Question

Question 1. The number of customers that bought a cup of coffee from a street coffee shop in a particular morning over a seven-day-period is as follows: 1 7 9 6 3 5 6 a. Find the mean, median and mode.

b. Estimate the values of the 1st and 3rd quartiles and determine the interquartile range.

c. Construct a box plot (note: make sure you indicate 5-number summary on the box plot).

d. On the basis of your results above, comment on the shape of this distribution.

Answer #1

Folloiwng is the ordered data set:

1, 3, 5, 6, 6, 7, 9

(a)

The mean is:

Theer are 7 data values so median will be 4th data value of the ordered data set. That is median is 6.

The mode is the data value with highest frequency. That is mode is 6.

(b)

First quartile: There are 7 data values so first half have 4 data values. That is first quartile will be average of 2nd and 3rd data values. So,

Third quartile:There are 7 data values so second half have 4 data values. That is third quartile will be average of 5th and 6th data values. So,

The interquartile range will be

(b)

The five number summary is :

Five number summary | |

Minimum | 1 |

First quartile | 4 |

Median | 6 |

Third quartile | 6.5 |

Maximum | 9 |

Following is the box plot:

(d)

Box plot is slightly skewed to left. It is not symmetric.

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