Question

) A sample of 77 individuals working at a particular office was selected and the noise level (dBA) experienced by each individual was determined, yielding the following data

55.3     55.3     55.3     55.9     55.9     55.9     55.9     56.1     56.1     56.1     56.1

56.1     56.1     56.8     56.8     57.0    57.0    57.0     57.8     57.8     57.8     57.9

57.9     57.9     58.8     58.8     58.8    59.8    59.8     59.8     62.2     62.2     63.8

63.8     63.8     63.9     63.9     63.9     64.7     64.7     64.7     65.1     65.1     65.1

65.3     65.3     65.3     65.3     67.4     67.4     67.4     67.4     68.7     68.7     68.7

68.7     69.0     70.4     70.4     71.2     71.2     71.2     73.0     73.0     73.1     73.1

74.6     74.6     74.6     74.6     79.3     79.3     79.3     79.3     83.0     83.0     83.0

1. Obtain stem and leaf plot   
2. Plot Histogram (Using MS Excel)   
3. Identify the distribution which fits the data
4. Find mean and variance   
5. Obtain Chebyshev’s Interval

Answer 1

Ans : from the given data obtain the stem plot and leaf plot using MinniTab software

software :

first enter data in c1 column then go to graph

2) Constructing a histogram  

k= = = 8.77 we will use 8 bin

the interval width = (Xmax-Xmin)/k

=(83-53.3) / 8

  ≈ 4

then following output of histogram  

3)

Therfore the shape of the distribution is bell sheped

(observation not fron normal distribution )

Chebyshev’s Interval :

1) at least 3/4 of the data lie within two standard deviations of the mean is : ( -62 , 206.9)

2) at least 8/9 of the data lie within three standard deviations of the mean is ( -129.24 , 274.24 )