In the mean

of the tabulated data, if the frequencies of n observations

x_{1}, x_{2}, x_{3}, ………. x_{n} are f_{1}, f_{2}, f_{3} ………. f_{n}, then

**Mean of the tabulated data**

= (f_{1}x_{1} + f_{2}x_{2} + f_{3}x_{3} ……… f_{n}x_{n})/( f_{1} + f_{2} + f_{3} ………. f_{n}) = (∑ f_{i}x_{i})/(∑f_{i})

**Worked-out examples on mean
of the tabulated data:**

**1.**

Find the mean weight of 50 girls from the following table.

Weight in kg |
40 | 42 | 34 | 36 | 46 |

No. of girls |
6 | 6 | 15 | 14 | 7 |

**Solution:**

Mean = (f_{1}x_{1} + f_{2}x_{2} + f_{3}x_{3} + f_{4}x_{4} + f_{5}x_{5})/(f_{1} + f_{2} + f_{3} + f_{4} + f_{5})

= (40 × 6 + 42 × 6 + 34 × 15 + 36 × 14 + 46 × 7)/(8 + 6 + 15 + 14 + 7)

= (240 + 252 + 510 + 504 + 322)/50

= 1828/50

= 36.56

**2. **If the mean of the following frequency distributions is 9, find the value of `a’. Write the tally marks also.

Variable (x_{i}) |
4 | 6 | 8 | 10 | 12 | 15 |

Frequency (f_{i}) |
8 | 9 | 17 | a | 8 | 4 |

**Solution:**

Frequency distribution table

Mean = (∑f_{i}x_{i})/(∑f_{i})

But given mean = 9

So, we have (378 + 10a)/(46 + a) = 9

378 + 10a = 9(46 + a)

378 + 10a = 414 + 9a

10a – 9a = 414 – 378

a = 36

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