Exercises : Data description

1. The following set of data shows the age, in year, of buildings of 10 schools in town.

38        17        43        m         40        33        10        n          74        31

            

    The mean age of the buildings is 37.3 years.        

   a)   If the mode for the age of the buildings is 31 years, determine the values of m and n such     that m < n.                                                                                    

(3 marks)

   b)    Based on the values of m and n obtained in (a),      
        i. Find the median for the age of the buildings.

                              ii. Calculate the standard deviation for the age of the buildings.                             (3 marks)

     2.    In a study, the lifespan of 100 halogen lamps manufactured by a factory is recorded in     the following table.

Lifespan (day)	Frequency
1 - 10	2
11 - 20	6
21 - 30	8
31 - 40	10
41 – 50	15
51 – 60	25
61 - 70	21
71 – 80	9
81 – 90	4

a)    Determine the mean, mode and median for the lifespan of the halogen lamps.

(6 marks)

b)    Find the third quartile for the liespan of the halogen lamps.                            

(3 marks)

   3.    The following set of data shows the width, in mm, of 10 books that are acquired by a              library.

171     190     183     169     p     188     152     q     208     183

   Given that the mean width of the books is 182.4 mm.

a)    If p – q=30, determine the values of p and q. hence, calculate the standard deviation or the width of the books.                                                

(4 marks)

b)    If p=135, determine the median width of the books.                       

(2 marks) 

   4.    Wahab made 108 telephone calls in the month of January. The duration of ach call is recorded in the following frequency table.

Duration(minute)	Frequency
1 – 3	7
4 – 6	16
7 – 9	35
10 – 12	33
13 – 15	15
16  – 18	2

      a)    Calculate the mean, median and standard deviation for the duration of telephone    calls.                                                                                                             

(6 marks)

    

      b)    Calculate

              i.        the third quartile for the duration of the telephone calls

            ii.        the percentage of the telephone calls with duration greater than 13.8 minutes

           iii.        the 20^th percentile for the duration of telephone calls                    

(9 marks)

   5.    The following set of data shows the age,in month, of 8 babies taking part in a photograph      contest organized by an emporium.

12        9          14        10        8          14        9          14

   a)    Determine the mean, median and mode for the age of babies.          

(4 marks)

   b)    Calculate the standard deviation for the age of babies.          

(2marks)

 ANSWERS :

      1 a)  m=31, n=56

         b) i. 35.5 ii.18.23
                                                                                                                              

           2 a)  \Mean=51.3

        Mode=57.46

        Median=54.1
    b) Q₃ =64.79

3  a)    p=175, q=205

    standard deviation=16.81

    b)    median=184

4 a)    mean=9.08, median=9.157, standard deviation=3.44
   b)    i. 11.59

        ii.percentage=9.72

        iii.6.238

5 a)    Mean=11.25, median=11, mode=14
   b)    Standard deviation=2.55