

21 17 24 23 43 42 14 51 22 18 17

15 16 23 33 21 12 13 34 22 15

12 17 22 28 29 32 38 12 11 8

**a)** By drawing a stem-and-leaf diagram find the median age of cinema goers, and the inter-quartile range.

**b)** Using the answers obtained in part a) draw a boxplot of the ages of cinema goers that afternoon and comment on the shape of the distribution, i.e. do you think there is any skew to the distribution?

**c)** Are there any 'outliers' in this distribution. Use the rule that an 'outlier' is a value more than 1.5 times of the inter-quartile range from either quartile.

**Answer outline and marking scheme for question: 1**

**1. a)** see ans sheet 1

the median is 16^{th} value = 21

upper quartile = 29

lower quartile = 15

inter-quartile range = 29 - 15 = 14

**b)** see ans sheet 1

there appears to be a slight positive skew to the distribution.

**c)** inter-quartile range = 14 so 14 x 1.5 = 21

do we have any values that lie 21 away from either quartile?

Upper end 29 + 21 = 50

Lower end 8 - 21 = -13

Hence 1 outlier the value of 51

**2.** 30 students were asked to attempt a maths problem. The time it took them to complete

the problem (to the nearest second) is given in the table.

Time (secs) | Frequency |
---|---|

0 = t < 10 | 3 |

10 = t < 15 | 7 |

15 = t < 20 | 10 |

20 = t < 30 | 6 |

30 = t < 50 | 4 |

**a)** explain why representing this data on a histogram is appropriate.

**b)** represent the data on a histogram.

**(Marks available: 5)**

**Answer outline and marking scheme for question: 2**

**a)** the data is continuous and we have been given unequal class intervals

**b)**

Time (secs) | Frequency | Class Width | Frequency density |
---|---|---|---|

0 = t < 10 | 3 | 10 |
0.3 |

10 = t < 15 | 7 | 5 |
1.4 |

15 = t < 20 | 10 | 5 |
2 |

20 = t < 30 | 6 | 10 |
0.6 |

30 = t < 50 | 4 | 20 |
0.2 |