## Answers

**Answer** :

Given data is :

Sample size n = 20

339 | 456 | 446 | 472 | 449 |

425 | 478 | 521 | 545 | 445 |

549 | 556 | 468 | 367 | 431 |

505 | 544 | 394 | 408 | 496 |

From the data we need to find the standard deviation S :

First find mean =

= [339 + 456 + 446 + 472 + 449 + ............ + 408 + 496] / 20

= 9294 / 20

= 464.7

** = 464.7**

**Standard deviation= S = **

**S = 61.355**

**Next we need to find interquartile range of data :**

**Take first 10 numbers :**

339 | 456 | 446 | 472 | 449 | 425 | 478 | 521 | 545 | 445 |

Sort this data into ascending order to find median :

339 | 425 | 445 | 446 | 449 | 456 | 472 | 478 | 521 | 545 |

Median of first 10 data numbers= = (449 + 456) / 2 = 905 / 2 = 452.5

** = 437**

Now take remaining 10 numbers :

549 | 556 | 468 | 367 | 431 | 505 | 544 | 394 | 408 | 496 |

We need to sort the above data to find the median :

367 | 394 | 408 | 431 | 468 | 496 | 505 | 544 | 544 | 549 |

Median of above 10 numbers = ( 468 + 496) / 2 = 964 / 2 = 482

is nothing but the median of all complete data.

Formula to calculate interquartile range of data is :

IQR = ** = 482 - 437 = 45**

**IQR = 45**

+ (408 - 464.7)2 + (496 - 464.7)2/20 - 1)