#### Question

Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years): | 16-18 | 18-20 | 20-22 | 22-24 | 24-26 |

Group A: | 50 | 78 | 46 | 28 | 23 |

Group B: | 54 | 89 | 40 | 25 | 17 |

#### Solution

Age (in years) |
Group ‘A’ |
Group ‘B’ |

16–18 | 50 | 54 |

18–20 | 78 | 89 |

20–22 | 46 | 40 |

22–24 | 28 | 25 |

24–25 | 23 | 17 |

For **group “A”**

The maximum frequency is 78 so the modal class is 18–20.

Therefore,

l = 18

h = 2

f = 78

f1 = 50

f2 = 46

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(78-50)/(156-50-46)xx2`

`=18+28/60xx2`

`=18+14/15`

= 18 + 0.93

= 18.93

For** group “B”**

The maximum frequency 89 so modal class 18–20.

Therefore,

l = 18

h = 2

f = 89

f1 = 54

f2 = 40

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(89-54)/(178-54-40)xx2`

`=18+35/84xx2`

`=18+35/42`

`=18+5/6`

= 18 + 0.83

= 18.83

Thus, the modal age of group A is 18.93 years whereas the modal age of group B is 18.83 years.

Is there an error in this question or solution?

#### APPEARS IN

Solution Compare the Modal Ages of Two Groups of Students Appearing for an Entrance Test: Concept: Mode of Grouped Data.