Find the sample standard deviation and the population standard deviation of the data set. 56, 65, 73, 66, 64, 58, 72, 52, 69, 71, 53, 66, 78, 58

population standard deviation = √58.79857 =  7.6680

sample standard deviation = √63.32154 = 7.9575

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

Arrange data in ascending order

56, 65, 73, 66, 64, 58, 72, 52, 69, 71, 53, 66, 78, 58

52,53,56,58,58,64,65,66,66,69,71,72,73,78

Find the mean of the data set;

=

Finding the deviations from the mean

              Deviations           square of deviations

52-64.36= -12.36                  152.77

53-64.36= -11.36                   129.05

56-64.36= -8.36                     69.89

58-64.36= -6.36                     40.45

58-64.36= -6.36                      40.45

64-64.36= -0.36                         0.13

65-64.36= 0.64                          0.41

66-64.36= 1.64                           2.67

66-64.36=  1.64                          2.67

69-64.36= 4.64                         21.53

71-64.36=6.64                           44.09

72-64.36=7.64                           58.37

73-64.36=8.64                            74.65

78-64.36=13.64                          186.05

Sum                                             823.18        

1. Treating the data set as an entire population;

population variance= 823.18/14 =58.79857

population standard deviation = √58.79857 =  7.6680

2. Treating the data set as a sample, the number of data points will be less by 1

n= 14-1 = 13

sample variance= 823.18/13 = 63.32154

sample standard deviation = √63.32154 = 7.9575

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: