The following data represent the afternoon high temperatures for 50 construction

Question

The following data represent the afternoon high temperatures for 50 construction days during a year in St. Louis. 38 48 25 55 85 10 24 45 31 62 47 63 84 16 40 81 15 35 17 40 36 44 17 38 79 35 36 23 64 75 53 31 60 a. Construct a frequency distribution for the data using five class intervals b. Construct a frequency distribution for the data using 10 class intervals. c. Examine the results of (a) and (b) and comment on the usefulness of the frequency distribution in terms of temperature summarization capability. 2, A northwestern distribution company surveyed 53 of its midlevel managers. The survey obtained the ages of these managers, which later were organized into the frequency distribution shown. Determine the class midpoint, relative frequency, and cumulative frequency for these data Class Interval Frequency 20-under 25 8 25-under 30 6 30-under 355 35-under 40 12 40-under 45 15 45-under 50 7

Explanation / Answer

1. Frequency Distribution with five class intervals

    Minimum value : 10
    Maximum value : 85
    Range : 85-12 = 75

    Considering the range a five class interval means we can take class interval as 75/5 = approx 15. Here we are condidering inclusive class intervals.
    Class Interval   frequency
    10 - 25            9
    26 - 41            15
    42 - 57            10
    58 - 73            10
    74 - 89            6

    Considering the range a ten class interval means we can take class interval as 75/10 = approx 7.Here we are condidering inclusive class intervals.

    Class Interval   frequency
    10 - 17            7        
    18 - 25            3
    26 - 33            5
    34 - 41            9
    42 - 49            7
    50 - 57            3
    58 - 65            6
    66 - 73            4
    74 - 81            2
    81 - 88            4
   
Frequency distribution tables are good way of summarizing the temperature data.The class
intervals are defined in such a way that each value falls in one or the other class.So
it summarizes all the data and show a catgorical information about distribution of data.
Whether data is ditributed evenly or there is some cluster gets visible in this   summarized view of data. So it is really useful representation of data.If we look at   the two intervals , then we can see clear cluster of values in the first distribution   but we can see a fairly even distribution in case of second distribution.So nuch depends on how many class intervals we are taking. We may get different views of data depending on that.

2.   Class Interval   Frequency
      20-24           8
      25-29           6
      30-34           5
      35-39           12
      40-44           15
      45-49           7

Class mid point is calculated as (upper class limit + lower class limit)/2
Relative frequency = frequency/Total entries

     Class Interval   Frequency   Mid-point Relatve Frequency Cumulative Frequency
      20-24                    8              22              8/53 = 0.150                           0.150
      25-29                     6             27               6/53 = 0.113                          0.15+0.11=0.263    
      30-34                     5             32               5/53 = 0.094                           0.26+0.09= 0.357
      35-39                     12            37             12/53= 0.226                           0.35+0.23 = 0.583
      40-44                     15            42             15/53= 0.283                           0.28+0.57 = 0.866
      45-49                      7             47        7/53= 0.132                                  0.85+0.13 = 0.998

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