13. Find the mean, mode and median for the following data:

according to given observation:

class interval (CI) | frequency f | cumulative frequency | midpoint of CI (x) | fx |

0-10 | 5 | 5 | 5 | 25 |

10-20 | 8 | 13 | 15 | 120 |

20-30 | 15 | 28 | 25 | 375 |

30-40 | 20 | 48 | 35 | 700 |

40-50 | 14 | 62 | 45 | 630 |

50-60 | 8 | 70 | 55 | 440 |

60-70 | 5 | 75 | 65 | 325 |

75 | 2615 |

mean =

to find the median : we will apply the formula ;

median =

75/ 2 = 37.5.

this lies in the interval 30-40.

i = size of the class interval

L = lower limit of the CI which includes the median score.

F = cumulative frequency up to median CI

f = frequency in the class interval that contains the median.

therefore L = 30 ; F = 28 ; f = 20 ; i =10

thus median =

mode =

where

L = lower class boundary of modal class

the frequency of the modal class

previous frequency of the modal class

the next frequency of the modal class

i = size of the modal class

modal class is the class with maximum frequency

from the observation: maximum frequency = 20.

modal class = 30-40

L = 30 ; 20 ; 15 and 14 ; i = 10

mode =

= 30 + (5/11)

= 30 + 0.4545

= 30.4545

hope this helps you.

cheers!!

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