Question

Between being a housewife and caring for her family and aging parents, Ashley is a very busy lady. Below are the number of errands (trips to the grocery store, school events, pharmacy, doctor's office, etc.) which Ashley has run on each day in June.

Day	Number of errands
June 1	7
June 2	4
June 3	6
June 4	2
June 5	2
June 6	7
June 7	6
June 8	5
June 9	5
June 10	5
June 11	7
June 12	7
June 13	3
June 14	3
June 15	2
June 16	5
June 17	3
June 18	6
June 19	1
June 20	3
June 21	5
June 22	4
June 23	1
June 24	1
June 25	4
June 26	5
June 27	4
June 28	2
June 29	3
June 30	6

a. Calculate the mean for the above set of errands.

Round your answer to two decimal places.

Mean = ?????errands

b. Calculate the median for the above set of errands.

Round your answer to one decimal place.

Median = ????? errands

c.  What is the mode for the above set of errands?

Enter your answer as a whole number.

Mode = ???? errands

Answer 1

a. Mean = 4.13 errands

Let us denote Xi = number of errands where i = 1,2,..,30

Xi is the number of errands for i th June.

Now , Mean = Xi/n , n=30

i.e. mean =(7+4+6+2+2+7+6+5+5+5+7+7+3+3+2+5+3+6+1+3+5+4+1+1+4+5+4+2+3+6)/30

= 124/30 = 4.13

b. Median = 4.0 errands

To calculate Median we will rearrange the values of Xi in increasing order. Then we will find the middle most value of the data.the middle value will be the median.If n is odd then median is (n+1)/2 th value and if n is even then median will be the average of n/2 th data and (n/2 +1)th data.

Rearranging the data in increasing order

1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,6,6,7,7,7,7

Here n=30 ,even number. So median will be average of 15th and 16th element which are 4 and 4

i.e. Median =(4+4)/2= 4

c. Mode = 5 errands

Mode is the value which has the maximum frequency.that means the number which occurred maximum times.

Clearly from the data 5 has occurred maximum of 6 times. So for this data mode is 5.